Machine method and apparatus for determining the presence and location of hydrocarbon deposits within a subsurface earth formation
This is a continuation of application Ser. No. 112,005 filed Feb. 2, 1971, now abandoned. 
    
    
     This invention relates to methods of investigating earth formations traversed by a borehole. More particularly, the invention relates to the processing of well logging data derived from apparatus lowered in a borehole for investigating subsurface earth formations. 
     In seeking to determine the presence and depth of hydrocarbon bearing zones (oil or gas) that may exist in the subsurface earth formations adjacent a borehole drilled into the earth, various types of exploring devices may be lowered into the borehole for measuring various properties of the formations adjacent the borehole. The three principal types of such exploring devices are electrical exploring devices (using either electrodes or induction coils), sonic exploring devices, and radioactivity exploring devices (gamma ray, neutron, etc.). 
     The electrical exploring devices measure the electrical resistivities (or conductivities) of the earth formations. These electrical resistivities are determined primarily by the amount, distribution and resistivity of the fluids contained in the formation pore spaces. The sonic exploring devices, on the other hand, measure the time required for sonic waves to travel across a given span of the earth formation. This sonic travel time is determined primarily by the nature of the rock structure and particularly its porosity. The radioactivity exploring devices measure either the natural radioactivity of the formations or the radioactivity induced therein by bombardment of the formations with radioactivity particles or rays. 
     Two particular radioactivity exploring devices used to investigate formations are the formation density logging tool and the neutron logging tool. The formation density logging tool emits gamma rays which are diffused through the formation and the number of diffused gamma rays reaching one or more nearby detectors are counted to provide a measure of the electron density of the adjacent formation. Moreover, it is known that this electron density is very closely proportional to the bulk density of the formation in substantially all cases. (For cases where this proportionality does not apply, appropriate corrections can be made.) 
     The neutron tool on the other hand utilizes a source for emitting neutrons into the adjacent formations. In one form of neutron device, these neutrons lose energy by collison with atoms in the formation. When the energy level of these neutrons is reduced to the epithermal energy range, they can be detected by a nearby detector which counts the number of epithermal neutrons. Since hydrogen atoms are the only ones whose weights are almost equal to that of the neutron, they are the most effective in reducing the energy level of the neutrons to enable their capture. Thus, it can be said that this type of neutron log is essentially a record of the hydrogen atom density of the rocks surrounding the borehole. Since the formation pore spaces are generally filled with either water or liquid hydrocarbons which both have about the same amount of hydrogen, the neutron log does not distinguish between oil and water, but is primarily affected by the formation porosity. Gas, on the other hand, will alter this porosity determination by the neutron log. 
     In general, none of these measurements taken alone give a direct and positive indication as to the presence or amount of hydrocarbons in the formations or the relative difficulty in removing these hydrocarbons. The various factors which affect each measurement have to be taken into account and an interpretation or deduction made as to the probable existence of hydrocarbons. Among the factors which are considered to be important in determining the location, amount, and ease of removal of oil is the porosity of the formations. Porosity is the fraction of the total volume of a given portion of the formation which is occupied by pores, or void spaces. Other such factors are the make-up of the solid formation material, the water and hydrocarbon saturation, and permeability (ease of fluid to flow in the formation. It is known that by combining the measurements derived from various exploring devices that these factors can usually be obtained. However, when a shaly sand formation is being investigated, the usual interpretation techniques do not apply very well since the responses of most of the tools are affected by shaliness. For example, the true formation resistivity is generally high in an oil or gas bearing formation and low in a water bearing formation. However, in oil or gas bearing shaly sands, the resistivity may very well be low since the shale or clay dispersed in the pore spaces of a sand will tend to have a low resistivity. Moreover, if the formations contain a significant amount of hydrocarbons, and especially gas, additional complications are introduced into the log interpretation process due to the variations in response of the various exploring devices to these hydrocarbons. 
     Two logs which are useful in distinguishing between sand and shale formations are the spontaneous potential and gamma-ray logs. The spontaneous potential logs gives a measure of the naturally occurring potential of the formations. This potential will be different in shale formations than in sand formations. The gamma-ray log is a measure of the natural radioactivity of the formations and is usually the greatest in shales. However, just distinguishing between sand and shale formations is not enough. It is becoming more and more necessary to evaluate these formations for their lithological make-up as well as for the presence, amount and type of hydrocarbons and their ease of removal. It is, therefore, an object of the present invention to provide new and improved methods for processing well logging data to enable evaluation of earth formations and more particularly, shaly sand formations. 
     The way shaliness affects well logging measurements depends on the proportion of shale, the physical properties of the shale and the way it is distributed in the formation. In the past it has been assumed that shale is distributed in formations in the form of shale laminae between adjacent layers of sand or of shale dispersed in the sand grains. In the case of laminated shale, the shale is considered to be in large continuous chunks in the formation. For the dispersed shale case, the shaly material is considered to be dispersed throughout the sand in the intergranular structure of the sand. The dispersed shale may be in the form of accumulations adhering to or coating the sand grains, or they may partially fill the smaller pore-channels. Dispersed shale in the pores significantly reduces the permeability of the formation. 
     In the past, formation models assuming either laminated shale or dispersed shale have been individually utilized to enable interpretation of shaly sand formations. It has been found, however, that either model alone does not adequately cover all formation conditions thus rendering interpretation of the measurements difficult. 
     It is therefore another object of the present invention to provide new and improved methods for processing well logging data which assume formation models which more nearly fit all formation conditions. 
     In accordance with the well logging data processing methods of the present invention, a plurality of well logging measurements are combined in a new manner to produce data useful in evaluating earth formations. 
    
    
     For a better understanding of the present invention, together with other and further objects thereof, reference is had to the following description taken in connection with the accompanying drawings, the scope of the invention being pointed out in the appended claims. 
     Referring to the drawings: 
     FIG. 1 illustrates exploring apparatus in a borehole for deriving a plurality of well logging measurements along with apparatus at the surface of the earth for digitally recording and processing the derived measurements; 
     FIGS. 2, 3, 11 and 15 are crossplots of certain of the derived measurements useful in explaining certain features of the present invention; 
     FIGS. 4, 5, 6 and 7 illustrate models of certain types of formation which models are useful in understanding certain features of the present invention; 
     FIGS. 8, 9 and 10 are crossplots of certain derived measurements which together are useful in understanding features of the present invention; 
     FIGS. 12 through 17 are illustrations of certain statistical analyses performed in accordance with certain additional features of the present invention; 
     FIG. 18 is a flow diagram representation of the &#34;preliminary pass&#34; portion of a computer program embodiment of the present invention; 
     FIGS. 19A, 19B and 19C are flow diagram representations of a first sweep of &#34;interpretation pass&#34; portion of the computer program which figures will hereinafter be referred to simply as FIG. 19; 
     FIGS. 20A and 20B are flow diagram representations of a second sweep of the interpretation pass and which will be hereinafter referred to simply as FIG. 20; 
     FIGS. 21A, 21B, 21C, 21D and 21E are flow diagram representations of a &#34;hydrocarbon analysis&#34; routine found in sweep 2 and subsequently described sweep 3 and which will hereinafter be referred to simply as FIG. 21; 
     FIG. 22 is a flow diagram representation of &#34;sonic statistics&#34; routine which forms a portion of sweep 2; 
     FIGS. 23A and 23B illustrate a flow diagram representation of a third sweep of the interpretation pass and will be hereinafter referred to simply as FIG. 23; 
     FIGS. 24A and 24B are flow diagram representations of a &#34;prepare data for output&#34; routine which forms a portion of sweep 3 and which will hereinafter be referred to simply as FIG. 24; 
     FIG. 25 is an illustrative example of a presentation of the computations made in accordance with the teachings of the present invention; 
     FIG. 26 is a graphical representation depicting an operation performed in the &#34;prepare data for output&#34; routine of FIG. 24; and 
     FIGS. 27, 28, 29 and 30 represent crossplots of various formation parameters and are useful in explaining other embodiments of the present invention. 
    
    
     Referring to FIG. 1, there is shown an investigating apparatus 20 located in a borehole 21 on the end of a multiconductor cable 22 which is raised and lowered in a borehole by a suitable drum and winch mechanism (not shown). Investigating apparatus 20 includes exploring devices for obtaining measurements of the acoustic travel time Δt, bulk density ρ b , the porosity φ N  derived from a neutron exploring device, the natural gamma ray content GR of a formation, the diameter of a borehole, the spontaneous potential SP, and deep and shallow resistivities, R t  and R xo . 
     An acoustic exploring device for deriving a measure of Δt can be found in U.S. Pat. No. 3,231,041 granted to F. P. Kokesh on Jan. 25, 1966. An example of an exploring device for obtaining a measure of the neutron derived porosity φ N  can be found in U.S. Pat. No. 2,769,918 granted to C. W. Tittle on Nov. 6, 1956. An exploring device for obtaining a measure of the bulk density can be found in U.S. Pat. No. 3,321,625 granted on May 23, 1967 to John S. Wahl. An exploring device for obtaining measurements of the spontaneous potential and deep and shallow resistivity can be found in U.S. Pat. No. 3,453,530 granted to G. Attali on July 1, 1969. 
     Measurement signals derived from the exploring device 20 are transmitted to suitable signal processing circuits 25 at the surface of the earth. The signal processing circuits 25 prepare the signals for application to a digital tape recorder 26 which converts the well logging signals to digital form for recording on magnetic tape. The resulting magnetic tape is either carried or transmitted via a telemetry link to a digital computer 27 which is programmed in accordance with the teachings of the present invention to process the data in a manner to provide valuable information relative to the nature of the earth formations 23. While all of the measurements to be used in practicing the present invention have, in FIG. 1, been shown derived from one exploring device, it is to be understood that these measurements could be derived from a plurality of exploring devices which are run through the borehole at different times. In this event, the data from each run would be recorded on individual magnetic tapes and the data on each tape would be merged onto a single tape for use by the digital computer 27. 
     The neutron tool responds to the amount of hydrogen in the formations. It is scaled to read porosity directly in mixtures of limestone and water. Through the use of suitable correction factors, it can be adjusted to read porosity correctly in water filled formations of other types of lithology. It is known that the neutron tool will indicate close to the true porosity in formations containing oil, since oil has approximately the same hydrogen content as water. However, in the formations containing gas, the neutron tool will give a value of porosity which is too low because of the low hydrogen concentration in gas. 
     In addition to deriving a measure of formation porosity from the neutron tool, the bulk density and acoustic travel time measurements can also be converted to measures of formation porosity. The bulk density measurement can be converted to a porosity measurement if the matrix and fluid densities ρ m  and ρ f  are known. The equation for convertng this bulk density measurement to a porosity measurement is: ##EQU1## In fresh muds the fluid density ρ f  is usually set equal to 1. However, in light hydrocarbon and gas bearing formations, the fluid density ρ f  will be less than 1, and thus the value of porosity φ D  derived from the density tool will be higher than the true porosity. 
     The acoustic travel time can also be converted to a measure of porosity provided the acoustic travel time of the rock matrix and fluid, Δt m  and Δt f  respectively are known. The relationship for the acoustic or sonic derived porosity in terms of Δt is: ##EQU2## 
     The resistivity tools used here measure the formation resistivity in a zone radially near the borehole and a zone radially spaced from the borehole. Either an induction logging tool or a deep reading focused electrode tool can be utilized to give a measure of resistivity of the zone radially spaced from the borehole. A pad type focused electrode tool or a focused or unfocused electrode array mounted on the central support member can provide the resistivity of the zone near the borehole. The resistivity reading provided by the shallow investigation devices is called R xo  and is usually primarily representative of the resistivity of the formation zone which has been invaded by mud filtrate from the borehole. The deep reading resistivity devices provide a measurement designated R t  which usually is primarily representative of the resistivity in the uninvaded or virgin formation zone. 
     The spontaneous potential measurement provided by the exploring apparatus 20 gives the difference between the potential of an electrode on the exploring device and the potential of an electrode located at the surface of the earth. Opposite shale formations, the spontaneous potential will usually remain fairly constant and thus end to follow a straight line on the log, called the &#34;shale base line&#34;. Opposite permeable formations, a spontaneous potential will show excursions from the shale base line. In thick permeable beds free of shale, the spontaneous potential will also reach an essentially constant value, defined as the &#34;sand line&#34;. 
     The gamma ray measurement provided by the exploring apparatus 20 gives a measurement of the natural radioactivity of the formations. Shaly formations generally tend to have a high radioactivity content because radioactive elements tend to concrete in shales. Clean formations usually have a very low level of radioactivity. Thus, the gamma ray log can usually distinguish between clean sand and shaly formations. 
     It is the purpose of the present invention to combine the measurements derived from the exploring apparatus 20 in such a manner as to provide information relating to shaly sand formations. The measurements derived from all of these exploring devices are affected in one way or another by the shale content of formations, thus complicating the interpretation of these measurements in such formations. Moreover, when oil or gas is contained in these shaly sand formations, the interpretation of the measurements becomes even more complex. By combining the measurements derived from many exploring devices, it is possible, in accordance with the present invention, to accurately interpret the measurements. However, before discussing how these measurements are utilized in accordance with the present invention, it would first be desirable to discuss the nature of shaly sand formations. 
     Shale is made up of a combination of silt and wet clay where wet clay is a combination of dry clay material called colloids and water. The relative proportions of silt and clay usually vary from one formation to the next. In the past it has been assumed that shale is distributed in formations in the form of shale laminae between adjacent layers of sand or of shale dispersed in between the sand grains. In the case of laminated shale, the shale is considered to be in large continuous chunks in the formation. For the dispersed shale case, the shaly material is considered to be dispersed throughout the sand in its intergranular structure. The dispersed shale may be in the form of accumulations adhering to or coating the sand grains, or they may partially fill the smaller pore channels. It has been found that either model alone does not adequately cover all formation conditions thus rendering interpretation of the measurements difficult. 
     In accordance with an important feature of the present invention, both laminated shale and dispersed shale models are combined into one model to enable a more accurate interpretation of shaly sand formations. Moreover, a third form of shale is added to the laminated and dispersed shale models to provide a shaly sand model which more accurately represents true formation conditions in shaly sands. This third form of shale is called &#34;structural shale&#34;. In this structural shale model, shale may exist as grains which replace sand grains in the formation matrix. This structural shale is considered to have properties similar to those of laminated shale. 
     It has been found that all of these forms of shale may occur simultaneously in the same formation. Frequently, however, shale in only one form is predominant but this can change from one depth level to the next. Thus, a good interpretation technique must be universal enough to handle situations where any one form of shale occurs as well as those cases where two or even all three forms occur. 
     After much experimentation it has been found that over large sections of any given borehole, certain shale parameter values used for interpretation will remain relatively constant, although the particular form of shale may change. Thus, regardless of the particular form of shale, the shale parameter values can be related to those of an average shale for large sections of a borehole. 
     Responses of the radioactivity tools (gamma ray, neutron, and density) are not affected by the way the shale is distributed in the formation, whether in laminated, dispersed, or structural form. However, the responses of the sonic, resistivity and SP tools are affected by the shale distribution. As will be set forth later, these distinctions are utilized in accordance with the present invention to provide valuable information concerning the character of the shaly sand formations. 
     A cross-plot of the density derived porosity φ D  versus neutron derived porosity φ N  is valuable in evaluating shaly sand formations. Referring now to FIG. 2, there is shown such a cross-plot. In FIG. 2, certain points can be readily placed on the cross-plot. It is known that in the water, both the density and neutron derived porosities will read values of one. Thus, the water &#34;w&#34; point can be placed on the cross-plot. It is also known that pure silt, which is made primarily of quartz, will be at the same point as quartz, designated &#34;Q-S&#34; on the cross-plot, and dry clay designated Cl d  will be at the point Cl d  on the cross-plot. A triangle can thus be drawn on the cross-plot connecting these three points. In water-bearing formations, all plotted φ N ,φ D  points will fall within this triangle. Furthermore, the relative distances of the plotted point from the three apexes of the triangle give the relative proportions of water, silt and quartz, and dry clay for the formation from which this plotted point is derived. 
     By plotting a plurality of φ N ,φ D  points from a formation interval, certain characteristics of the formation can be ascertained. For example, assume that a formation interval has produced the plotted points shown in FIG. 2. Those points falling in the area x are known to correspond to shale formations. Thus, a line can be drawn through the center of gravity of these shale points from the origin. This line is called the &#34;shale line&#34;. Since it is known that pure shales generally have almost no porosity, this shale line will correspond to zero porosity. Thus, any point plotting on the shale line can be said to have zero porosity. The intersection of the shale line with the line between the points Cl d  and W gives the tool response characteristics for wet clay associated with this shale and is thus designated Cl w . The position of this point Cl w  relative to the water &#34;W&#34; and dry clay Cl d  points gives the amount of water associated with clay, W cl . 
     It is known that clean sand formations affect φ N  and φ D  equally. Thus, any points falling on or near a line which subtends an angle of 45° with the φ N  and φ D  axes are derived from clean sand formations. Those points falling in the area y between the sand and shale lines correspond to shaly sands. These points in the area y exhibit a definite trend between the sand and shale lines. A line which best fits these points can be drawn between the sand and shale lines. The intersection of this shaly sand trend line with the sand line defines a point designated (φ z ) max . (φ z ) max  is the maximum porosity associated with the formations considered in this example of FIG. 2. The intersection of the shaly sand trend line with the shale line gives a point designated Sh o . The fact that this trend line points toward a unique point on the shale line indicates that the shale normally associated with the sand has the unique composition represented by the point Sh.sub. o. After a great deal of research, it has been found that for most all levels in the formation interval represented by the FIG. 2 example, the type of shale, whether dispersed, laminated, or structural, associated with shaly sand formations in this interval can be defined in terms of the response of the density and neutron tools by this point Sh o . The neutron and density derived porosity characteristics for this type of shale are designated (φ N ) Sh .sbsb.o and (φ D ) Sh .sbsb.o respectively. 
     The points plotting in the area Z above the clean sand line most likely represent hydrocarbon bearing formations since hydrocarbons and especially gas decrease φ N  and increase φ D . 
     It is known that the effective porosity φ e  and the volume or amount of shale V sh  in a formation at any given depth level can be ascertained by the location of the plotted φ D ,φ N  point on the φ D  -φ N  cross-plot. Thus, turning to FIG. 3, there is shown a portion of the cross-plot of FIG. 2 reproduced to illustrate this. In the FIG. 3 cross-plot, a plurality of lines can be drawn parallel to the shale line and each of these lines will indicate a given constant effective porosity. As stated earlier, the shale line itself indicates zero porosity. Thus, as one moves away from the shale line, the amount of porosity will increase 
     In the same fashion a plurality of lines indicating the volume of shale can be drawn parallel to the clean sand line. Obviously, any point falling on the clean sand line itself indicates a shale volume of zero percent. As one moves away from the clean sand line, the volume of shale will progressively increase. 
     Taking an example of how φ e  and V sh  can be obtained from the φ N  -φ D  crossplot, if φ D  and φ N  measurements should give the point 30 of FIG. 3, a formation having an effective porosity of 15% and a shale volume of 15% would be indicated. 
     The influence that each mode of repartition of shale has on the formation porosity will be discussed now. FIG. 4 represents a unit volume of clean sand for which each grain is quartz. The porosity is the ratio of the area in white to the total area of the figure. This is the porosity φ z  which is called framework porosity. FIG. 5 represents the same sand but a quantity V D  of dispersed shale has been introduced in the pore space. The remaining porosity designated φ e , has been decreased such that φ e  =φ z  -V D . 
     FIG. 6 represents the same sand but for which a quantity V sh  of structural shale has been substituted for the quartz grains. Although the sand contains shale, its porosity has not been changed by the presence of structural shale. Thus, φ e  =φ z . 
     FIG. 7 represents the same sand but for which a part of the sand has been replaced by a quantity V L  of laminated shale. The porosity in the sand fraction has not changed but only (1-V L ) of the sand initially there remains. Consequently, the effective porosity φ e  of the mixture of sand and shale will represent only (1-V L ) φ z . 
     Concerning the effect of each type of shale on the φ N  -φ D  crossplot, if dispersed shale is added to a clean sand formation, it occupies part of the framework porosity of the sand. Thus the effective porosity will decrease. Thus, referring to FIG. 3 and assuming a sand formation of porosity φ z1 , the addition of dispersed clay to this sand formation will tend to move the plotted φ N , φ D  point in the direction indicated by the dispersed clay effect vector, i.e. such that ΔV sh  =Δφ e . 
     Structural shale, since it takes the form of clay grains replacing said grains of the same or similar size, will not affect the effective porosity φ e . Therefore, as shown in FIG. 3, the structural shale effect will tend to move the plotted φ N , φ D  point to the right parallel to the shale line (i.e., along a constant φ e  line), as indicated by the structural shale effect vector. 
     An increase in the laminated shale in the formation will tend to decrease the effective porosity φ e  because shales have no porosity and laminated shales replace part of the sand of porosity φ z1 . Since the formation is presumed to have shale of type Sh o , laminated shale will move the point towards the Sh o  point as illustrated in FIG. 3. 
     The addition of hydrocarbons, and especially gas, to this clean sand formation will tend to move the plotted φ N , φ D  point to the northwest in the FIG. 3 crossplot as represented by vector 29a. This is evident since, as stated earlier, an increase in hydrocarbons will increase the density derived porosity φ D  and decrease the neutron derived porosity φ N , especially if the density of this hydrocarbon is low as in the case of gas. Higher density hydrocarbons have very little affect on the neutron tool and thus the data point will tend to move in a more northerly direction, as represented by the vector 29b. 
     As stated earlier, any given formation can contain shale in all three forms and, at the same time, can also contain hydrocarbons. Thus, through the use of the neutron density crossplot alone, it is not possible to properly evaluate both the hydrocarbon and shale effects. 
     Let us consider a series of clean sands for which structural porosity may be between φ z1  and φ z2  due to the geological process. As stated earlier, it was assumed in the past that either dispersed shale or laminated shale would be associated with these sands. 
     In the dispersed shale model only the points falling between the two &#34;dispersed shale&#34; lines for φ z1  and φ z2  could be truly taken into account and still fit the model (FIG. 8). In the laminated model, only the points falling between the two &#34;laminated shale&#34; lines could be truly taken into account (FIG. 9). In particular it was not possible to explain the presence of points falling to the right of the (φ z1 , Sh o ) line except by assuming a φ z  larger than the one truly created by geological sedimentation. The addition of the structural shale model permits us to justify and understand why such points may exist. 
     The simultaneous presence of the three types of shales permit justification of the position of any points inside the area of FIG. 10. However, it was found by a great deal of research that structural shale cannot replace all quartz grains (the point 31a in FIG. 10). Thus, it has been found that the position of the shaly sand points on the plot was in practice limited to the right by a curve (dashed curve 30 between φ z1  and Sh o ) well approximated by a parabola as shown in FIG. 10. The parabolic representation of this limit of the domain of shaly sand was developed by empirical analysis and is not obvious. Its physical meaning is that the amounts of structural shale and laminated shale which can be associated with the sand are not independent from one another. On the contrary, it indicates that for points falling on this limit and which do not contain dispersed shale, the smaller the amount of shale, the larger the relative amount of structural shale with relation to laminated shale; and the larger the amount of shale, the smaller the relative amount of structural shale. 
     Now turning to FIG. 11, there is shown the neutron density crossplot of FIG. 3 redrawn to illustrate the various areas or sections of the crossplot and their significance. The area defined by the letters SS (standing for shaly sand) defines an area for which all plotted points should fall when derived from formations having a characteristic shale given by the point Sh o  and a sand framework porosity which is practically constant. In terms of exploring tool readings, this type of shale is defined by the φ N  and φ D  values of the Sh o  point, designated (φ N ) sh  and (φ D ) sh . Any points falling in the shale area designated Sh define their own characteristic shale type, depending on the particular location of the point within this shale area. Likewise, any point plotting within the dispersed shale area to the left of the dispersed shale line will, in accordance with its position on the crossplot, define a specific type of shale. Nonetheless, most shaly sand data points falling in the hatched line are and the definition of one characteristic shale type for all points in this area represents a dramatic improvement in shaly sand interpretation. If a point should fall to the left of dispersed shale line for φ zmax , it indicates that the formation has a lower φ z  than (φ z ) max  at that level and thus (φ z ) max  should be changed to account for this. Thus, assume the plotted point 33 in FIG. 11. The dispersed shale line would then move over to accommodate this new point as illustrated by the line 33a to thus give a new framework porosity of φ z3 . 
     In discussing types of shale, one parameter that is informative is the relative proportion of silt and wet clay in the shale. To define the relative proportions of silt and wet clay, a linear relationship between the plotted point on the shale line relative to the silt and wet clay points will define the type of shale. In this connection, a term defined as the &#34;silt index&#34; SI of the shale is used throughout the discussion here and can be defined as the ratio of silt to shale and thus the ratio of the distance between the designated point on the shale line and the wet clay point C1 w  to the total length of the shale line between the silt and wet clay points. Thus the silt index of the shale type associated with the shaly sand area SS in FIG. 11 will be Sh o  -C1 w  /0-C1 w . The silt index of this shale point Sh o  is designated SI o . 
     Since shale consists of silt and wet clay, the following relationship holds: 
     
         V.sub.sh =V.sub.silt +V.sub.clay                           (3) 
    
     The slit index defines the ratio of silt to shale. Thus: 
     
         SI=V.sub.silt /V.sub.sh                                    (4) 
    
     Combining equations (3) and (4), we have: 
     
         V.sub.clay =V.sub.sh (1-SI)                                (5) 
    
     Points falling in the shale area X of FIG. 2 are essentially shales. These shales do not have uniform composition. Their composition (i.e., the relative amount of clay and silt) is related to the partition of the shale part in this area. To define the composition of this shale is has been found that one may draw a limit parabola equivalent to (30) but which passes through the plotted φ N ,φ D  point under evaluation, using the maximum framework porosity point (φ z ) max  as the pivot point. Thus, for example, assume that the plotted φ N ,φ D  point is given by the point 32 in FIG. 11. The parabola 30 would then be swung to the position given by the dashed line parabola 30a which passes through the plotted point 32 and intersects the shale line at the point SH 1 . In this case, the type of shale associated with the plotted point 32 will be defined by the shale SH 1 . As before, the point Sh, is defined by the characteristic tool responses, designated (φ N ) sh  and (φ D ) sh . 
     It is possible that φ N , φ D  points could also fall in the area to the right of the shaly sand area SS and avove the shale area Sh. As stated earlier, the parabola 30 defines the practical limit for φ N , φ D  points in shaly sands. Therefore, if points fall to the right of this parabola and are not close enough to the shale line to designate the investigated formation as a shale, it is assumed, in accordance with another feature of the present invention, that the porosity data does not correspond to a shaly sand or to a shale. It may correspond either to a different type of lithology or to a level for which the φ N , φ D  data is bad due to borehole effect on the measurements. Therefore, this area to the right of the parabola 30 and above the shale area is designated the &#34;unlikely area&#34;. (Unlikely to be either shaly sand or shale.) In accordance with still another feature of the present invention, data falling in this unlikely area is verified and, if necessary, corrected using data derived from other exploring devices. How this is accomplished will be described in detail later. 
     Having now discussed the density and neutron responses in view of the density-neutron crossplot, it would be desirable to discuss the responses of these tools in mathematical terms. The equations for the density and neutron derived porosities φ D  and φ N  in terms of the effective porosity, φ e , shale volume, V sh , water saturation of the invaded zone, S xo , and the characteristic neutron and density response to shale and hydrocarbon are: 
     
         φ.sub.D =φ.sub.e +V.sub.sh φ.sub.D(sh) +φ.sub.e (1-S.sub.xo)(φ.sub.D(hy) -1)                          (6) 
    
     
         φ.sub.N =φ.sub.e +V.sub.sh (φ.sub.N).sub.sh +φ.sub.e (1-S.sub.xo)[(φ.sub.N).sub.hy -1](1+2φ.sub.e S.sub.xo) (7) 
    
     where 
     (φ D ) sh  is the characteristic density derived porosity reading in the shale associated with the sand, 
     (φ N ) sh  is the characteristic neutron derived porosity reading in shale, 
     (φ D ) hy  is the characteristic density derived porosity reading for hydrocarbons, and 
     (φ N ) hy  is the characteristic neutron derived porosity reading for hydrocarbons. 
     (φ D ) sh  and (φ N ) sh  have been discussed above, and (φ D ) hy  and (φ N ) hy  are unknowns. 
     In the absence of hydrocarbons, S xo  is equal to &#34;1&#34; and equations (6) and (7) become: 
     
         φ.sub.D =φ.sub.e +V.sub.sh (φ.sub.D).sub.sh    (8) 
    
     
         φ.sub.N =φ.sub.e +V.sub.sh (φ.sub.N).sub.sh    (9) 
    
     In the absence of hydrocarbons, the density and neutron derived porosity readings φ D  and φ N  provide sufficient information to solve for effective porosity φ e  and shale volume V sh . The mathematical solution of equartions (8) and (9) is analogous to the graphical solution depicted in FIG. 3. The selection of (φ D ) sh  and (φ N ) sh  determines the scaling for this graphical technique depicted in FIG. 3, i.e., the shale point Sh o  gives the V sh  =100% point and thus if the type of shale associated with the particular formation under investigation changes, the scale will change correspondingly. 
     It is obvious by inspecting equations (6) and (7) that when hydrocarbons are present in the formation, the density and neutron derived porosity readings φ D  and φ N  will not provide sufficient information by themselves, and thus other steps must be taken to properly analyze the formation. 
     Before deciding whether to utilize other input parameters to correct equations (8) and (9) for hydrocarbon effect, it must first be known whether hydrocarbons do in fact exist in the formation under investigation. The location of the plotted φ D , φ N  point on the crossplot does not indicate whether hydrocarbons are present or not. From FIG. 3 it can be seen that hydrocarbons have the effect of pulling plotted points in a northwesterly direction on the crossplot. However, the effects of structural, laminated, and dispersed shale tend to displace the points to the right and parallel to the shale line. 
     In clean or non-shaly formations, the effect of hydrocarbons will be readily discernible because all of the plotted points would fall to the northwest of the sand line if the tool readings are accurate. (Of course, if the tool readings are inaccurate, the plotted points could fall anywhere.) However, since it is usually not initially known how much shale, if any, is present in any given formation, it is not known how much the effect of shale offsets the effect of hydrocarbons. As seen from equations 3 and 4, if hydrocarbons affect the tool readings at all, the values of effective porosity, φ e , and shale volume, φ sh , given by equations (8) and (9) and the crossplot will be inaccurate. 
     To overcome this inability to produce correct answers when hydrocarbons are present, two additional pieces of information are utilized. One is a value of V sh  derived from other logs which are sensitive to the amount of shale present in the formation under investigation. These are called shale indicators. The second additional piece of information is an assumed relationship between (φ D ) hy  and (φ N ) hy  which reduces these two variables to one. This relationship can be described by writing the expressions for (φ D ) hy  and (φ N ) hy  in terms of hydrocarbon density P hy  as follows: ##EQU3## Equations (10) and (11) comprise another aspect of the present invention and have been derived from considerations of the chemical composition of hydrocarbons and its relation to its physical properties. The value of hydrocarbon density P hy  is an unknown and is determined by the analysis described hereinafter. 
     Before discussing how the various formation parameters can be determined when hydrocarbons are present in the formation under investigation, it would first be desirable to discuss the shale indicators mentioned above. These shale indicators are logging parameters or combinations thereof which are strongly influenced by shale content. An approximation of V sh  is computed from each shale indicator in such a manner that it is supposed to always be equal to or greater than the true V sh . Accordingly, the smallest of these values of V sh  derived from the shale indicators will be the closest to the true V sh  and is, therefore, retained to represent the value of V sh  in the equations discussed above. 
     These shale indicators are: (1) spontaneous potential; (2) gamma ray; (3) the value of resistivity in hydrocarbon zones; (4) gas-sandline limit; (5) the saturation ratio S xo  /S w  ; (6) a relationship between porosity derived from the neutron log, φ N , and the value of φ N  for the shale point, (φ N ) sh  ; and (7) the hydrocarbon density. 
     Taking first the spontaneous potential as a shale indicator, it has been found that the spontaneous potential varies in a linear manner with the ratio CEC/U where CEC is the cation exchange capacity of the clay material and W is the total water of the shaly sand in the zone of ionic diffusion. It has been found that the cation exchange capacity is proportional to the volume of clay V clay  in the formation and that W is always equal to or less than the volume of water in the invaded zone W xo  which is equal to: 
     
         W.sub.xo =φ.sub.e S.sub.xo +V.sub.clay W.sub.clay      (12) 
    
     In equation (12) the term φ e  S xo  gives the total water content of the invaded zone and the term W clay  gives the amount of water bound to the clay particles. To determine the magnitude of W clay  the following equation can be used: 
     
         P.sub.wet clay =(1-W.sub.clay)P.sub.dry clay +W.sub.clay   (13) 
    
     The density of dry clay, P dry  clay, is usually of the order of 2.85 although other values may be used according to geological experience. The density of wet clay can be determined from the φ D  -φ N  crossplot by utilizing the value of φ D  for wet clay and solving equation (1) for P m . To determine the magnitude of V clay , it is only necessary to know the silt index and V sh  to find V clay  from equation (5). 
     It has been found that the relationship between V clay  /W xo  versus the spontaneous potential can be approximated with a linear relationship. Thus, if this relationship is known and W is known, then the measure of spontaneous potential at each depth level can be used to find V clay . Then, using equation (5), V sh  can be determined. However, it is first necessary to determine the relationship between V clay  /W xo   and the spontaneous potential. 
     In accordance with another feature of the present invention, this is accomplished by plotting V clay  /W xo  versus spontaneous potential and drawing a line which incorporates the best fit to the plotted points. Such a plot is shown in FIG. 12. 
     Rather than consider all spontaneous potential values, i.e., those falling along the entire length of the calibration curve 33 of FIG. 12, it has been found preferable to consider only those points corresponding to pure shales and clean sands, and define the center of gravity of both clouds of points. Then, a calibration line can be drawn between these two centers of gravity. In FIG. 12, the points 34 and 35 represent the center of gravity for the clouds of points corresponding to shale and sand, respectively. The reason for this center of gravity approach is that if all points were considered, an excess of either shale or sand points could unduly influence the position of the calibration line 33. 
     Once the position of the calibration line 33 is known, measured values of the spontaneous potential can be utilized with the plot of FIG. 5 to determine the magnitude of V clay  /W xo  for each depth level. Values of φ e , S xo , and SI can be determined with other data in a manner to be described later and equations 5 and 12 can then be solved for V sh , 
     As will be set forth in detail later, the characteristic spontaneous potential in clean sands and shales should be determined. The characteristic spontaneous potential in shales is designated SP sh  and the characteristic spontaneous potential in sands is labeled the &#34;static spontaneous potential&#34; or SSP. In the past, it has been necessary to obtain such values from a visual inspection of a spontaneous potential log. However, such a visual inspection method does not always give accurate values of these two parameters. For example, a shale or sand bed must be fairly thick before an accurate value of SP sh  and/or SSP can be determined. If the shale or sand beds are not thick enough, the chosen values of these two parameters may be in error. 
     SSP is the SP value in clean sands and SP sh  is the SP value in a formation of 100% shale. It has been found that neither of these parameters will vary significantly over the length of a borehole provided the water salinity remains constant. Thus by determining these two parameters, the SP calibration for all depth levels in terms of V clay  is known. 
     In accordance with another feature of the present invention, values of SP sh  and SSP can be determined from the V clay  /W xo  versus SP crossplot of FIG. 12 in the following manner. To determine the value of SP sh , V clay  is set equal to &#34;1&#34; to give the quantity l/W xo  on the vertical axis of the FIG. 5 crossplot. Then the value l/W xo  is utilized in conjunction with the calibration line 33 to determine the value of SP sh . To determine the value of SSP, the fact that V clay   must equal zero in clean sands is utilized. Thus, the intersection of the calibration line with the V clay  /W xo  =0 axis gives the value of SSP. 
     Knowing SP sh  and SSP which gives the position of the calibration line 33 of FIG. 12, V clay  can be determined. Then, combining equations 5 and 12, V sh  from the spontaneous potential log, (V sh ) SP , can be written as: ##EQU4## 
     Another log which can provide an indication of the amount of shale is the gamma ray log. In this regard, it has been found that the relationship for the magnitude of the gamma ray log normalized for bulk density in terms of the volume of silt and clay, V silt  and V clay , respectively, can be written as 
     
         GR·ρ.sub.b =A+B V.sub.silt +CV.sub.clay       (16) 
    
     where: &#34;A&#34; is a calibration coefficient giving the background radiation, i.e., the gamma ray count rate in clean water sands; and &#34;B&#34; and &#34;C&#34; are calibration coefficients relating to V silt  and V clay , respectively. By multiplying the natural gamma ray count rate GR by the bulk density ρ b , the gamma ray count rate is normalized for variations in bulk density. By combining equations 3, 4, 5 and 16, the volume of shale given by the gamma ray log, i.e., (V sh ) GR  is given by the relationship: ##EQU5## 
     Before using the gamma ray log to provide a quantitative indication of the shale volume, it is first necessary to determine the calibration coefficients A, B, and C. To accomplish this, in accordance with still another feature of the present invention, a statistical fit is made between the gamma ray measurement and the amount of silt, clay and background radiation in the formations. 
     Turning now to FIG. 13 a three-dimensional plot of gamma ray versus V clay  and V silt  is illustrated. The gamma ray axis is the vertical axis in FIG. 6, while the V silt  and V clay  axes are the horizontally aligned axes to the left and right respectively in FIG. 13. By utilizing measures of V silt  and V clay  derived from the φ N  -φ D  crossplot in conjunction with the gamma ray count rate, GR, for each depth level, a point can be plotted on the three-dimensional plot of FIG. 13 for each depth level. A plane of best fit can then be drawn in FIG. 13. The intersection of this plane with the GR axis gives the magnitude of the calibration coefficient &#34;A&#34; since the GR axis coincides with V silt  =V clay  =0, i.e., clean sands. 
     To determine the calibration coefficient &#34;B&#34;, it is only necessary to set V silt  equal to &#34;1&#34; and V clay  equal to &#34;0&#34; in equation 17 which corresponds to looking at the axis V silt  =1 in FIG. 13. The total length of the vector from the V silt  axis at the point V silt  =1 to the plane of best fit gives the total normalized gamma ray reading in this case. Thus, since in this case, V silt  is equal to &#34;1&#34;, the length of this vector from the V silt  axis to the plane of best fit along the V silt  =1 axis will be equal to A+B from equation (12). Since A has already been determined by the intersection of the plane of best fit with the GR axis and can be projected onto the V silt  =1 axis, as indicated in FIG. 13, the remainder of the length of this vector is equal to &#34;B&#34;. The same reasoning applies to the determination of the calibration coefficient &#34;C&#34; from the vector between the V clay  axis and the plane of best fit along the V clay  =1 axis, as shown in FIG. 13. 
     If all of the gamma ray measurements were indiscriminately plotted in FIG. 13, it would be conceivable that there would be a great many more points plotting near one apex of a triangle which defines the plane of best fit than the others, thus giving rise to the possibility of points derived from one type of formation unduly affecting the position of the plane of best fit. To alleviate this problem, the plotted points are segregated into three groups corresponding to clean sand formations, shales having a predominance of clay, and shales having a predominance of silt. Clouds of points corresponding to clean sands, predominantly clay formations and predominantly silty shales are indicated generally in FIG. 13 by the designations 37, 38 and 39 respectively. The centers of gravity for each of these three clouds of points are then computed and such centers of gravity are utilized to define the plane of best fit. Thus, the points 40, 41 and 42 represent such centers of gravity. The determination of the calibration coefficients A, B, and C is then made in the manner described above. 
     Once the calibration coefficients A, B and C are determined, these coefficients can be used in conjunction with the measurements of gamma ray, GR, and bulk density, ρ b , and values of the silt index, SI, derived from the φ D  -φ N  crossplot, for each depth level in the borehole in accordance with equation (17), to give indications of the volume of shale indicated by the gamma ray measurement, i.e., (V sh ) GR . 
     A third indication of shale volume can be derived from the measurements of resistivity in hydrocarbon zones. In hydrocarbon zones of irreducible water saturation, the following expression applies: ##EQU6## where R t  is the resistivity of the non-invaded portion of the formation; 
     R w  is the resistivity of the connate or natural formation water which can be derived from water tables supplied by geologists or by other well-known techniques; 
     and 
     
         W.sub.irr =φ.sub.e S.sub.irr                           (19) 
    
     where S irr  is the irreducible water saturation. Irreducible water takes the form of water which clings to the grains of the formation material because of capillary forces and which cannot be displaced. 
     In clean formations, W irr  tends to remain constant and can be described by the relationship: ##EQU7## In shaly formations, the irreducible water volume can be described by the relationship: 
     
         W.sub.irr =W.sub.clean +i V.sub.sh                         (21) 
    
     where i is usually chosen to be 0.1. 
     After computing a lower limit of W clean  by using in equation (20) the highest resistivity recorded in the hydrocarbon zone, a value of V sh  derived from the R t  tool, (V sh )R t , can be found by simultaneously solving equations (18), (19), (20), and (21). Since the lowest limit of W clean  was selected, (V sh )R t  will be equal to or greater than the true value of V sh . 
     Another shale indicator based on the maximum volume of shale permissible for clean sands fully saturated with gas can be derived. On the φ N  -φ D  crossplot, clean sands fully saturated with gas will fall on a straight line passing through the origin of the crossplot. The slope of this gas sand line depends solely on gas properties. As will be set forth in detail later, the data points on the φ N  -φ D  crossplot are corrected for shaliness in accordance with the amount of shaliness indicated by the shale indicators. If this shaliness correction moves the φ n ,φ d  data points beyond this gas sand line limit, it is known that the amount of V sh  indicated by the shale indicators was too high. Since all of the shale indicators are presumed to indicate maximum limits of shaliness, the magnitude of V sh  which would correct the data points to the gas sandline limit: is chosen to be the most accurate indication of shale volume. It has been found that the relationship for the volume of shale given by the gas sandline limit shale indicator, (V sh ) g , can be written as: ##EQU8## The lower limit of gas density (ρ g ) lim  is computed as a function of depth in accordance with the following expression: ##EQU9## where &#34;depth&#34; is in feet. 
     Another upper limit on the volume of shale can be found based on the fact that the invaded zone water saturation S xo  must always be equal to or greater than the uninvaded zone water saturation S w . The reason for this is that, before the borehole is drilled, both the uninvaded zone and the region called the invaded zone after the borehole is drilled have the same water saturation. When the borehole is drilled, the drilling mud will invade a portion of the formation called the &#34;invaded zone&#34; displacing the naturally occurring fluids therefrom. The affect of this invasion is to increase the water saturation if oil was present and displaced by the invading fluid, and to cause little change if no hydrocarbons were initially present. 
     The water saturation of the uninvaded zone, S w , can be found from the following relationship: ##EQU10## The terms of equation (25) have all been previously defined. 
     The saturation of the invaded zone, S xo , can be obtained from the following expression: ##EQU11## where R xo  is resistivity of the invaded zone, (R sh ) xo  is the invaded zone resistivity of shale formations, R mf  is the resistivity of the mud filtrate which invades the invaded zone. R mf  can be determined by well known techniques. If an R xo  device is not available, the invaded zone water saturation can be approximated from S w  in accordance with the following expression: 
     
         (1-S.sub.xo)=0.5(1-S.sub.w)                                (27) 
    
     Since, as discussed above, S xo  must always be equal to or greater than S w , S xo  in equation (26) can be set equal to S w  in equation (25) and these equations solved for V sh  to give an upper limit on V sh  based on the water saturation ratio. By so doing, V sh  given by the saturation ratio shale indicator, i.e., (V sh ) s , is given by the following relationship: ##EQU12## 
     Another indicator of the upper limit of shale volume is derived from the ratio between the neutron derived porosity φ n  to this porosity in shale. Thus ##EQU13## The reason why this gives an upper limit on V sh  is obvious from equation (7) since φ e  is minimal when shale is the greatest. 
     A seventh indicator of the upper limit of shale volume can be derived from the fact that a solution of equations (6), (7), (10), (11) and (26) should give a value of hydrocarbon density ρ hy  which is equal to or greater than the gas density limit (ρ g ) lim . Reciprocally setting ρ hy  =(ρ g ) lim  permits us to compute from the same set of equations, a value (V sh ) hy  which is at least equal or larger than the true value thereof. 
     The terms R sh  and (R sh ) xo  have been used in a number of equations expressing the shale indicators discussed above. In the past, the determinations of R sh  and (R sh ) xo  have been brought about by inspection of R t  and R xo  logs in front of what was estimated to be representative of shale zones. In this prior technique, values of R t  and R xo  in shale zones was assumed to represent R sh  and (R sh ) xo , respectively. 
     Thus, in accordance with another feature of the present invention, more accurate values of R sh  and (R sh ) xo  are computed. These values of R sh  and (R sh ) xo  can, in accordance with the present invention, vary from one depth level to the next according to the composition of shale. 
     To determine a representative value of R sh  at each depth level, in accordance with the present invention, a statistical routine is utilized to determine the resistivity of a formation as if it had 100% clay. It has been found that the resistivity of the clay, R clay , usually does not vary from one formation to the next in any geological area. However, as discussed above, the resistivity of the shale, R sh , will vary in dependence on the distribution of the clay and silt. Thus, the statistically derived value of R clay  can be utilized in conjunction with the silt index SI to determine the value of R sh  at each depth level. 
     It has been found that the relationship between R sh , R cl , and SI is: ##EQU14## By plotting the resistivity R t  derived from a deep investigation resistivity tool in shale beds versus 1/(1-SI) 2 , a family of points such as shown in FIG. 14 will result. A line 45 can then be drawn in a manner to represent the best fit of all of the plotted points. In a 100% clay filled formation, the silt index will be zero and thus the term 1/(1-SI) 2  will be equal to one. Thus, by projecting a line from the &#34;one&#34; point on the 1/(1-SI) 2  axis to the line 45 and from there to the R t  axis, a value of R clay  is established. Then, as will be discussed later, a value of the silt index, SI, at each depth level is computed and used with the statistically determined value of R clay  in equation (32) to determine R sh  at each depth level. 
     The same technique is used to find the value of (R clay ) xo  except that a shallow investigation R xo  tool is utilized in place of the R t  tool. This value of (R clay ) xo  can be utilized with values of the silt index, SI, to compute (R sh ) xo  at each depth level in the same manner as for R sh . The relationship for (R sh ) xo  is: ##EQU15## 
     Having explained how the various shale indicators can be derived, the overall interpretation method of the present invention can now be discussed. For this purpose, refer to the φ D  -φ N  crossplot of FIG. 15 where the sand and shale lines and limit parabola 30 have been reproduced. As discussed earlier, the φ D  -φ N  crossplot can be utilized to determine the parameters V sh  and φ e  in the absence of a hydrocarbon effect. In mathematical terms, this means that there are as many unknowns in equations (8) and (9) as equations. As discussed earlier the shale terms (φ N ) sh  and (φ D ) sh  in equations (8) and (9) constitutue the values of φ N  and φ D  at the point on the crossplot where the limit parabola 30 intersects the shale line (See FIG. 11). If this point of intersection is to the left of the shale point S ho , S ho  is taken to be the characteristic shale point and (φ  N ) sh  and (φ D ) sh  will thus become (φ N ) sho  and (φ D ) sho . As discussed earlier, the silt index is determined from the location of this characteristic shale point. 
     Mathematically, this operation can be performed as follows. The limit parabola 30 in FIG. 4 can be expressed as: ##EQU16## (φ D ) sh  can be expressed in terms of the φ D  value of the wet clay point, (φ D ) clay , and the silt index SI as: 
     
         (φ.sub.D).sub.sh =(φ.sub.D).sub.clay (1-SI)        (35) 
    
     Likewise, (φ N ) sh  can be expressed in terms of the φ N  value of the wet clay point, (φ N ) clay , and the silt index SI as: 
     
         (φ.sub.N).sub.sh =(φ.sub.N).sub.clay (1-SI)        (36) 
    
     Since (φ D ) clay , (φ N ) clay  are known parameters, equations (34), (35) and (36) can be solved for (φ D ) sh , (φ N ) sh  and SI. If SI is greater than SI o  (the silt index of point S ho ), it is limited to SI o  and (φ D ) sh  and (φ N ) sh  are set equal to (φ D ) sho  and (φ N ) sho . 
     If there is a hydrocarbon effect, the crossplot will give inaccurate values for V sh  and φ e . In mathematical terms, this means that there are more unknowns in equations (6), (7), (10), (11) and (26) than there are equations. To eliminate one unknown parameter, the lowest value of V sh  produced by a plurality of the shale indicators discussed above is utilized. This lowest value is designated (V sh ) ind . Since (V sh ) ind  is on upper limit value and not always the actual value, it must be checked. To accomplish this, it is initially assumed that there is no hydrocarbon effect and equations (8) and (9) are solved for φ N  and φ D  using (V sh ) ind . The new shale corrected values for φ N  and φ D  are designated ψ N  and ψ D . Thus, ψ N  and ψ D  can be written as: 
     
         ψ.sub.N =φ.sub.N -(V.sub.sh).sub.ind (φ.sub.N).sub.sh (37) 
    
     
         ψ.sub.D =φ.sub.D -(V.sub.sh).sub.ind (φ.sub.D).sub.sh (38) 
    
     These shale corrected readings ψ N  and ψ D  are then compared to determine the location of the new ψ N , ψ D  point relative to the clean sand line. 
     Graphically, referring to FIG. 15, this operation is depicted by moving the original plotted φ D , 100  N  point parallel to the shale line by an amount dependent on the computed value of V sh  from the shale indicators, as represented by the vectors 47, 48 and 49 in FIG. 15. These equations cause the plotted point to move parallel to the shale line, and thus along one of the φ e  lines (see FIG. 3). The slope of this line will be (φ D ) sh  /(φ N ) sh . 
     Initially, only one value of shale indicators (V sh ) sp , (V sh ) GR , (V sh ) Rt , (V sh ) N  and (V sh ) g , is retained for the purpose of this correction. As noted before, the volume of shale computed for each shale indicator has been derived in such a way that it must be always either equal to or larger than the true volume of shale. Consequently, the lowest value obtained from any of the shale indicators must be the closest to the true value and is the one retained for subsequent use. 
     If the correction provided by (V sh ) ind  causes the plotted φ D , φ N  point to move to the 45° clean sand line it normally signifies the absence of a hydrocarbon effect on the tool readings, provided that the tool readings are themselves correct. (Correct tool reading refers to the absence of such upsetting factors as borehole enlargement, thick mudcake, etc.) An example of this is shown in FIG. 15 where the log readings give a plotted point 50 and the amount of shale, given by the shale indicators moves the data point by the length of the vector 47 to the point 51 on the sandline. In other words, the amount of shale given by (V sh ) ind  was most likely correct since the points should plot on the sandline in the absence of shale and hydrocarbons, i.e., the shale correction given by vector 47, in effect, moves the plotted point 50 to a position on the sandline where the point would have plotted in the same formation if free of shale. This being the case, the initial point 50 can be utilized in conjunction with the φ D  -φ N  crossplot to determine V sh , φ e , and SI (and from SI, V clay  and V silt ) in the manner represented in FIGS. 2, 3 and 11. Mathematically speaking, equations (8) and (9) are solved for V sh  and φ e  using the values of (φ D ) sh  and (φ N ) sh  determined from equations (34), (35), and (36) for the original, measured values of φ N  and φ D . The solution of equations (34), (35) and (36) for the measured values of φ N  and φ D  also gave SI which can be combined with V sh  in equations (4) and (5) to compute V clay  and V silt . 
     Now consider the case where hydrocarbons are present and do have an effect on the tool readings φ D  and φ N . It will be recalled from FIG. 3 that hydrocarbons move the data point to the northwest. Thus, assuming that (V sh ) ind  is accurate, the shale correction given by (V sh ) ind  will move the point across the 45° clean sand line. Thus, assume that hydrocarbons were added to that formation which gave the data point 50. In this case, the data point 50 would be moved to the northwest and the shale correction would move the point across the 45° clean sand line. 
     Taking an example of this, assume that φ N  and φ D  plot at the point 52 in FIG. 15 and that the shale correction provided by the shale indicators moves the plotted point the length of the vector 48 to a new position represented by the point 53. In this case, the fact that the shale correction has moved the point beyond, or to the northwest, of the clean sand line indicates that the tool readings are probably affected by hydrocarbons in the formation. However, this must be verified since it is also possible that the magnitude of the shaliness correction given by the shale indicators may be too great. 
     To verify that the lowest possible value for (V sh ) ind  has been computed, in accordance with another feature of the present invention, a test is made to determine if S xo  is less than S w . If it is, as discussed earlier, something is wrong since S xo  should never be less than S w . It is then assumed that (V sh ) ind  is too large and a new shale indicator is introduced. Since S xo  or S w  appears to be in error, the water saturations in the invaded and uninvaded zones are computed with equations (25) and (26) and used to compute a value for (V sh ) s  with equation (28). Since V sh  and φ e  are not known at this time, the V sh  value provided by the shale indicators, (V sh ) ind , is used for V sh  in equations (25) and (26) and φ e  is approximated with the following expression: ##EQU17## where ψ N  and ψ D  are the shale corrected values for φ N  and φ D , e.g., the values for the shale corrected data point 53 in FIG. 15. 
     If (V sh ) s  becomes the minimum V sh  value given by the shale indicators, it becomes the value of V sh  provided by the shale indicators, i.e., it becomes (V sh ) ind . In this event, it is also possible that the value of V sh  provided by the spontaneous potential shale indicator, i.e., (V sh ) sp , may turn out to be less than (V sh ) ind . It will be recalled from the discussion concerning equation (15) that the magnitude of (V sh ) sp  is dependent on the invaded zone water saturation S xo  which initially was set equal to 1 to give a first approximation of (V sh ) sp . Thus, a new value of (V sh ) sp  is computed using the newly computed value S xo . Then, if this new value of (V sh ) sp  is less than (V sh ) ind , this new value becomes the new V sh  value provided by the shale indicators. 
     After the best possible value of (V sh ) ind  is derived, the next step is to determine if the new shale correction moves the data point to or near the clean sand line. If the data point still moves past the clean sand line, it is determined if the resistivity logs agree with the apparent answer provided by the φ N  -φ D  crossplot, i.e., that hydrocarbons are present in the formations. S w  and S xo  are recomputed and used to check this. To this end, if the recomputed values of S xo  and S wx  are both approximately &#34;1&#34;, it means that the resistivity logs are indicating that there are no hydrocarbons. This, in effect, means that the answers provided by the φ N  -φ D  crossplot and those provided by the resistivity tools are in conflict. The logical reason for this conflict is that (V sh ) ind  is too large, which is always a possibility in view of the manner it is derived. Consequently, (V sh ) ind  is then decreased until either the shale corrected data point is on or near the clean sand line or the resistivity tools indicate the presence of hydrocarbons. (Recall that S w  and S xo  are both functions of V sh  and thus will change as (V sh ) ind  changes.) 
     Referring back to FIG. 15 the shale corrected data point 53 on the crossplot indicates that there is a hydrocarbon effect because the point 53 plots to the northwest of the clean sand line. Assume that the resistivity tools, on the other hand, indicate that there could not be any hydrocarbon effect and thus the amount of shale correction provided by the shale indicator (V sh ) ind  should have brought the originally plotted point 52 to the sand line at the point 55. The length of the shale correction vector is then decreased until either the point 53 is returned to or near the clean sand line or the resistivity tools represented through S w  and S xo  indicate a possibility of hydrocarbon effect. In this latter case, the original data point 52 is corrected in accordance with the magnitude of the hydrocarbon effect. As an example of this, assume that the shale corrected point 53 is moved back to the point 56 before the resistivity tools give an indication of hydrocarbons. In this event, the vector 57 closes the gap to the clean sand line. This has the effect of moving the initial point 52 in a direction parallel to the vector 57 and by the same length to provide a data point 57a which corresponds to the initial data point 52 corrected for the hydrocarbon effect. This corrected data point 57a is then analyzed by the φ N  -φ D  crossplot in the manner discussed earlier to derive values of φ e , V sh  and SI. 
     If, on the other hand, the shale corrected point 53 had been moved all the way back to or near the clean sand line, the original data point 52 would be used for this purpose. In otherwords, there would be no hydrocarbon correction. 
     Referring back to the point in the discussion where S w  and S xo  were both checked for an indication of hydrocarbon, if it had been determined that both S w  and S xo  are sufficiently less than 1 to indicate the presence of hydrocarbon, the value of hydrocarbon density ρ hy  used in equations (10) and (11) is checked to determine if it is lower than the lowest possible value of hydrocarbon density. This lowest possible value is the gas density limit value (ρ g ) lim  given by equation (24). To compute the value of ρ hy , equations (6), (7), (10), (11) and (2) are solved using the value of V sh  given by the shale indicators and value of SI, (φ d ) sh  and (φ n ) sh , picked from the φ N  -φ D  crossplot or from equations (34), (35) and (36). 
     If ρ hy  is greater than (ρ g ) lim , i.e., ρ hy  is acceptable, it is assumed that the answers provided by the solution of equations (6), (7), (10), (11) and (26) with values of (φ D ) sh  and (φ N ) sh  produced from equations (34), (35) and (36) are accurate. Then, knowing V sh  and SI, V clay  and V silt  can be computed from equations (4) and (5). 
     Turning to FIG. 15, this operation takes the form of moving the shale corrected point 53 the length of the vector 54 to a new point 58 on the 45° sandline. The corresponding correction due to hydrocarbon can be applied to the original point 52 and moves this point to a new location 58A. This is the location of the shaly sand point as if not affected by hydrocarbon. Consequently, this point 58A can be validly utilized in conjunction with the φ e  and V sh  lines of the φ N  -φ D  crossplot to compute φ e  and V sh  (or with equations (8) and (9)). Additionally, the location of this point 58A also determines SI. In this example, the point 58A is within the shaly sand area of the crossplot and thus the silt index is SI o  corresponding to the shale point SH o . 
     If, on the other hand, the hydrocarbon density test had failed, i.e., ρ hy  had been less than (ρ g ) lim , there is a clear indication that something is wrong-one of the readings or computations is in error. A likely candidate is the value of S xo  given by the R xo  tool, often influenced by borehole or mudcake effect. To check this, an approximate value of S xo  is computed using the value of S w  given by the R t  tool in accordance with equation (27). This equation is rather empirical and leads generally to reasonable values of S xo . If this new computed value of S xo , designated (S xo ) w , is less than the value of S xo  computed from the R xo  tool, it is assumed that the value of S xo  computed from R xo  is wrong. Then, the aforementioned test for S w  and S xo  sufficiently less than 1 is made using this new value of S xo . On the other hand, if (S xo ).sub. w is greater than or equal to the value of S xo  derived from R xo , it confirms that S xo  from the R xo  tool is reasonably accurate and that the error is caused by the value of V sh  given by the shale indicators being too large. Consequently, V sh  is decreased until the ρ hy  is equal to (ρ g ) lim  whereupon the hydrocarbon effect is computed to enable the subsequent computation V sh  and φ e , with equations (6), (7), (10), (11), (26) using values of (φ N ) sh  and (φ D ) sh  given by equations (34), (35) and (36). From these new values of V sh  and φ e , a new value of S w  can also be computed, S xo  being computed from the simultaneous solution of equations (6), (7), (10), (11) and (26). Graphically, the operation of reducing (V sh ) ind  is the same as discussed earlier where the data point 53 was moved back to the point 56 to give the hydrocarbon effect vector 57 which in turn moved the original data point 52 to the new position 57A for analysis by the φ N  -φ D  crossplot. 
     Now, consider what happens when the shale correction vector moves the plotted data point to a position to the right or southeast of the 45° sandline. Such a situation is depicted in FIG. 15 by the shale correction vector 49 moving the initial data point 63 to the position 64. This situation is incompatible with the underlying criterion of the method that the value of V sh  given by the shale indicators should always be equal to or greater than the true value of V sh . It is, therefore, assumed in this case that V sh  given by the shale indicators was correct but that either the value of φ N  or φ D  is inaccurate. 
     This implies that either φ N  reads too high (effect of borehole enlargement or mudcake) or the density of the sand grains has locally increased (φ D  too low). Then, ψ N  is checked to determine if it is compatible with the maximum value that can be expected in this sand. Mathematically, the ψ N  value of the shale corrected data point ψ N  is given by: 
     
         (ψ.sub.N).sub.lim =φ.sub.z (1-(V.sub.sh).sup.2.sub.ind (1-SI).sup.2)                                             (40) 
    
     If ψ N  is greater than (ψ N ) lim , φ N  is adjusted until the corrected dta point falls on the 45° sandline. 
     In FIG. 15, this operation is depicted by the vector 65 moving the corrected point 64 to a new position 66 on the clean sandline. Accordingly, the original data point 63 is moved in the same direction as the vector 65 and for the same distance thereasto the new position 66A. (Note: In this case, the original data point would fall to the right of the limit parabola even though not shown that way in FIG. 15.) This new data point 66A is then analyzed by the crossplot to find the values of V sh , φ e  and SI. 
     If φ N  is compatible with the above text, then it is assumed that the value of matrix grain density, ρ m , is in error and ρ m  is adjusted until the data point moves to the clean sand line. In FIG. 15, this operation is depicted by the vector 67 moving the shale corrected point 64 to the new position 68 on the clean sand line and the corresponding movement of the original data point 63 to the new position 68A. 
     There is a limit on the amount of adjustment made to ρ m . ρ m , and thus φ D  (See eq. 1), is adjusted only until it is equal to a predetermined limit value of matrix grain density. (In the example given by the vector 67 in FIG. 15, it was assumed that this limit condition was not exceeded.) Thereafter, φ N  is adjusted until the clean sand line is reached. 
     The discussion up to this point has assumed that the data points do not fall in the unlikely area. If a point falls into the unlikely area, it must first be verified and eventually corrected before the analysis discussed above can be performed. Since φ N  and φ D  is now presumed to be doubtful, other data not influenced by the borehole effect is used to control these values and to correct φ N  and φ D . To this end, in accordance with other features of the present invention, the porosity φ s  derived from the acoustic travel time log and computed in accordance with equation (2) and the values of V sh  given by the SP and gamma ray shale indicators are utilized to correct φ N  and φ D . After making these corrections, the adjusted data point can be analyzed in the manner set forth above. 
     Before discussing how the acoustic travel time derived porosity φ s  can be utilized to correct data falling in the unlikely area, it would first be desirable to explain how the acoustic data can be calibrated for compaction correction in accordance with other important features of the present invention. This compaction correction factor is designated 1/C p . 
     It is known that the porosity reading given by the neutron tool is reasonably accurate in clean water sands. It is also known that the value of porosity given by the sonic tool is also accurate in clean water sands after it has been corrected for compaction. Thus, to determine the magnitude of the compaction correction, a crossplot of φ s  versus φ N  can be used. Such a crossplot is shown in FIG. 16. By plotting a plurality of points on the φ s  versus φ n  crossplot, a line 70 describing the best fit of the plotted points can be drawn. The angle between this line 70 and a line 71 designating φ s  =φ n  gives the value of 1/C p . In other words, multiplying φ s  by the factor 1/C p  should move the statistical best fit line 70 to the position given by the line 71. 
     Having determined the factor 1/C p , it is now possible to determine the response of the sonic tool in shales. To this end, a crossplot of φ s  versus silt index, SI, can be used. Referring to FIG. 17, there is shown such a crossplot. A statistical fit of the points given by this crossplot will give a line 72 which indicates the relationship between φ s  versus SI. The intersection of this line with the SI=0 axis gives the value of φ s  in pure clay, i.e., (φ s ) clay  and the intersection of this line with SI=SI o  gives φ s  in the silty shale (φ s ) sh .sbsb.o. From this data the value of φ s  in any shale formation can be determined by its silt index from the equation: ##EQU18## 
     To correct data points on the φ N  -φ D  crossplot falling in the unlikely area with the acoustic derived porosity φ s , it is assumed that if φ n  is greater than φ s , the value of porosity given by the neutron tool is inaccurate and the acoustic derived porosity is used in its place. However, the data point is moved towards the origin until φ n  =φ s  /C p . This correction is applied only when shale content is low because it has been found that this correction is not usually accurate when the formation is shaly. This correction is graphically depicted in FIG. 15 by the vector 75 moving the original data point 76 to a new position 77. 
     In addition to using the compaction corrected sonic derived porosity φ s  /C p  to correct unlikely data points, a shaliness check is also made which will correct these points which are very shaly. In this regard, a value of V sh  is computed from the new position 77 of the data point after the φ s  /C p  correction and this value of V sh  is compared with the minimum value of V sh  computed from the gamma ray and SP shale indicators, i.e., (V sh ) GR  and (V sh ) sp . If the value of V sh  computed from the crossplot is less than the minimum value of V sh  computed from the gamma ray and SP shale indicators, the data point is moved in a southwesterly direction towards the intersection of the line W, CL d  of FIG. 2 with the φ N  =0 axis until these new values of V sh  from the corrected point on the crossplot becomes equal to (V sh ) ind . This operation is depicted in FIG. 15 by the vector 78 moving the corrected data point 77 to a new position 79. This new position 79 then is analyzed in accordance with previous discussion, i.e., the point 79 corresponds to the initial data points discussed earlier. 
     After the best values of V sh , φ e , SI have been computed in accordance with the techniques discussed above, these new values can be utilized in equations (25) and (26) to compute new and more accurate values of S w  and S xo . All of this data, V sh , φ e , SI, S w  and S xo  can then be recorded as a function of depth to thereby produce logs. Additionally, new values of hydrocarbon density ρ hy  can be computed by simultaneous solution of equations (6), (7), (10) and (11) using the last computed values of φ e , V sh , S xo  and (φ N ) sh  and (φ D ) sh . Additionally, a parameter representing the fluid density in the invaded zone, (ρ f ) xo , can be computed in accordance with the expression: ##EQU19## Additionally, the permeability K can be computed in accordance with one of the following two expressions: ##EQU20## where c, n, and m are coefficients chosen by the log analyst based on geologic considerations, or ##EQU21## where W irr  is given by equation (21) when water saturation S w  is appreciable, e.g., greater than two-thirds, and is equal to S w  ×φ e  when S w  is not appreciable, e.g., less than two-thirds. The choice in selecting equations (43) or (44) depends on what local experience in the area has shown to apply. 
     With accurate values of φ e , S xo  and ρ hy , it is possible to compute both the volume of residual hydrocarbon and the weight of such residual hydrocarbon in accordance with the following expressions: 
     
         V.sub.rhy =φ.sub.e (1-S.sub.xo)                        (45) 
    
     
         Weight.sub.rhy =V.sub.rhy ×ρ.sub.hy              (46) 
    
     Additionally a gas index which permits us to recognize the presence of free gas in formations can be derived from the values of φ s , C p , φ e  and φ N  as follows: ##EQU22## In water or oil zones, φ s  /C p  and φ N  are mathematically equal and GI remains close to zero. In gas zones, the porosity φ N  is decreased due to the low concentration of hydrogen in gas whereas the value φ s  is usually increased--consequently the (GI) s  value increases significantly above zero. 
     As discussed earlier, there are three forms of shale which can be found in any given formation, namely, dispersed shale, laminated shale, and structural shale. The volume of each of these forms of shale should equal V sh . Thus, 
     
         V.sub.sh =V.sub.d +V.sub.L +V.sub.str                      (48) 
    
     where 
     V d  is the volume of dispersed shale, 
     V L  is the volume of laminated shale, 
     V str  is the volume of structural shale. 
     These forms of shale are differentiated by the manner they affect porosity in accordance with the following expression: ##EQU23## Laminated and structural shales have been related through the following expression: 
     
         V.sub.L =(V.sub.L +V.sub.str)(2-V.sub.L -V.sub.str)        (50) 
    
     This distribution can be solved by a simultaneous solution of equations (48), (49) and (50) assuming φ z  to be constant and equal to the value of (φ z ) max  given by the φ N  -φ D  crossplot. Such conditions are often considered in recent depositions. There is no need to assume that φ z  is constant and when the sonic log is available, the following expression can be substituted for equation (49) to thereby give an accurate indication of the shale distribution in a more general way: 
     
         φ.sub.s =φ.sub.e +V.sub.D +(V.sub.L +V.sub.str)(φ.sub.s).sub.sh (51) 
    
     where (φ s ) sh  is determined from the statistical routine depicted in FIG. 17, i.e. (φ s ) sh  is determined from SI and the position of the calibration line in accordance with equation (41). 
     In the above discussion of the analysis of the φ N  and φ D  data, it has been assumed that the shale indicators had already been properly calibrated. Since the φ N  and φ D  data for the entire formation interval is used to compute several parameters used for this purpose as depicted in FIGS. 12, 13, 14 and 15, the data derived over the formation interval of interest is analyzed for calibration purposes before the φ N  and φ D  data is analyzed to produce V sh ,φ e , etc. Thus, the data is processed in a preliminary, first sweep before the final interpretation sweep is made. 
     However, as can be seen from a number of the shale indicator equations, hydrocarbons will have a significant effect on the shale indicator calibration. Since the extent of the hydrocarbon effect can not be accurately determined until the shale indicator have been calibrated and the shale indicators can not be properly calibrated until the hydrocarbon effect is determined, a difficult situation arises. 
     To overcome this problem, in accordance with other important features of the present invention, three sweeps of the data are made. The first sweep calibrates the shale indicators with the neutron and density data, assuming the absence of hydrocarbons. On a second sweep, a complete interpretation of the data, including analysis of the hydrocarbon effect, is made, using this preliminary calibration of the shale indicators. The hydrocarbon effect corrected data is then used during sweep 2 to more accurately recalibrate the shale indicators. It can be assumed that, after this second sweep, the shale indicators are properly calibrated. However, since the shale indicators may not have been properly calibrated during sweep 1, the interpretation analysis during sweep 2 may be inaccurate. Therefore, a third sweep is made to analyze th data using the recalibrated shale indicators. 
     As many sweeps as desired could be made. The accuracy would improve with each additional sweep. However, it has been found that three sweeps are sufficient in most cases. 
     To make the shale indicator calibration as accurate as possible, data falling in the unlikely area is rejected during sweeps 1 and 2. During the final sweep 3, this &#34;unlikely&#34; data is corrected and analyzed. 
     These three sweeps comprise what is defined as the &#34;interpretation pass&#34;. Prior to the interpretation pass, a &#34;preliminary pass&#34; is run to prepare the data for the interpretation pass and to produce a φ N  -φ D  frequency cross plot. (In a frequency crossplot, the number of times that a data point fell into each defined sector of the crossplot is printed at the sector location on the crossplot). This frequency crossplot can then be used to calibrate the tools and to select the parameters discussed earlier, i.e., SI o ,(φ z ) max , etc. Concerning the first pass in greater detail, the data is corrected for certain errors caused by borehole, invasion, mudcake, calibration, etc. Also, the neutron and density data is converted into porosity units, the gamma ray measurements are normalized for variations in density, and the apparent water resistivity, R wa , is computed. A log of R wa  can be used to determine the water resistivity R wa  for the formation interval of interest. How to accomplish all of these corrections and computations is well known in the well logging art and need not be discussed here. 
     After this preliminary pass, the interpretation pass is run using the measured data at each depth level as well as the parameters derived from the preliminary pass. Concerning the interpretation pass in detail and first considering sweep 1, after rejecting data which falls in the unlikely area on the φ N  -φ D  crossplot, the data from each depth level is analyzed for shaliness according to the position of the data point on the φ N  -φ D  crossplot. By so doing, initial values of φ e  and SI can be derived for use in the shale indicator statistical routines. Since, during this first sweep it is assumed that all formations are free of hydrocarbon effect, equations (8) and (9) can be utilized instead of equations (6), (7), (10) and (11). Thus, equations (8) and (9) in conjunction with equations (34), (35) and (36) will be sufficient to solve for these parameters on the first sweep. Of course, if a hydrocarbon effect in fact exists, the parameters produced by the statistical routines may be in error. However, this error is substantially eliminated during subsequent sweeps. 
     Once the shale indicators have been calibrated during sweep 1, it is now possible to make a complete interpretation utilizing the φ D  and φ N  data in conjunction with the calibrated shale indicators. This is done during sweep 2 of the interpretation pass. During sweep 2, the hydrocarbon effect can be accounted for since values of (V sh ) ind  are available even though not the most accurate values thereof. Upon making a complete interpretation, including correction for hydrocarbon effect, during sweep 2, more accurate values of φ e , SI and S xo  are available. These more accurate values are utilized to recalibrate the shale indicators. Thus, after the statistical routines run during sweep 2, the shale indicators will be accurately calibrated including taking into account the hydrocarbon effect. 
     Now that the shale indicators have been accurately calibrated, it only remains to use these newly calibrated shale indicators in conjunction with the derived well logging measurements to make a complete and final interpretation for each depth level. This is the function of sweep 3 of the interpretation pass. During sweep 3, data points falling in the unlikely area are analyzed and corrected so that no depth levels will be passed over during sweep 3. 
     Finally, the data computed during sweep 3 is prepared for display or recording and then outputted. The parameters computed in the interpretation analysis, i.e., V sh , V clay , V silt , φ e , S w  and S xo , can all be outputted. Additionally, the volumes of laminated, dispersed, and structural shale, V L , V D , V str , permeability, gas index, residual hydrocarbon by volume and weight, bulk volume water (φ e  S w ), can also be computed for display and recording. Moreover, synthetic gamma ray, SP and resistivity data can be computed for comparison with the original data. Also, statistical coefficients of fitness which can be used to evaluate the reliability of the gamma ray spontaneous potential shale indicators can be computed and displayed. 
     Having now discussed the underlying techniques of the present invention, it is possible to discuss a specific embodiment for implementing these techniques. In this connection, it would be possible to use a special purpose computer for performing the analysis or it would be possible to use a computer program for use on a general purpose digital computer. Because of the complexity of the analytical techniques of the present invention, it is considered preferable to utilize the computer program approach. 
     In this connection, FIGS. 18, 19, 20, 21, 22 and 23 are programming flow diagrams representing one embodiment of the present invention. First, referring to FIG. 18, there is shown a flow diagram representing the steps performed by the preliminary pass discussed above. Each element in these flow diagrams represents a step in the program. After initiation of the preliminary pass represented by an element 90, the input constants (ρ m , Δtf, etc.) for the formation interval of interest are read as represented by block 91. Next, the data logging parameters are read level by level as represented by the block 92. Next, the logging data is corrected for such things as borehole and calibration errors, as represented by the block 93. Then the values of φ s , φ N  and φ D  are computed level by level from the logging data as represented by the block 94. The corrected logging data, input parameters, and computed values of φ S , φ N  and φ D  are stored on magnetic tape, for subsequent use in the interpretation pass as represented by the block 95. At the same time as the data is being written on magnetic tape, the φ N  and φ D  data is being stored on a drum to enable the production of a frequency φ D  versus φ N  crossplot by, for example, a line printer, as represented by the blocks 96 and 97. As discussed in connection with FIG. 2, the φ D  versus φ N  frequency crossplot is used to draw the shale line and shaly sand trend line from which (φ z ) max , Cl w , Sh o , (and consequently SI o ) can be selected. 
     After the preliminary pass has been completed, the interpretation pass (see FIG. 19) is initiated, as represented by the element 100. The interpretation pass immediately enters sweep 1 for the determination of the calibration coefficients by statistical routines, as represented by the element 101. Once sweep 1 is entered, the data stored on magnetic tape from the preliminary pass is read level by level, as represented by the block 102. Next, the constant parameters derived from the frequency crossplots and logs produced by the preliminary pass are read and stored in memory, as represented by the block 103. 
     Each data point which falls into the unlikely area of the φ N  -φ D  crossplot (see FIG. 11) is discarded and thus not considered during sweep 1. How to write equations to segregate those data points falling in the unlikely area can be easily accomplished by standard analytical geometry techniques. Alternatively, approximation could be made which would require only linear first order equations. Thus, for example, equations could be written to segregate data points falling to the right of the line 106 and above line 107 in FIG. 11 to segregate those data points falling in this approximation of the unlikely area. How to write equations for such lines is well known and need not be discussed further here. 
     After data falling in the unlikely area has been discarded, equations (34), (35), and (36) are utilized to compute the silt index, SI, (φ D ) sh  and (φ N ) sh  as represented by the block 109. Graphically, referring to FIG. 11, this operation corresponds to drawing the parabola 30 through the data point and the φ z  point. The point where this parabola strikes the shale line is designated as the characteristic shale for this depth level and the silt index is computed from this characteristic shale point in accordance with the procedure discussed earlier. If SI is greater than SI o , SI is set equal to SI o , (φ N ) sh  is set equal to (φ N ) sh .sbsb.o, and (φ D ) sh  is set equal to (φ D ) sh .sbsb.o as represented by the block 191. In FIG. 11, this corresponds to designating the shale point as Sh o  if the parabola 30 crosses the shale line on the silt side of Sh o . Having the value of silt index SI, it is now possible to compute values for φ e , V sh , V clay , and V silt  using equations (4), (5), (8) and (9), as represented by block 192. Graphically, in FIG. 11, this corresponds to analyzing the data point for these parameters assuming the absence of a hydrocarbon effect. 
     At this point, values of φ e , V sh , V clay , V silt , and SI have been computed for use in statistical routines to calibrate the shale indicators. These values are approximations because the hydrocarbon effect has not been considered. During sweep 2, the hydrocarbon effect will be taken into account to improve this calibration. 
     Now that a first approximation of V sh  and SI is available, it is possible to undertake a statistical analysis of the resistivity of shale formations to determine R clay  in accordance with the technique depicted in FIG. 14. It will be recalled from a discussion of FIG. 14 that this statistical analysis is undertaken only for points corresponding to data derived from shale formations. If the magnitude of V sh  derived from step 192 and the gamma ray count rate are both high and R t  is low, it can reasonably be assumed that the data is from a shale formation. The decision element 193 determines if V sh  is greater than (V sh ) l , GR greater than (GR) l , and R t  less than (R t ) l  where l defines a limit value for these parameters. If the answers to the questions asked by decision element 193 are yes, the value of SI computed by step 109 and the measured value of R t  are utilized to compute a running average of R clay  and (R clay ) xo  in accordance with equations (32) and (33) respectively, as represented by block 194. In equations (32) and (33), R sh  and (R sh ) xo  constitutes R t  and R xo  for purposes of making the statistical analysis. If the answers given by the decision element 193 are no, step 194 is bypassed so that only data which is thought to be derived from shale formations will be considered in making these running averages. 
     It will be recalled from the discussion of FIG. 12 that the spontaneous potential log is calibrated to provide indications of (V sh ) sp  by plotting V clay  /W xo  versus the spontaneous potential for shale formation beds and clean water-bearing sand formation beds. The center of gravity of the data points for each of these two types of formations are then computed to designate the position of the calibration line 33. 
     The data points falling into these two classes are segregated in sweep 1 through the use of the gamma ray and deep resistivity logs, as well as the magnitude of V sh  computed in step 192. Additionally, the spontaneous potential log itself is also utilized for this purpose. 
     If the spontaneous potential is relatively high and the magnitude of V sh  computed in step 192 is relatively low, it can reasonably be assumed that the formation under consideration is a nearly clean sand formation. Thus, a decision element 195 determines if the spontaneous potential is greater than a given limit value, SP Ll , and if V sh  is less than a designated limit value (V sh ) Ll . If the answer to both questions is yes, it can be assumed that a sand formation is being logged. In this event, a running average of V cl  /W xo  is computed according to ##EQU24## where W xo  is obtained from equation (12), and n l  is the number of samples. This value is designated (AVC) sd . Also, a running average of the spontaneous potential is computed in accordance with the expression ##EQU25## This value is designated (AVSP) sd . These two operations are depicted in blocks 196 and 197 respectively. 
     If the answer to the questions asked by decision element 195 is no, the data is checked to determine if it corresponds to a shale formation. In a shale formation, the spontaneous potential and deep resistivity, R t , should both be relatively low and both the gamma ray count rate and V sh  computed in step 192 should be high. It is the function of decision element 198 to ask all of these questions and thereby determine if the data is being derived from a shale formation. If the answer is no, the program exits these spontaneous potential statistical routine. If the answer is yes, a running average of V clay  /W xo  using the expression ##EQU26## where n 2  is the number of samples. This running average is called (AVC) sh . Also, a running average of the spontaneous potential is computed for n 2  samples, which is called (AVSP) sh . These operations are depicted in blocks 199 and 200 respectively. After computing these running averages, the program exits the spontaneous potential statistical routine. 
     Next, the program enters the gamma ray statistical routine to perform the operation depicted in FIG. 13. It will be recalled from the discussion of FIG. 13 that the data is segregated into three categories corresponding to clean sands, shale formations having a preponderance of silt in one case and clay in the other case. If the gamma ray count rate is less than a given limit value (designated l 3 ) and V sh  is less than a limit (V sh ) 13 , (see blocks 201 and 202) it can be assumed that the data is derived from a clean sand and running averages are made on GR·ρ b , V clay  and V silt  according to the expressions ##EQU27## 
     If the decision element 201 had indicated that the gamma ray was above the limit (GR) 13 , then a series of tests are run to determine if the data points were derived from shale formations having a preponderance of either clay or silt. First, a test is run to determine if the formation under investigation is primarily a shaly one. To this end, as represented by the decision element 204, determination is made as to whether V sh  given by step 192 is greater than a limit value thereof. If the answer is no, the program exits the gamma ray&#39;s statistical analysis. (It is possible that data from some depth levels will not fit either sand or shale formations sufficiently well for statistical purposes). On the other hand, if the answer is yes, a test is made to determine if the formation is primarily either silt or clay. In this connection, as represented by the decision element 205, the question &#34;is SI greater than (SI) l3  &#34; is asked. If SI exceeds this limit value, the formation is presumed to have a preponderance of silt and if it is less, the formation is presumed to have a preponderance of clay. For those data points falling in the silty class, a running average of normalized gamma ray (GR·ρ b ) V clay  and V silt  are computed as represented by the block 206. The same operation is performed for the data points which fall into the clay class as represented by the block 207. The equations for steps 206 and 207 are the same as for step 203. (except for the sample designations N 3 , N 4  and N 5 ). 
     The computational data derived from the statistical routines of sweep 1 are stored in memory as represented by the blocks 25. If the level considered was not the last level, which question is asked by the decision element 226, the program proceeds to the next level as represented by the element 227 to run the same statistical routines for that level. If the presently considered level was the last level, the data stored in memory is utilized to compute SSP and SP sh  from the SP statistics as represented by the block 228 in accordance with the following expressions: ##EQU28## 
     The calibration coefficients A, B, and C from the Gamma Ray statistics are computed as represented by block 229 in accordance with the following: 
     Calling the results of the running averages made during the GR statistical routine in the following way: 
     
         ______________________________________                                    
Running Averages                                                          
            Sand Class                                                    
                      Silty Shale Class                                   
                                   Clay Class                             
______________________________________                                    
 ##STR1##   G.sub.1   G.sub.2      G.sub.3                                
 ##STR2##   C.sub.1   C.sub.2      C.sub.3                                
 ##STR3##   S.sub.1   S.sub.2      S.sub.3                                
______________________________________                                    
 ##STR4##                     (54)                                        
(S.sub.2 C.sub.1 - S.sub.1 C.sub.2) G.sub.3 ]                             
 ##STR5##                     (55)                                        
 ##STR6##                     (56)                                        
where                                                                     
Δ = (S.sub.2 C.sub.1 + S.sub.1 C.sub.3 + S.sub.3 C.sub.2) -         
(S.sub.2 C.sub.3 + S.sub.1 C.sub.2 +  S.sub.3 C.sub.1)                    
______________________________________                                    
 
    
     Before proceeding to discuss sweep 2, it would first be desirable to summarize the operation of sweep 1. As discussed earlier, the purpose of sweep 1 is to run statistical analyses on a number of parameters used for V sh  determination from the shale indicators. Since accurate determinations of V sh  given by the shale indicators is necessary before a complete interpretation analysis of the data can be performed, it is assumed, as a first approximation, that the data from all depth levels exhibits an insignificant hydrocarbon effect. Having made this assumption, it is possible to solve equations 4, 5, 8, 9, 34, 35 and 36 and to use the results in calibrating the shale indicators. Having a first approximation of the calibration parameters for the shale indicators, it is now possible to compute values of V sh  from the shale indicators and thus examine the effect of hydrocarbons on the derived data. This is the function of sweep 2. 
     Unfortunately, if there is a significant hydrocarbon effect in the formation being investigated, the calibration coefficients for the shale indicators which were derived during sweep 1 will be inaccurate and thus values of V sh  derived from the shale indicators will also be inaccurate. It therefore follows that the interpretation analysis made during sweep 2 would also be inaccurate. Therefore, the results produced from sweep 2 will not be outputted as the final results but will instead be utilized to recalibrate the shale indicators, this time taking into account the hydrocarbon effect. After this recalibration operation during sweep 2, the calibration coefficients for the shale indicators will be substantially accurate and thus can be utilized during a final sweep to produce a complete and accurate analysis of the data. Thus it can be said that sweep 2 is for the purpose of recalibrating the shale indicators for the effect of hydrocarbon. 
     Turning now to FIG. 20, there is shown a flow diagram representing the operations performed in sweep 2. After entering sweep 2, the data representing the constant parameters and calibration coefficients which have been stored in the memory, are read as represented by the block 240. As in sweep 1, the data from levels where the φ N ,φ D  points fall in the unlikely area are discarded, as represented by block 241. Next, that data which has not been discarded is analyzed and corrected for hydrocarbon effect to produce new data values for φ N  and φ D , designated φ NC  and φ DC  as represented by the block 242. This step comprises the operations depicted by vectors 47, 48, and 49 in FIG. 15. 
     Before proceeding with the remainder of sweep 2, it would be desirable to discuss the operations performed in Step 242. Thus referring to FIG. 21 there is shown the hydrocarbon analysis portion of the program in detail. 
     After entering the hydrocarbon analysis routine, the value for silt index SI is initially set equal to SI o  and S xo  is set equal to 1 as represented by the block 250. 
     Next, (V sh ) GR  is computed in accordance with equation (17) utilizing the calibration coefficient A, B and C computed during sweep 1, as represented by the block 252. 
     Next, (V sh ) SP  is computed with equation (15) using values of SSP and (SP) sh  computed in sweep 1, S xo  =1 (see Step 250), and W clay  determined from the crossplot (block 253). It will be noted that equation (15) for (V sh ) SP  includes the term φ e . No value of φ e  is available at this time. To get around this, a first approximation to φ e , designated (φ e ) app  is computed with the following expression: ##EQU29## Since (V sh ) SP  is a term in equation (59), equations (15) and (59) are solved simultaneously to derive a value of (V sh ) SP . Then, as represented by the blocks 254 and 254a, (V sh ) Rt  and (V sh ) N  are computed with equations (18) through (21) and (29), respectively. 
     The next step, as represented by block 255, is to compute a value for the shale indicator (V sh ) g  with equations (22) and (23) using the Neutron and Density derived porosity parameters for the characteristic shale SH o , i.e., (φ N ) sh  and (φ D ) sh  and a computed value of the gas density limit, (ρ G ) lim . This last parameter (ρ G ) lim  is computed from equation (24), as represented by the block 256. 
     The five shale indicators just discussed, i.e., (V sh ) GR , (V sh ) SP , (V sh ) Rt , (V sh ) N  and (V sh ) g , are considered to be the most reliable of the shale indicators. Therefore, these four indicators are utilized, at least initially to determine the value of (V sh ) ind . As represented by the block 257, (V sh ) ind  is set equal to the smallest of these four shale indicators. As will be discussed later, other shale indicators are introduced if inconsistencies appear in the results. 
     Having a value for (V sh ) ind , it is now possible to correct the φ N  and φ D  data points for shaliness. To this end values of ψ D  and ψ N  are computed with equations (37) and (38) as represented by the block 258. 
     Now that the φ N ,φ D  data has been corrected for shaliness with the shale indicator (V sh ) ind , the next step is to determine the position of the corrected data point ψ N ,ψ D  relative to the 45° clean sand line. It will be recalled from the discussion of FIG. 15 that if the corrected data point falls on or near the 45° sand line, the hydrocarbon analysis portion of the program is completed. Then, the original data point is analyzed for V sh , φ e , SI. On the other hand, if the corrected data point falls either above or below the clean sand line, further steps must be taken. 
     In this connection, as represented by the decision element 260, the question &#34;is ψ D  less than ψ N  &#34; is asked. If the answer is no, it is next determined whether ψ N  is approximately equal to ψ D , as represented by the decision element 261, i.e., is the corrected data point on or within a given range of the 45° clean sand line. If the answer is yes, i.e., if the corrected data point is on or near the clean sand line, the program exits the hydrocarbon analysis routine after setting the corrected φ N  and φ D  values, designated φ NC  and φ DC , equal to the original value of φ N  and φ D , as represented by the elements 262 and 263. 
     If the corrected data point had fallen above the 45° line, the underlying assumptions of the method would be satisfied. In other words, since all of the shale indicators are supposed to give indications of V sh  which are either equal to or greater than the true V sh , the shale corrected data point ψ N ,ψ D  should fall either on or above the clean sand line. If the shale corrected data point falls above the clean sand line, it can be assumed that either (V sh ) ind  was too large or that a hydrocarbon effect does exist. Both of these assumptions come within the basic underlying premise of the method. However, if the shale corrected data point falls below the 45° line, it can only be assumed that the derived measurements themselves were inaccurate or did not fit the model, or that one or more of the constants have been incorrectly selected. In this event, the program proceeds to make certain tests to determine what is wrong and to make suitable corrections. 
     Before continuing with the discussion of the hydrocarbon analysis routine, it would first be desirable to discuss some notations used in this routine. The subscript &#34;C&#34; is placed after data which has been finally corrected. Thus, ψ NC  and ψ DC  represent the final shale corrected data points and φ NC  and φ DC  represent the final hydrocarbon corrected (if any) data values which are outputted from the hydrocarbon analysis routine. Graphically speaking, in FIG. 15, φ NC , φ DC  would represent the point 58a and ψ NC , ψ DC  would represent the point 53. Those parameters with numeral subscripts, i.e., φ N1 , φ D2 , etc. represent interim data values. 
     Concerning first the case where the shale corrected data point falls below the line, a test is made to determine if φ N  is less than a given limit value representing the φ N  value of the limit parabola. If it is not, the shale corrected data point ψ N , ψ D  is moved to the 45° clean sand line along a constant φ D  line, as represented by the vector 65 in FIG. 15, the original data point is then corrected by the same amount. 
     In FIG. 21, to accomplish this, the limit value for ψ N , designated (ψ N ) lim , is computed with equation 40, as represented by block 261. Next, as represented by the decision element 262, ψ N  is checked against (ψ N ) lim . If ψ N  is greater than (ψ N ) lim , i.e., ψ N  is out of limits, as depicted in block 263, a corrected value of φ N  is computed in accordance with the following expression: 
     
         φ.sub.N =104 .sub.DC +(V.sub.sh).sub.ind ·(φ.sub.N).sub.sh (60) 
    
     As depicted by block 264, the final shale corrected density tool value ψ DC  is set equal to the ψ D  value computed in step 258. The new value of φ N  is designated φ N1  to distinguish it from the original φ N . 
     The computation of φ N1  in step 263 corresponds to moving the original data point, φ N , φ D , an amount equal to the correction applied to the ψ N , ψ D  point. Thus, in FIG. 15, it would correspond to moving the original data point 63 to the point 66a. 
     Since only the neutron data is altered, the final value of φ D  outputted from the hydrocarbon analysis, designated φ DC , is set equal to the original measured value φ D . This operation is depicted by block 264. As depicted by block 272, φ NC  is set equal to φ N1  computed in step 263. 
     Returning to decision element 262, if ψ N  is within limits, the program proceeds to determine what change of the matrix grain density, ρ M  would be required to move the ψ D , ψ N  point over the 45° line. Then, as represented by the block 266, φ D  is corrected according to the following expression: 
     
         φ.sub.D =ψ.sub.NC +(V.sub.sh).sub.ind ·(φ.sub.D).sub.sh                            (61) 
    
     Since only the density data is being corrected at this time, ψ NC  is set equal to ψ N , as represented by block 273. 
     This new value of φ D  is designated φ D1 . Equation (61) has the effect of moving the data point to the clean sand line by making ψ NC  =ψ DC . 
     using φ D1 , the value of ρ M  is recomputed and designated ρ M1 . With this new matrix density parameter ρ M1 , it is now possible to check if ρ M1  is greater than a value of grain density which is known by local experience to be unlikely to be exceeded. This limit value is labled (ρ M ) lim . This function is represented by the decision element 267. If ρ M1  is less than (ρ M ) lim , it means that the full correction is possible with the density measurement φ D , i.e., it means that the data point can be moved to the 45° sand line without ρ M  exceeding this limit. Thus, φ DC  is set equal to φ D1  computed in step 266 and φ NC  is set equal to the original data point φ N . In FIG. 15, this corresponds to moving the data point from the position 63 to the position 68a. This operation is depicted by block 268. 
     If the total φ D  correction cannot be made because of ρ M1  exceeding its limit, ρ M  in equation 1 is set equal (ρ M ) lim  and φ D  is re-computed, as represented by the block 269. Since this new value of φ D , designated φ D2 , represents the maximum acceptable correction for φ D , i.e., the maximum movement of the shale corrected data point 64 of FIG. 15 towards the clean sand line, the final corrected value φ DC  can now be set equal to φ D2 , as represented by the block 270. 
     At this stage, the corrected data point has not reached the clean sand line because of the limit (ρ M ) lim . To bring the data point the remainder of the way to the clean sand line, ψ D  is re-computed with equation (38) using the new value φ D2 , as represented by the block 271. Then a new value of φ N  is computed according to equation (60), as represented by the block 263. This new value φ N1  is set equal to φ NC  and the hydrocarbon analysis routine is excited as represented by blocks 272 and 265. The operation of blocks 271, 263 and 272 corresponds to, in FIG. 15, moving the shale corrected data point to the 45° sand line by changing ψ N . Thus, the original data point would change to a new φ N  value. 
     The discussion to this point in FIG. 21 has concerned the analysis which is undertaken when the shale corrected data point falls below or to the right of the clean sand line. Now consider what happens when the shale corrected data point falls above or to the left of the clean sand line. As discussed earlier, this corresponds with the basic premises of the interpretation method of the present invention in that it indicates that either a hydrocarbon effect exists or that (V sh ) ind  is greater than the true V sh . 
     When the shale corrected data point falls above the clean sand line, the deep and shallow resistivity measurements R t  and R xo  are utilized to determine which of these two conditions exists. To this end, first approximations of S w  and S xo  are computed from equations (25) and (26) using (V sh ) ind  and (φ e ) app-1 , as represented by blocks 280 and 281. If an R xo  measurement is not available, which question is asked by the decision element 282, S xo  is computed from equation (27) using the value of S w  derived in step 280, as represented by the block 283. 
     Now, having first approximation values of S xo  and S w , it is possible to compare S xo  with S w  to determine if the saturation computations S w  and S xo  appear to be feasible. This test is depicted by the decision element 284. 
     As discussed earlier, it is known that S xo  must be equal to or greater than S w . If S xo  is greater than S w , i.e., the answer given by decision element 284 is &#34;no&#34;, it is initially assumed that something is wrong with (V sh ) ind . (From equations (25) and (26), it can be seen that V sh  is a parameter in deriving S w  and S xo , the value being used for V sh  in these equations at this time being (V sh ) ind .) 
     In this event, the R t  and R xo  measurements are utilized to compute a new shale indicator (V sh ) s  in an attempt to provide a value of V sh  less than (V sh ) ind . 
     In FIG. 21, (V sh ) s  is computed utilizing equation 28, as represented by element 310. Then, as represented by the decision element 311, a test is made to determine if (V sh ) s  is less than (V sh ) ind . If (V sh ) s  is less, then (V sh ) ind  is set equal to (V sh ) s  as represented by block 312. 
     A further check can be made on (V sh ) ind . Since test 284 has indicated S xo  to be less than S w , and thus presumably less than 1, a new (V sh ) SP  can be computed taking the hydrocarbon effect into account, i.e., a value of S xo  from either steps 281 or 283 is available for use in equation (15). (Remember that S xo  was initially set equal to &#34;one&#34; in step 250.) This operation is depicted by block 313 and the new value of (V sh ) SP  is designated (V sh ) SP1 . As represented by the decision element 314, a test is then made to determine if this new value of V sh  is less than (V sh ) ind . If it is less, (V sh ) ind  is set equal to this new value (V sh ) SP1  as represented by block 315. 
     With a new lower value of (V sh ) ind , those computations which require (V sh ) ind  as a parameter can now be improved since a new more accurate value for (V sh ) ind  is available. Thus, after setting (V sh ) ind  equal to (V sh ) SP1 , this new value of (V sh ) ind  is introduced back into the program just prior to the ψ N ,ψ D  computation step 258. The program then recomputes ψ N  and ψ D  and goes through all of the analyses discussed above. If, after the second time through this portion of the program, S xo  is still less than S w , (V sh ) SP1  is recomputed using the newest (φ e ) app1  and S xo  data. If the newest (V sh ) SP1  value is still less than the new value of (V sh ) ind , the program recycles again. This continues over and over again until this portion of the program is exited either by the S xo  &lt;S w   test 284 being satisfied or V sh  values lower than the last (V sh ) ind  value being no longer computed. 
     Upon either event taking place, the program next determines if the R t  and R xo  data is indicating the presence of hydrocarbons, i.e., the &#34;no&#34; answers from decision element 284, 311 and 314 carry the program to a decision element 288. If the resistivity tools indicate the presence of hydrocarbons, it only remains to make the hydrocarbon effect correction to the original measured φ N ,φ D  data. Prior to making this correction, the program insures that the computed hydrocarbon density is at least equal to the density of gas (ρ g ) lim  computed in block 256. 
     To accomplish this in FIG. (21), a test is then made to determine if S w  and S xo  are both less than a given value approximating 1. In this example, the given value is 0.9. The asking of this question is depicted by the decision element 288. 
     Next, as represented by block 320, the hydrocarbon density is computed using the last values of ψ N  and ψ D  computed in step 258 and the last value of S xo  computed in either step 281 or 283. 
     The following five equations are solved simultaneously: ##EQU30## 
     This corresponds to solving for ρ hy  in the set of equations giving φ N ,φ D  for clean formations (8), (9) together with equations (10) and (11) relating (100  D ) hy  and (100  N ) hy  to the density ρ hy  and the S xo  equation (26). This operation is depicted in block 320. 
     The value of ρ hy  computed in step 320 is compared with (ρ G ) lim  which has been previously computed, as represented by the decision element 321. If ρ hy  is within limits, i.e., the answer is &#34;yes&#34;, a new value of φ e , designated φ e1 , is computed through a simultaneous solution of equations (6), (7), (10), (11) and (26) as represented by the block 322. Next, this φ e1  value is compared with the earlier computed (φ e ) app  1, as represented by decision element 324, and if they differ by more than a limit value designated (Δφ e ) lim , a new value (φ e ) app  1 is taken, equal to φ e1 , (block 323a) and new values of S w  and S xo  are computed using this new value, as represented by the block 323. This new value is then utilized to compute the new value of ρ hy , i.e., the program returns to step 320. The program continues to circle through this loop until the newly computed values of φ e1  and (φ e ) app  1 becomes approximately equal, at which time new values of φ N  and φ D  are computed using the last computed values of φ e1 , S xo , and (V sh ) ind  in equations (6), (7), (10), (11), and (26), as represented by the block 325. The new φ N  and φ D  values are designated φ N3  and φ D3 . These values are the ones corrected for any hydrocarbon effect and therefore may be used to recompute V sh , φ e , SI, (φ D ) sh , (φ N ) sh . 
     The purpose of this loop is to improve the value of (φ e ) app  1 and, therefore the values of S xo  and ρ hy . Initially the value of (φ e ) app  1 was only an approximation which could not take into account the exact value of hydrocarbon effect on the porosity tools, because the exact value of ρ hy  was not yet known. After each successive approximation of ρ hy  on this loop, more exact values of φ e  can be evaluated. 
     After these new values of φ N  and φ D  have been computed in step 325, new values of SI, V sh  and φ e  can be computed. Of these values, SI is of particular interest because it was assumed that SI=SI o  when computing (V sh ) ind . The new value SI which is more correct, will be used now to recompute new values of (V sh ) ind  by returning to block 252. Also the true value S xo  will be used in the computation of the SP shale indicator. These values are set in block 328 and the data goes through the same analysis again. These new values are entered into the program just ahead of step 251. 
     It has been found that this recycling operation with the new data values SI and S xo  is, at the most, necessary only once. Thus, as represented by decision element 326, the hydrocarbon analysis routine is exited (see element 328) after one pass through this decision element 326. 
     Referring back to the decision element 321, if the computed ρ hy  value had failed the limit test, it is first assumed that S xo  is reading too low. As a check on this, another S xo  value is computed from equation (27) using the computed value of S w , as represented by the block 330. Then, as represented by element 331, a test is made to determine if (S xo ) w  is greater than the last computed value of S xo  (Step 281 or 323). If it is less than S xo , it is assumed that the R xo  measurement was erroneous and S xo  is set equal to (S xo ) w , as represented by the block 332. With this new value of S xo , the program returns to the step 320 to recompute ρ hy . 
     If the new value of S xo  brings the computed value of ρ hy  above the limit, the program proceeds as discussed earlier with this new value of S xo . On the other hand, if the new computed value ρ hy  is still too low, this indicates that the cause of wrong values of ρ hy  was not a bad R xo  value but excessive value of (V sh ) ind . The program then branches to block 334 by the following process: it recomputes a value of (S xo ) w  (block 330) which is evidently equal to the value S xo  (because S xo  has been already set to (S xo ) w  in block 332). 
     Then the decision making block 331 recognizes that both S xo  and (S xo ) w  are equal and therefore branches to block 334 whose function is to decrease (V sh ) ind  by 1% before re-entering the program just ahead of step 258 with this new value of (V sh ) ind . Then the program proceeds as explained next. 
     If (S xo ) w  computed in step 330 turns out to be greater than S xo  derived from equation 26, the program presumes that the R xo  measurement is not at fault and instead assumes that (V sh ) ind  is too large. In this event, as represented by block 334, (V sh ) ind  is decreased by 1% and entered into the program just ahead of step 258. The program proceeds to take this lowered value of (V sh ) ind  and go through the entire analysis discussed above. The program will continue to recycle and recycle, each time decreasing (V sh ) ind  by 1% until an exit from the hydrocarbon analysis routine is found. For example, graphically speaking, the shale corrected data point may eventually be brought back to a location near the clean sand line and thus the decision element 261 will cause an exit from the hydrocarbon analysis routine, etc. 
     At this point, the hydrocarbon analysis has been completed and new corrected values of φ N  and φ D , designated φ NC  and φ DC , are available for analysis by the remainder of sweep 2. 
     Now returning to FIG. 80, sweep 2 uses these new values φ NC  and φ DC  to compute a new value of SI using equations (34), (35) and (36), as represented by the block 340. This new value of SI is designated SI 4 . As before, SI 4  is limited to SI o  if it is greater than SI o , as represented by block 341. Along with this, (φ N ) sh  and (φ D ) sh  are limited to (φ N ) sho  and (φ D ) sho  if SI&gt;SI o . Next, new values of φ e , V sh , V Cl  and V silt  are computed using equations (4), (5), (8) and (9) as represented by block 342. These new values are designated φ e4 , V sh4 , V Cl4  and V silt4 . With these new values of φ e4  and V sh4 , it is now possible to compute new values of S.sub. w and S xo  using equations (25) and (26). This operation is depicted in block 343. 
     At this point, the analysis of the measured φ N  and φ D  data has been completed for sweep 2 and the corrected φ N  and φ D  data can now be used to rerun the statistical analyses to define the calibration parameters for the shale indicators. 
     In addition to recalibrating the shale indicators, sweep 2 also computes the sonic compaction correction factor C P , calibrates the sonic data and produces synthetic spontaneous potential, gamma ray, and resistivity data derived from the equations used in the statistical routines. This synthetic data is then compared with the measured data to give indication of the figure of merit of the statistical routines. 
     Now concerning how the synthetic data is produced, in FIG. 20, the spontaneous potential is reconstructed using the values of V clay , φ e  and S xo  computed in steps 342 and 343, i.e., V clay4 , φ e4  and S xo4 , as well as the values of SSP and SP sh  computed during sweep 1. The expression for the reconstructed SP is: ##EQU31## This function is represented by block 344. This reconstructed SP value is a synthetic value derived from the equation (15). 
     If the SP data was properly calibrated, the reconstructed SP value should be substantially the same as the measured SP value. 
     A figure of merit for the SP, designated FM SP , is computed by comparing the reconstructed SP,SP rec  with the measured SP, as represented by block 345. The expression for this SP Figure of Merit is: ##EQU32## A decision element 346 determines if V sh4  is greater than a limit value thereof and bypasses step 345 if V sh4  is too large. The reason is that we are interested in the quality of the reconstruction of the SP only where the SP is important as a shale indicator to determine the hydrocarbon effect. Hydrocarbons appear in sands and not shales. Thus, the quality of reconstruction of the SP in shale has no practical significance for present purposes. 
     A reconstructed gamma ray is also computed from the values of V C14  and V silt4 , as well as the calibration coefficients A, B and C computed in sweep 1, according to equation (16). This function is represented by block 347. The reconstructed gamma ray, designated GR rec , is compared with the measured gamma ray and a figure of merit for the gamma ray, designated FM GR , is computed according to the following expression: ##EQU33## This function is represented by block 348. As for the SP, the quality of merit of the reconstruction of GR is of practical importance only when the formation is not too shaly and therefore is computed when V sh  is not too large. When this is not the case, the decision element 346 causes the program to bypass the gamma ray reconstruction and comparison. 
     Both FM SP  and FM GR  can be averaged on a running basis to provide figures of merit for data over the entire formation section of interest. 
     Next, using SI 4 , φ e4  and V sh4 , the deep resistivity measurement R t  is reconstructed, assuming 100% water bearing formation of resistivity R w , in accordance with the following: ##EQU34## (The term R o  is used here because it has come to be the designation for the resistivity of a formation where S w  =1.) This function is represented by block 349. The reconstructed R t  is designated (R o ) rec . Next as represented by the decision element 350 and block 351, the same operation is performed to reconstruct R xo  according to the following equation if an R xo  measurement is available: ##EQU35## These reconstructed resistivity values can be compared with the measured values to determine the presence of hydrocarbons. 
     Running averages of data to calibrate the SP, gamma ray and resistivity data recomputed in the same manner as for sweep 1. Since sweep 2 has considered the hydrocarbon effect, the calibration coefficients will be more accurate after sweep 2 (if there is a hydrocarbon effect than after sweep 1. This operation is depicted by element 99 in FIG. 20. This element 99 is shown in detail as the dashed line box 99 in FIG. 19. 
     Next the program enters a statistical routine to compute running averages of data which can be used to compute the acoustic or the sonic compaction correction factor 1/C p  and sonic response in shale in accordance with the techniques described in FIGS. 16 and 17. This is represented by element 99a in FIG. 20 which is shown in detail in FIG. 22. 
     First, concerning 1/C p , it will be recalled from the discussion of FIG. 16 that the slope of the line which best fits data points on a φ s  versus φ N  crossplot relative to the slope of the line representing φ s  /φ N  =1 gives a statistically averaged value of 1/C p . However, as discussed earlier, this statistical averaging must utilize points derived from clean water sands. To insure that only such data points are utilized, a series of tests are run on the data from each depth level. 
     Referring to FIG. 22, step 210 determines if V sh4  computed in step 342 is greater than a limit value thereof. If V sh4  is less than this limit value, a test is made to determine if the sonic travel time readings Δt are valid, i.e., to determine if they are low enough to insure the absence of a cycle skip effect. (Cycle skip is caused by a tool malfunction which causes the Δt measurement to be too high.) This test is performed by decision element 211. Next, a test is made to determine if the V sh4  value computed in step 342 is less than a limit value thereof, which limit value is less than the limit value given in decision element 210. This test is represented by the decision element 212. 
     If the test of decision element 212 is passed, the water saturation S w  is computed from equation (25), as represented by the block 213, and a test is made to determine if S w  is greater than a given limit value thereof as represented by the decision element 214. If the test of decision element 214 is passed, i.e., the clean sand formation is primarily water bearing, then a running average of φ s  /φ N  is computed as represented by block 215. Since φ s  /φ N  gives the slope of a line between the origin and the data point φ s ,φ N  (see FIG. 16), a running average of φ s  /φ N  will give the slope of the line 70 in FIG. 16 which represents a statistical fit of all of the points corresponding to a clean water sand. If any of these tests (211, 212 or 214) were failed (answer of no), the sonic statistical routine is exited. 
     To determine the response of the sonic log in shale, i.e., (φ s ) sh , in accordance with the operation depicted in FIG. 17, running averages of φ s , SI 4 , SI 2   4  and SI 4  ×φ s  are computed for data derived from shale formations. To determine if a formation is primarily shaly, a series of tests are run, the first test being the V sh  limit test represented by decision element 210. If this first test is passed, i.e., V sh4  is greater than the limit value therefor. Thereafter, tests to determine if Δt, SP and R t  are less than given limits and if the gamma ray count rate is greater than a given limit are made as represented by decision elements 216, 217, 218 and 219. If all of these tests are passed, i.e., if the answer to each test is yes, running sums of φ s , SI, SI 2 , and SI 4  ×φ s  for N (number of levels) are computed using the latest data (i.e., SI 4 ), as represented by block 220. If any one of these tests are failed, the program exits the sonic statistical routine. 
     The running averages from sweep 2 are stored in memory represented by the block 352. If the data being considered is derived from a depth level other than the last depth level, which question is asked by the decision element 353, the program then goes to the next level as represented by the element 354. If it is the last depth level, new values of SSP, SP sh , R Cl , (R Cl ) xo , A, B and C are computed from these new running averages, as represented by the block 355. 
     Additionally, the sonic travel time in shale of silt index SI o , (φ s ) sh  is computed from the sonic travel time statistics, as represented by block 357, in accordance with the following expressions: ##EQU36## 
     The average of φ s  /φ NC  is automatically calibrated in terms of the sonic compaction factor C p . (See block 356.) 
     Lastly, the program proceeds to sweep 3 as represented by element 358. As with the change from sweep 1 to sweep 2, the calibration coefficients are carried over to sweep 3. The original measured values of φ N  and φ D  are used for each depth level during sweep 3, the φ N ,φ D  values computed during sweep 2 being discarded. 
     At this point, the shale indicators have been recalibrated to take into account the hydrocarbon effect and figures of merit have been computed to give an indication of the accuracy of the calibration performed during sweep 1. With properly calibrated shale indicators, it is now possible to run a complete analysis of the derived well logging measurements and produce computed output data for presentation. This is the function of sweep 3 which will be described next. 
     Referring now to FIG. 23, there is shown a flow diagram of the operation of sweep 3. In sweep 3, the calibration data from sweep 2 which has been stored in memory is read for use during sweep 3. It will be recalled that during sweeps 1 and 2, data falling in the unlikely area is discarded because of the possibility of its having an adverse effect on the statistical routines used for selecting the calibration coefficients. In sweep 3, data points in the unlikely area are corrected before being analyzed. The sonic derived porosity φ s  and (V sh ) ind  are utilized for this purpose. 
     As represented by the decision element 371, it is first determined whether the plotted data point φ N , φ D  is in the unlikely area, as represented by the decision element 371. This same test is performed in blocks 104 and 241 in sweeps 1 and 2. The technique for determining if a φ N , φ D  point is in the unlikely area has been discussed earlier. 
     If the data point does not fall in the unlikely area, the program then proceeds to analyze the data for hydrocarbon effect, as represented by block 242. This hydrocarbon analysis is identical with the analysis undertaken in sweep 2 and need not be discussed further at this point. If the data point does fall in the unlikely area, and if φ e  is less than two-thirds of φ z , which question is asked by the decision element 372, the φ D , φ N  point is adjusted towards the origin φ D , φ N  =0 until φ N  becomes equal to φ s  /C p , as represented by block 373. These new values for φ N  and φ D  are designated φ N  &#39; and φ D  &#39;. 
     Next, as represented by blocks 374, 375 and 376, gamma ray and SP shale indicators are utilized to compute V sh  and the smaller of the two is selected. Before (V sh ) SP  and (V sh ) GR  can be computed, a value of Sl is necessary. This value can, for example, be selected as the Sl of the shale point defined by the intersection of the shale line with a line from the sonic corrected data point to a point defined by the intersection of the W-Cl d  line with the φ N  =0 avis (See FIG. 2). How to accomplish this entails standard analytic geometry techniques and need not be discussed further here. The value of Sl so defined is labeled Sl app   and is computed in step 373a. Step 374 uses SI app  and the calibration coefficients A, B and C computed during sweep 2 to compute (V sh ) GR  with equation (12). As represented by block 375, the calibration parameters SSP and SP sh  computed during sweep 2, and SI app , are utilized to compute (V sh ) SP  with equation (15). Then, as represented by block 376, the smaller of these two values of V sh  are selected and called (V sh ) ind  &#39;. Next, another value for V sh  is computed using the φ N  &#39; and φ D  &#39; values produced in step 373 with equations (8) and (9), as represented by block 377. As represented by block 378, a test is made to determine if this computed value of V sh  computed in step 377, i.e., (V sh ) nd  &#39; is greater than (V sh ) ind  &#39; computed in step 376. If (V sh ) nd  &#39; is less than (V sh ) ind  &#39;, the φ N  &#39;,φ D  &#39; point is adjusted towards the intersection of the W-φ d  line with the φ N  =0 line until (V sh ) ind  &#39; is equal to (V sh ) ind  &#39;, as represented by block 379. The new values for φ N  and φ D  are used to enter the hydrocarbon analysis routine of step 242. If (V sh ) ind  &#39; had been greater than (V sh ) ind  &#39;, the parameters φ N  &#39; and φ D  &#39; would have been used to enter the hydrocarbon analysis portion of the program. 
     After the new corrected values of φ N  and φ D , i.e., φ NC  and φ DC , have been produced by step 242, these new values are used to compute new values of φ e , V clay , V silt , V sh  and SI, as represented by block 381. These new values are designated φ e5 , V Cl5 , V silt5 , V sh5  and SI 5 . With the values of V Cl5 , V silt5  and SI 5 , as well as the gamma-ray calibration coefficients A, B and C computed during the sweep 2, the gamma ray is reconstructed as represented by block 382. Next, the reconstructed gamma ray is compared with the measured gamma ray and a figure of merit is computed according to equation (69) as represented by block 383. 
     Additionally, the spontaneous potential is reconstructed from the recomputed values of S xo , V Cl5  and the values of SSP and SP sh  computed during sweep 2, as represented by block 384. The reconstructed SP is then compared with the measured SP and a figure of merit is computed in accordance with equation 68 in the same manner as during sweep 2, as represented by block 385. The data is then prepared for output, as represented by block 386. A detailed flow diagram of how this is accomplished is shown in FIG. 24 and will be discussed next. Lastly, the prepared data is printed out and/or recorded on magnetic tape or a film recorder, as represented by elements 387, 388 and 389. As shown by elements 433, 434 and 435, the program processes data from each depth level in turn until the last depth level is reached, at which time it stops. 
     Now, turning to FIG. 24, there is shown a flow diagram representing the steps performed in preparing the data for output during sweep 3. After the &#34;prepare data for output&#34; routine is entered, new values of S xo  and S w  are computed using the latest available data, i.e., that calibration data computed during sweep 2. This function is represented by a block 400. Next the hydrocarbon density ρ hy  is recomputed by simultaneously solving equations (6), (7), (10), (11) and (27) using the latest computed values of φ N , φ D , φ e  and S xo , as represented by block 401. 
     When S w  or S xo  is close to 1, thus indicating that very little hydrocarbons are present, the computed value of hydrocarbon density ρ hy  will show large fluctuations for small errors in the parameters which are used in the computation of ρ hy . In this case it might be preferred to compute and print out optionally the fluid density in the invaded zone, (ρ f ) xo , instead of ρ hy . Thus, the invaded zone fluid density (ρ f ) xo  is computed using equation (42) as represented by block 402. A decision element 403 is used to select whether (ρ f ) xo  is to be printed out (see block 404). If (ρ f ) xo  is not to be printed out, ρ hy  is printed out (see block 405) but only if there is a sufficient hydrocarbon effect for the computed value of ρ hy  to be meaningful. As represented by decision block 406, the function φ e  BB ρ hy   2  is computed and compared with a limit value, where ##EQU37## ρ hy  is printed only if this function is greater than the limit value. 
     The next routine prepares the computed water saturation S w  value for output. When S w  is near 100%, the same type of problem discussed above for the hydrocarbon density ρ hy  also affects the water saturation S w . To circumvent this, the computed values of S w  are manipulated such that large fluctuations in S w  on the high end of the scale will produce small fluctuations in the recorded value of S w . Moreover, an expansion of S w  is made for very low computed S w  values to take into account the fact that at this low water saturation, the rock matrix becomes partly oil wet which leads to erroneously low computed values of S w . 
     Turning to FIG. 26, there is shown a plot of measured S w  on the horizontal axis versus recorded S w  on the vertical axis. The dotted line 410 represents the linear one for one relationship of computed S w  versus recorded S w . The solid line curve 411 gives the recording function applied to the computed S w  values. It can be seen from FIG. 26 that for values of computed S w  near 0 and 100%, there is very little fluctuation in the recorded values of S w . 
     This function is performed in the flow diagram of FIG. 24 as follows. First, the computed S w  is limited to one as represented by block 415. If S w  is between 0.6 and 1.0, which question is asked by decision element 416, S w  is computed in accordance with the following expression: ##EQU38## (See block 417.) If S w  is between 0.4 and 0.6, which question is asked by the decision element 418, the actual computed value of S w  is printed, as represented by block 419. If S w  is between zero and 0.4, which question is asked by the decision element 420, S w  is computed in accordance with the following equations: ##EQU39## 
     S xo  is function formed and printed in the same manner as S w  is and need not be discussed further. This function is represented by block 422. 
     Next, cumulative values of φ e  and φ e  ×(1-S w ) are computed. This corresponds to integrating values of φ e  and φ e  ×(1-S w ). This function is represented by block 423. A pip is then printed for every predetermined unit of cumulative φ e  and φ e  ×1-S w , as represented by block 424. 
     The next portion of the &#34;prepare data for output&#34; routine is to compute permeability using either equation (43) or (44). Which equation is to be used is determined by the decision element 425. This decision is set by the operator before running the program. 
     If equation (44) is to be used, it must first be determined whether W irr  is to be set equal to S w  φ e  or a value determined from solving equations (20) and (21). This is determined by looking at the value of water saturation S w , (see decision element 427). If S w  is greater than two-thirds, W irr  is set equal to the value formed from equations (20) and (21), as represented by block 428. On the other hand, if S w  is less than two-thirds, W irr  is set equal to S w  φ e , as represented by block 429. 
     Steps 439-442 are used in the computation of the percentages by volume of the different forms of shale using equations (48), (49) or (51) and (50). It will be recalled from the discussion of FIG. 11 that if the measured values of φ N  and φ D  give a point on the φ N  -φ D  crossplot which falls to the left of the dispersed shale line, the originally selected value of (φ z ) max  cannot be correct and still be consistent with the model. Such an occurrence is represented by the point 33. In this event, it is assumed that the original (φ z ) max  is not applicable and a new φ z  is chosen such that the dispersed shale line will pass through the point 33. This new φ z  value is then entered into equation 49 for the φ z  term therein. 
     To accomplish this in the &#34;prepare data for output&#34; routine of sweep 3, step 440 determines if the measured φ N ,φ D   point is to the left of the dispersed shale line defined by (φ z ) max  by asking &#34;Is (φ z ) max  -φ e5  &gt;V sh5  ?&#34;. If it is, (φ z ) max  is set equal to φ e5  +V sh5  (step 441) for entry into equation 49. V D , V L  and V str  are then computed with equations (48), (49) and (50). (See step 442.) Of course, if sonic data is available (Step 439), equations (48), (50) and (51) are used instead (step 443). 
     Then the residual hydrocarbon saturation and weight are computed in accordance with expressions (45) and (46) and printed out, as represented by block 432. Next, the gas index as given by the sonic log is computed according to equation (47), as represented by block 433. 
     Finally, if the level being considered is not the last level, the program returns to the beginning of sweep 3 to consider data from the next level, as represented by element 434. See FIG. 23. It it is the last level, the program stops, as represented by element 435. 
     Now referring to FIG. 25, there is shown an example of a log produced in accordance with the teachings of the present invention. The pip on the left-hand side of the depth track corresponds to the integration of porosity. The distance between two consecutive pips represents a selected number of feet of 100% porosity of pore volume per acre. Each pip on the right-hand side of the depth track represents a selected number of feet of hydrocarbon in place. 
     In track I, V sh  and permeability K are recorded. In track II, S w , φ·S hyr  and φ·S hyr  ·ρ hy  for hydrocarbon analysis are recorded. S w  is the fraction of pore volume filled with formation water. φ·S hyr  is the residual hydrocarbon per bulk volume and φ·S hyr  ·ρ hy  is the weight of residual hydrocarbon per bulk volume. The two curves, φ·S hyr  and φ·S hyr  ·ρ hy  coincide in oil zones since the density of oil is close to unity. In light hydrocarbon zones, the two curves diverge. The ratio of φ·S hyr  ·ρ hy  to φ·S hyr  is the hydrocarbon density. 
     In track III, porosity analysis curves φ e  and φ e  S w  are recorded. φ e  is the formation porosity corrected for hydrocarbon and shale effect and φ e  ·S w  is the water-filled porosity. Thus, the area between the two curves corresponds to hydrocarbon filled porosity. A bulk volume analysis is recorded in track IV. In this regard, V clay , V silt  and φ e  are recorded. 
     It can be seen from the foregoing that new and improved methods have been invented for analyzing shales and shaly sand formations. With these improved methods, more data than has ever before been available can now be computed and displayed to enable a complete interpretation of shaly sand and shale formations. 
     When the shale and hydrocarbon corrected φ N ,φ D  point falls above the 45° clean sand line, instead of using the S W  and S xo  tests and corresponding corrections discussed earlier, it would be possible (though not always as accurate) to simply check the value of (V sh ) ind  with V sh  given by the crossplot to make suitable corrections as discussed below. When the density-neutron crossplot is used for the determination of a shale content V sh  and of φ e , it is desirable to ensure that results from the crossplot are not affected, at least under certain conditions, by defective logs due for example to borehole effect. In this latter case, the density provided by the density tool may become quite erroneous and the shale content V sh , but especially the porosity φ e , determined by the density-neutron crossplot might then be very substantially underestimated. 
     In order to limit this risk, an automatic checking procedure can be provided according to which the value (V sh ) ND  finally determined from the density-neutron crossplot previously corrected for the possible influence of hydrocarbons is compared to the value (V sh ) ind  provided by the shaliness indicators. (V sh ) ND  is retained as the probable value of V sh  only if it is, on the one hand lower than the value (V sh ) ind  provided by the shaliness indicators, but at the same time if it is not different from this latter value (V sh ) ind  by an amount greater than a value λ fixed arbitrarily in advance, for example, λ=0.10. The computed (V sh ) ND  is thus retained only if (V sh ) ind  &gt;V sh2  where V sh2  =(V sh ) ind  -λ. If (V sh ) ND  &gt;(V sh ) ind , the porosity φ e  can be taken equal to φ D  corrected for shale and hydrocarbons. In hydrocarbon bearing intervals, if V sh2  &gt;(V.sub. sh) ND  then φ e  can be computed with a value of shale content equal to V sh2 . 
     It is also possible to place a security or upper limit on the calculated value of φ e . In this case, the calculated porosity φ e  would be retained only if it is smaller than an upper limit related to the shale content: 
     
         φ.sub.e ≦φ.sub.max (1-V.sub.sh) 
    
     Otherwise this maximum value of porosity is retained. The value φ max  is a datum provided at the beginning of the calculation from the preliminary analysis. It can in certain cases be derived from the value of the porosity for sands of identical nature, but clean and entirely saturated with water. If a sonic log is available, an upper limit of the porosity can also be calculated from the measurement of the speed of the acoustic wave without correction for the shale or the hydrocarbons. In the type of formation considered (sand), secondary porosity need not be feared. 
     For the cases of both the V sh  and φ e  securities just discussed, the calculations would be performed again this time using the new values of V sh  and/or φ e . 
     The techniques of the present invention can also be modified and/or used for interpretation of other types of shaly formations. This will be illustrated by showing how some aspects of the invention can be applied in a somewhat different way, to the cases where one mineral, like sand, or several minerals are present in the formation, in addition to shale. It has been seen that when the formation is made of sand plus shale, the points corresponding to clean levels of the formation with no hydrocarbon will fall on a 45° line on a φ N , φ D  crossplot. However, if the lithology of the formation changes, the points corresponding to clean levels with no hydrocarbon will fall on other lines on the crossplot (assuming the calibration of the neutron and density porosities remains the same) and this will be a further factor disturbing the points representing the various levels of the formation. 
     FIG. 27 illustrates this phenomenon for the neutron density combinations of porosity logs. Considering the ρ b ,φ N  crossplot of FIG. 27, the straight line L is the geometric locus of the points representative of pure limestone formations (its porosity scale varying from 0 to approximately 20), the neutron tool being calibrated in limestone. In other minerals the response of the same neutron tool calibrated in limestone will be different for an identical porosity. Moreover, since the matrix is different, the density at equal porosity will also be different. Thus a basically dolomite formation whose porosity is variable and a sandstone formation will be represented by more or less rectiliner lines D and S respectively. 
     Given a point Q of porosity 15% representing a porous formation at a given depth level containing 40% limestone and 60% sandstone, it will be located on the one hand substantially on the equiporosity line EQ joining the points of porosity 15% of the lines S and L, and on the other hand on the dashed line of intermediate lithology LI starting from a matrix point M corresponding to the average density of the matrix ρ ma  of this formation at the level under study. Conversely, from the location of a point Q furnished by the logs, its porosity and its lithology can be determined if the constituents of its matrix are known. It is nevertheless interesting and very important to note that, in the case of the neutron-density crossplot of FIG. 27, an error in the determination of the lithology would cause only a very small error in the porosity determined by the crossplot. This is particularly true for the minerals of the group quartz, limestone, dolomite and anhydrite. Moreover, the results are correct even in the presence of secondary porosity. 
     On a crossplot such as that shown in FIG. 27, the analytic expression for the lithology lines corresponding to each pure mineral can be derived analytically. Similarly, the equiporosity lines between two given minerals are substantially parallel to one another and their equation can be determined analytically. For a point Q which falls between the lithology lines of two minerals, it will be possible to determine analytically on which equiporosity line it is located and then to determine its matrix density ρ ma , if the corresponding level is indeed composed of these two minerals. In other words, from experimental data concerning these minerals, the relations 
     
         φ.sub.N =φ.sub.N (φ.sub.e ρ.sub.ma)        (74) 
    
     
         ρ.sub.b =ρ.sub.b (φ.sub.e ρ.sub.ma)        (75) 
    
     can be determined giving respectively φ N  and ρ b  as a function of φ e  and ρ ma  for all the matrices furnished by combinations of these minerals. Consequently, knowing the nature of the minerals of a formation which is clean and devoid of hydrocarbons, it is possible to determine analytically the porosity φ e  and the matrix density ρ ma  of all its levels. 
     The identification of the minerals, if not known by the geologists, can be made by analysis of crossplots. In this connection one of the most useful is the so-called MN plot as described for example in &#34;The Litho-Porosity Crossplot&#34; SPWPLA Symposium 1969 by J. A. Burke, R. L. Campbell, Jr., and A. W. Schmidt. 
     In the alternate embodiment of the present invention, where a single or multimineral shaly type formation is encountered, a V sh  value is derived with the help of shale indicators. As previously mentioned, a large number of such indicators can be used. 
     In addition to the shale indicators discussed earlier, another shale indicator based on the most northwesterly line drawn on a crossplot of neutron and density data over a formation section of interest can be derived. This will now be explained. If the neutron porosity φ N  is the abscissa and the density porosity φ D  the ordinate, FIG. 28, (or the density ρ b  graduated in decreasing value), the shift R-R&#39; of a given point on the crossplot because of the effect of the hydrocarbons with respect to the case of a formation saturated with water takes place in a northwest direction (i.e., increasing φ D  and decreasing φ N ). If on this crossplot, in the absence of information on the influence of hydrocarbons, the limit straight line LNP is drawn passing through the matrix point 0 and through the points situated the farthest to the northwest in the cloud of points P plotted on the graph, it is reasonable to suppose that this line corresponds to points of the formation which are practically clean and have the lowest hydrocarbon density (i.e., gas) and highest hydrocarbon saturation. In this case, the most northwesterly line can be called the limit line of the clean levels and designated (V sh ) ND  =0. Starting from this hypothesis, if a point is considered corresponding to a maximal content of residual hydrocarbons in the interval of the formation examined, the value of V sh  from the crossplot, designated (V sh ) ND , will be its real value. In order to find it, straight lines parallel to (V sh ) ND  =0 can be drawn on this crossplot for various values of (V sh ) ND  as previously shown with FIG. 3. The analytic determination of (V sh ) ND  and φ e  can be made once the equation of line (V.sub. sh) ND  =0 has been derived from the crossplot by determining coordinates of two points on this line. If on the contrary the residual hydrocarbon content S hyr  is smaller than this maximal value, the shale content (V sh ) ND  found by applying the preceding formula will constitute an upper limit of the real shale content of the point (see FIG. 30). 
     The same reasoning remains valid if in addition to or instead of hydrocarbons, the density-neutron crossplot concerns a zone of complex lithology whose characteristics are not known. The straight line limiting the cloud of points to the northwest, called the clean levels line, corresponds to the clean levels of the formation (if there are any), and the shift of the other points in the direction of the clay point from this line defines an upper limit of V sh . This crossplot is very useful. However, it should be used with caution when the readings of porosity φ D  are liable to be affected by the bad condition of the borehole. Sonic-neutron and density-sonic crossplots provide analogous results and constitute further indicators. 
     Instead of using equations (6), (7), (10), (11) a hydrocarbon correction Δ of these values can be made according to the formulas: ##EQU40## The above formulas can be expressed in the form of correction charts. It is quite possible, as the preceding formulas indicate, instead of using the combination of the neutron and density porosities, to use the combination of the neutron porosity φ N  and the bulk density ρ b  which leads directly (by taking into account the densities of the matrix and of the fluid) to the density porosity φ D . 
     Now concerning the situation where a formation has complex lithology, if such a formation of complex lithology is devoid of shale and of hydrocarbons, the determination of its porosity and of its average matrix density at each level of the formation interval considered can be dealt with the aid of the neutron-density crossplot as for shaly sands, i.e., with the aid of equivalent analytic formulas as mentioned above. The identification of the minerals which are jointly present and more particularly of their clean characteristics (neutron and density responses, etc.,) is required and can be derived from a preliminary analysis as indicated above. 
     FIG. 29 illustrates a case with a formation composed of both sandstone and mica (φ Nmica  =0.10). The equations of the lithology lines in this figure are the following: ##EQU41## ρ s  and ρ mf  being the densities of the sand and mud filtrate respectively. These two equations permit the matrix density ρ ma  and porosity φ e  to be determined at each level. 
     In practice, in the example chosen, the calculation is made from two logs of porosity as if the section of formation whose representative point falls between two lithology lines (such as S and L, for example) were constituted by the two minerals corresponding to these lines. Thus, in the case of the evaluation of a formation of complex lithology, the method here described proposes two options for determining the matrix density and the porosity at each depth level depending on whether the minerals in the formation are known or if the formation is known to only contain minerals of the group silica, limestone, dolomite and anhydrite. The preliminary analysis permits the appropriate option to be selected. This being the case, the evaluation of these formations when they contain shale and/or hydrocarbons makes use of relations analogous to those for shaly sands. The readings from the porosity tools can be corrected to give ψ N  and ψ D  with a first approximation (V sh ) ind  providing an upper limit of the shale content derived from shale indicators in the same manner as discussed earlier. (See equations (37) and (38).) 
     If hydrocarbons are present, these values of ψ N  and ψ D  are used to further correct the hydrocarbon effect and determine at each level the porosity φ e , the matrix density ρ ma , and the hydrocarbon residual saturation S hyr . An approximate value of the density ρ h  of the hydrocarbons present in the formation is preselected in order to carry out the method. This value can in general be provided by the knowledge of the zone explored. 
     With a value of ρ h  and computed values of ψ N  and ψ D , the proper hydrocarbon correction formulas are selected among the Δ formulas (76) through (80) and the two equations (81) and (82), corrected for shale content and hydrocarbon effect, are solved with equation (26) for the three unknowns, φ, ρ ma  and S hyr  or S xo . 
     The solutions of the equations for these three unknowns can be accomplished by an iteration method. To begin this iteration, a value of S hyr  can be set arbitrarily or an approximate value of the porosity φ e  can be set. This approximate value can be obtained from the observation that the shift of the points of a neutron-density crossplot under the influence of hydrocarbons generally takes place substantially in the direction of the lines of equiporosity. 
     The following technique can be used, in particular in the presence of light or gaseous hydrocarbons. The Δ formulas (76) through (80) show that the directions Δφ N  /Δρ b  of the shift of the points depend only on the density ρ h  of the hydrocarbons. From the hypothesis made about this density ρ h , the points of the neutron-density crossplot are consequently shifted in a direction opposite to the effect of the hydrocarbons in the direction corresponding to their assumed density ρ h  (direction oriented substantially towards the southeast; see FIG. 30) until the first lithology line is met corresponding to a pure mineral (line S, L or D). The porosity read on this lithology line is used as the approximate value φ a  of the porosity of the level considered in order to begin the iteration procedure. This entire operation is carried out automatically. For this purpose the analytic expressions of the various lithology lines are used in conjunction with the directions of shift due to the hydrocarbons (Δρ h  /Δφ N ). 
     The value of the porosity φ a  is introduced with (V sh ) ind  in the formula for R xo  (26) to provide a first value of S hyr1  with which a new approximation φ a1  of the true porosity φ e  and a value of ρ ma  can be derived from the neutron and density equations (81) and (82) corrected as indicated. From this new φ a1 , a new value S hyr2  can be derived and used for recommencing the preceding cycle. When after n cycles the porosity φ an  found does not differ by more than one porosity unit from the approximation φ a (n-1) derived from the preceding cycle, the iteration is stopped and the last computed values of the parameters of interest are printed out. 
     Steps can be taken to minimize the effect of occasional bad log readings. Based on geological information, or on the study of the crossplots, a lower limit ρ ma1  and an upper limit ρ ma2  of the grain density of the non-shaly fraction of the formation are chosen. If the computed ρ ma  is smaller than ρ ma1 , V sh  is decreased by steps of 0.02 up to a maximum of 0.10, with V sh  =0 being a limit of course, until a satisfactory ρ ma  value is obtained. If this is not enough, the last V sh  value is retained, and ρ ma  is taken equal to ρ ma1 . The value of φ e  is then derived from neutron and density equations after eliminating the hydrocarbon effect. If the computed ρ ma  is greater than ρ ma2 , φ N  is decreased by steps of 0.01 until a satisfactory value is obtained; if the computed porosity reaches zero the process is stopped and ρ ma  is taken equal to ρ ma2 . A porosity limit, φ max  (1-V sh ) can also be used as explained above. In the two mineral option, another porosity limit based on the sonic can also be used. This is derived from Δt, corrected for shale, and assuming for Δt ma  the lowest Δt reading in the formation section of interest. The value of ρ ma  is the density of the non-shaly portion of the matrix. In the case where the shale content is very high, the computed value of ρ ma  is not very precise. It is then preferable to calculate the average density of the matrix including the shale. 
     When the formation has fissures or fractures, an index of secondary porosity can be calculated as: ##EQU42## φ ND  being the porosity calculated from neutron-density crossplots and φ S  the sonic porosity after possible corrections. This index can be printed out. 
     While there have been described what are at present considered to be preferred embodiments of this invention, it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the invention, and it is, therefore, intended to cover all such changes and modifications as fall within the true spirit and scope of the invention.