WHITE, J.E., MARTINEAU-NICOLETIS, L. and MONASH, C. 1983, Measured Anisotropy in Pierre Shale, Geophysical Prospecting 3 1, 709-725.The five elastic coefficients which characterize a transversely isotropic medium have been measured for the Pierre Shale. The first-arrival times deduced from two closely spaced vertical seismic profiles provide values of magnitude and direction of the phase velocity at a given depth for different locations of the sources. From these velocities, we can estimate the five elastic coefficients by assuming that the P-and SV-wave velocities have only a small dependence on the angle of propagation. On the other hand, it is shown that the accuracy in the difference between the directions of propagation and particle motion is not sufficient to determine the anisotropy.

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There are numerous modeling techniques commonly employed for the computer simulation of seismic wave propagation. The capabilities of these techniques vary according to the theoretical foundations and subsequent approximations upon which the algorithms are based. This paper constitutes a comparative review of seven modeling methods: geometric ray theory, asymptotic ray theory, generalized ray theory, Kirchhoff wave theory, Fourier synthesis, finite differences, and finite elements.These methods can be categorized as ray or wave, acoustic or elastic, and can be contrasted according to their relative abilities to simulate such behavior as wave interference effects, diffractions, and mode conversions. As is implied by their names, geometric ray theory and asymptotic ray theory are both ray methods. The other five methods provide wave theory simulations. Geometric ray theory and Kirchhoff wave theory are normally implemented in acoustic form, while the other methods are readily adapted for computing elastic theory solutions. Generalized ray theory and Fourier synthesis are more limited in the complexity of geological model they can accommodate than are the other techniques. The methods which typically demand the greatest computer resources are the finite-difference and the finiteelement techniques. All methods can incorporate at least some multiple events. Diffractions, however, are only inherent in the solutions computed by Kirchhoff wave theory, finite differences and finite elements. Attenuation is readily incorporated in both the Fourier synthesis and the finite-element methods.As an example of the application of seismic modeling, a geological model representative of a typical petroleum exploration target is used to compare vertical seismic profiles calculated by different modeling methods.