1. Field of the Invention
This invention primarily pertains to a method of deterministically calculating a synthetic seismic wavelet, or voltage waveform, for any desired source-to-receiver offset and any target reflector depth for the seismic, particularly, the marine environment. This invention also pertains to a method of establishing performance criteria for a data gathering system or a portion thereof.
2. Description of the Prior Art
In a typical marine seismic gathering system, it is customary that a vessel be equipped with both an acoustical energy source, usually on a submerged carrier towed by the vessel with certain control apparatus herefore being located on the vessel itself, and seismic detector array, usually in the form of a complex cable also towed by the vessel. Such a detector cable is typically towed at a shallow depth behind the vessel and is best characterized as a streamer or an extended cable including a plurality of seismic detectors or hydrophones. It is also usual for such detectors to be spaced along the streamer in arrays, rather than singly.
The returns incident on the hydrophone arrays are a result of the seismic impulses from the source being reflected from the various subsurface geologic interfaces. One such interface is the water bottom or interface between the ocean and the land. Other interfaces occur wherever there is a lithological variation or impedance change creating subsurface layers. Knowledge of such interfaces is extremely valuable in evaluating for the presence of hydrocarbon deposits and the like.
FIG. 1 herein shows the factors affecting the pulse radiated by the source. A non-isotropic source has directivity and the receiving system has a capture area. The capture area impacts the signal in other ways than just the receiving array. Subsurface related factors include divergence, transmission loss, frequency dependent absorption (Q-loss), and interbed multiple interference. Also, the target interface's reflection coefficient directly impacts the received signal, and its behavior with offset can be very important. Ambient noise and scattering contribute to degrading the signal-to-noise ratio.
Many ways exist to enhance the signal relative to noise. For example, it is well recognized that a common-depth-point (CDP) stack improves the signal-to-noise ratio over non-stacked data.
For an understanding of the concept, consider a horizontal reflecting interface with a point thereon as the "CDP". Along a parallel "datum" line above the interface, and to one side of a normal drawn to the CDP, are evenly spaced detectors. (Actually, there is normally a detector array, but for discussion herein "detector" is used to signify an associated arrayed group of individual detectors.) Along the datum line and to the other side of the normal drawn to the CDP, are equally evenly spaced sources. A first data trace would be the result of an impulse from the closest source being reflected off the interface and received at the closest detector. A second data trace would be the result of an impulse from the next closest source being reflected off the interface and received at the next closest detector. Similarly, data traces developed from successive sources to successive detectors, each resulting from a reflection off the interface at the CDP, would develop a "common depth point gather".
However, there is normally only one source in a typical marine seismic system. It is towed at a predetermined rate. Assuming that the detectors were stationary and evenly spaced, when the source was at a position corresponding to the first source in the above example, then the second, and so forth, an ideal CDP gather could be developed. In the normal system, however, the detectors are not stationary, but are towed in conjunction or at the same rate as the source. Therefore, it may be seen that a two-trace, or "two-fold" common depth point gather is developed when the source is impulsed at an initial position and then impulsed again when it and the detector cable have been towed together one-half of the detector spacing distance, the first impulse being detected by the first detector and the second impulse being detected by the second detector. The process can then be repeated for as many detectors as there are on the cable for a full-fold CDP file.
Of course, data is not actually collected in the field in the manner just described. In actual practice, a source impulse is detected at all of the detectors, and not from a common depth point. Then at a second location of the source, which normally would be at a distance from the place where the source was first impulsed, the source is again impulsed and detected at each of the detectors, again following reflection from different depth points. From the individual field recordings, data associated with a common depth point is selected and is built up in what is truly a common "CDP gather". Hence, the signal-to-noise improvement is not gained from the field recordings but from the CDP gather.
Because the travel time for an impulse from the source to the reflecting interface to the detector is longer for the second detected trace than for the first detected trace in a CDP gather, and for the third detected trace than for the second detected trace, and so forth, a time correction is necessary for the subsequent traces to position them in time with the first data trace or event so that the signal will coherently add when the traces are summed. Such a correction is referred to as the normal moveout (NMO) correction. Factors involved in making this correction, which is different for each detector event resulting from a successively spaced detector, are well-known in the art and are explained, for example, in Geophysics, a publication of the Society of Exploration Geophysicists, Vol. 27, No. 6, published in 1962 at page 927, in an article entitled, "Common Reflection Point Horizontal Data Stacking Techniques", W. H. Mayne, which is incorporated herein by reference for all purposes.
Once the CDP gather has undergone NMO correction, the data can be observed as is or it can be stacked. A stack is a sum of traces which correspond to the same subsurface reflection with different offset distances. The objective of stacking the CDP gather is to coherently add signal and noncoherently add random noise. This improves signal-to-noise ratio, thus, effectively increasing the primary signal amplitude. Hence, creating a CDP stack, improves the likelihood of discovery of hydrocarbon accumulation in subsurface layer.
Of all visual indicators (high amplitude, phase change, flat spot, etc.) of hydrocarbon, a high-amplitude anomaly is most obvious on a CDP stack and thus most often used. Yet unfortunately, it is also difficult to differentiate a high-amplitude reflection caused by a gas layer from that caused by a nongas layer like a high-velocity hard streak.
An effective means to distinguish a gas layer from a nongas layer resides in the amplitude-versus-offset reflection behavior in a CDP gather. For instance, in many cases the reflection coefficient at a shale-to-gas-sand interface increases in amplitude with offset, while there may be no increase of reflection coefficient with offset at a nongas interface.
A key factor for successfully evaluating either direct hydrocarbon indicators or offset-amplitude variations is called relative-amplitude processing. Its purpose is to restore the amplitude losses; i.e., divergence, transmission, absorption, and the like. This allows the reflection coefficient behavior to be revealed.
A comprehensive amplitude processing flow for obtaining improved amplitude information pertaining to the geology is "Controlled-Amplitude" processing, as suggested in Geophysics, Vol. 50, No. 12, published in 1985 beginning at page 2697, in an article entitled, "Offset-Amplitude Variation and Controlled Amplitude Processing", Gary Yu.
It includes (1) applying an exponential gain for any intermediate test and processing, (2) suppressing coherent noise such as multiples or ground roll, (3) removing the exponential gain of step (1), (4) restoring amplitude losses with offset compensation, (5) deconvolution, (6) NMO correction, (7) surface-consistent consideration, (8) partial trace sum to enhance the S/N ratio for the offset amplitude study, (9) band-pass filter, (10) section-dependent equalization for a CDP gather display, (11) stack, and (12) region-dependent equalization for the stacked section.
This processing flow has been used successfully. Yet there is still a degree of uncertainty because the actual data is used for making the estimations to minimize the amplitude losses with offset, and the data (particularly prestack data) can be highly contaminated with noise. Also there is no way to monitor the accuracy of the results in mid-process.
This invention is the response to the need for the development of a model of the offset dependent factors which can be used to correct the seismic data. Motivation for this work initially came from radar. Radar echo calculations are normally made for received pulse power. The formula used for radar echo calculations is called the "radar range equation". The radar range equation permits echo strength calculations from known system parameters, the propagation path, and the target characteristics. It can be found in any standard radar text, for example, Introduction to Radar Systems Analyses, a publication of a McGraw-Hill Book Company, N.Y., published in 1962, M. I. Skolnik especially at pages 3-5 and 570-579, or Radar System Analysis, a publication of Prentice Hall, Inc., Englewood Cliffs, N.J., published in 1965, D. K. Barton. The seismic equivalent to the radar range equation can be referred to as the "seismic range equation". However, there are significant differences.
In radar, the propagation medium is often assumed to be homogeneous and isotropic so that spherical spreading or divergence is usually assumed from the transmitting antenna to the target and also back from the target to the receiving antenna. Quite often a radar radiates a train of identical high energy rectangular sine wave pulses. Each pulse is generated by a transmitter and radiated into space by an antenna. Even when the pulse is short it is radiated on a large carrier frequency so that the radiation approximates being monochromatic. The antenna usually has high gain or directivity, and the target is usually assumed to reside at some range on the antenna boresight. A single antenna is often used for both transmission and reception. A radar operating in this fashion is called monostatic. The pulse duration, antenna beam, and target range are usually all large enough that the target can be treated as a point. It intercepts and re-radiates a portion of the beam and a small amount returns to the antenna. Some of the return is collected by the antenna and dissipated in the load impedance. The antenna and load impedances are almost always assumed to be complex conjugate matched.
The seismic case is more complicated. Seismic signals are broadband. They cannot be treated as monochromatic. The amplitude and phase spectra must be determined for many frequencies across the seismic band in order to calculate a wavelet. The source and receiver are at different locations making seismic systems bistatic rather than monostatic. The source and receiving system both impact the wavelet differently depending on their offset. A different radiated source pulse must be considered depending on the offset distance. Also, the receiving pattern and phase effects due to the hydrophone array image depend on offset. Another major factor is that the propagation medium is not homogeneous and isotropic. Rather, it consists of perhaps hundreds of layers of materials exhibiting different physical characteristics. The target is an interface in this medium. It is quantified by its P-wave reflection coefficient. Spherical spreading does not apply because of refraction at each interface. The subsurface also exhibits dissipation into heat, conversion of P-wave energy into S-wave energy, P-wave energy lost to reflected P-waves, and interference effects due to interbed multiples. The attenuation acts as a minimum phase filter. The interbed multiples are superimposed on the primary. All these subsurface effects depend on the ray paths through the subsurface and hence on the selected offset. The target reflection coefficient also depends on the offset distance between the source and receiver.
Since a homogeneous isotropic medium, often assumed for radar calculations, is not appropriate for the seismic problem, a horizontally layered medium shown in FIG. 3 herein is assumed. Each layer is homogeneous and isotropic. The i.sup.th layer has with thickness h.sub.i, P-wave velocity .alpha..sub.i, S-wave velocity .beta..sub.i, density .rho..sub.i, and attenuation constant, Q.sub.i. For a given offset and target depth, Snell's Law is used to find the ray path from the source to the hydrophone array thereby determining the ray angle, .theta..sub.i, in each layer. This calculation is well understood. Unlike a radar point target, the seismic target is an interface between two beds having specified P-wave velocities, S-wave velocities, and densities. Target strength is quantified by the P-wave reflection coefficient for the angle of incidence found when determining the ray path.
For seismic work, the idea of pulse power at a precise frequency simply does not have the same meaning as it can for radar. Power can make sense by imagining that a seismic source is fired periodically and then considering the power at a precise Fourier frequency. In the limiting case of a single firing, this power becomes energy density times the differential frequency increment, df. Energy density is energy per hertz.
Radiated energy density from the source does not spread spherically. One reason is because of the refractions at the interfaces. By following an approach similar to that as suggested in Geophysics, Vol. 38, No. 3, published in 1973 at pages 481-487, in an article entitled, "Divergence Effects in a Layered Earth", P. Newman, a factor can be found which when divided into radiated energy density yields the incident energy density per unit area on the hydrophone array. This factor is referred to as "divergence" herein. It is slightly different from the factor that Newman calls divergence. The energy density dissipated in the load attached to the hydrophone array is equal to the incident energy density per unit area times the receiving system's capture area. This received energy density is then scaled by source directivity, the target interface's power reflection coefficient, and losses associated with the layered subsurface. Three losses are introduced: transmission loss, interbed multiple loss, and Q-loss. The subsurface loss is their product. Other losses such as those associated with layers not being truly homogenous or isotropic could be incorporated in this subsurface loss. Transmission and reflection coefficients at each interface are found by solving the Zoeppritz equations described in Reflection Seismology a Tool for Energy Resource, a publication of John Wiley and Sons, N.Y., published in 1981, K. H. Waters, especially at pages 27-47 and 254-259. Transmission loss is found by determining the product of the transmission coefficients for the entire ray path. Interbed multiple loss is found by noting that reflected rays at each interface can be reflected again and again and end up at the offset of interest. These interbed multiples interfere with the direct primary signal incident on the hydrophone array. This interference, generated from the entire subsurface is referred to herein as "interbed multiple loss". The Q-loss is the frequency-dependent absorption taking place in the layers (Waters, 1981).
Therefore, it is a feature of this invention to deterministically calculate the offset-dependent factors attributable to the geology above the target beds and the data collection means by utilizing what is referred to herein as the "seismic range equation". A result of this feature is the ability to model fully uncorrected seismic data. Modeling uncorrected data is advantageous because these models can be processed along with the data for comparison at any stage of processing. The processing consists of using the offset-dependent factors to correct the data and the model.
It is another feature of this invention to provide an improvement in the ability to sharpen both processed and unprocessed seismic data and model for both prestacked and stacked seismic data and model.
It is still another feature of this invention to provide an improved method of seismic system analysis and seismic system design.