Direct traveltime inversion of VSP data for elliptical anisotropy in layered media
This paper presents an exact method for inversion of VSP data for anisotropic parameters that uses traveltimes directly, rather than phase slownesses computed from traveltime differences. There is a tradeoff in the present traveltime-based method compared with the slowness-based method. In our method we have to assume some function representing the vertical velocity variation, something that is not necessary in the phase-slowness method. There is, however, a higher numerical accuracy in the direct traveltime method. This is due partly to our using observed traveltimes directly in the computations rather than taking differences between values of comparable size, which greatly magnifies the relative errors. Error analysis shows that there also are other intrinsic reasons why our technique has less error. A numerical example representing a typical VSP yielded errors from the phase-slowness method (requiring two sources and two receivers) that were about 18 times larger than for a single determination by the direct traveltime method. Furthermore, in cases where the VSP has been acquired with a single source offset, e.g., for some offshore wells, the traveltime method will yield results, whereas the slowness method will not. INTRODUCTION In the last decade or two there has been a greatly increased recognition that significant seismic anisotropy is rather common in sedimentary rocks. It has also been shown that neglecting even a seemingly modest degree of anisotropy can lead to significant degradation in processed seismic images (e.g., Winterstein, 1986; Wright, 1987; Larner, 1993; Tsvankin, 1996; Chen and Castagna, 2000) or to significant errors in vertical or lateral positioning of subsurface features (e.g. Banik, 1984, 1987; Isaac and Lawton, 1999; Vestrum et al., 1999). Gaiser (1990) determined how to estimate the anisotropic parameters of a transversely isotropic medium from VSP data using vertical and horizontal phaseslowness measurements. Miller and Spencer (1994) and Miller et al. (1994) presented methods for inverting phase slowness estimates from walkaway VSPs for anisotropy parameters. Using a similar method, Leaney et al. (1999) have inverted multiazimuthal multioffset VSP P-wave data over a marine carbonate reservoir to determine azimuthal anisotropy in the carbonate and transverse isotropy in the overlying shale. Leslie and Lawton (1999) present a method for inverting refraction seismic data for the anisotropic parameters of steeply dipping strata. Tsvankin and Thomsen (1994) and Alkhalifah and Tsvankin (1995) deal with the problem of inverting for longer spreads, beyond the near-vertical elliptic-anisotropic approximation, in order to recover velocity fields for processing. * Authors listed in alphabetical order.
Analytical inversion for Thomsen's γ parameter in weakly anisotropic layered media
An analytic scheme for traveltime inversion in horizontally layered media exhibiting transverse isotropy with a vertical symmetry axis (TIV) is presented. It pertains to SH waves, i.e., characterized by a single ‘Ihomsen parameter, y, or to other waves exhibiting approximately elliptical velocity dependence. The proposed method incorporates ray bending at interfaces. The suggested approach is particularly suitable for vertical seismic profiling as best providing required information. The input information consists of traveltime for obliquely travelling downgoing waves which can be measured by an offset survey, vertical wave speed from the zero-offset survey, and layer thicknesses directly from the wellbore. Correct results necessitate high accuracy of all input parameters. The proposed inversion method is particularly sensitive to errors in measured traveltime. ( 4 )
Azimuthal variation in AVO response for fractured gas sands
Natural fractures in reservoirs play an important role in determining fluid flow during production, and hence the density and orientation of fractures is of great interest. In the presence of aligned vertical fractures, the reflection amplitude at finite offset varies with azimuth. The effect of natural fractures on the azimuthal AVO response from a gas‐sandstone reservoir encased within shale is investigated. A simple expression for the difference in P‐wave reflection coefficient from the top of the reservoir parallel and perpendicular to the strike of the fractures is obtained in terms of the normal and tangential compliances, ZN and ZT, of the fractures. This expression is valid for small anisotropy and material contrasts and is compared with the results of numerical modelling. For a given value of ZT, the azimuthal variation in reflection coefficient at moderate offsets is found to increase with decreasing ZN/ZT. For gas‐filled open fractures ZN/ZT ≈ 1, but a lower ratio of ZN/ZT may result from the presence of cement or clay within the fractures, or from the presence of a fluid with non‐zero bulk modulus. For ZN/ZT = 1 and moderate offsets, the variation with offset of the reflection coefficient from the top of the fractured unit is dominated by the contrast in Poisson's ratio between the gas sand and the overlying shale, the effect of fractures only becoming noticeable as the critical angle for the unfractured sandstone is approached. However, for reflections from the base of the fractured unit, the variation in reflection amplitude with azimuth is much greater at conventional seismic offsets than for the reflection from the top. Azimuthal variations in the strength of the reflection from the top of the reservoir depend only on the variation in reflection coefficient, whereas the raypath is also a function of azimuth for reflections from the base of the fractured unit, leading to stronger, more visible, variations of AVO with azimuth. It follows that an azimuthal variation in AVO due to fractures in the overburden may be misinterpreted as due to the presence of aligned fractures in the reservoir.