Inversion of P-wave VSP data for local anisotropy: Theory and case study

Abstract

We discuss, improve, and apply the slowness-polarization method for estimating local anisotropy from VSP data. Although the idea of fitting a given anisotropic model to the apparent slownesses measured along a well and polarization vectors recorded by three-component downhole geophones is hardly new, we extend the area of applicability of the technique and make the anisotropic inversion more robust by eliminating the most operationally difficult and noisy portion of the data, the shear waves. We show that the shear-wave velocity is actually unnecessary for fitting the slowness-of-polarization dependence of P-wave VSP data. For the most common geometry of a vertical borehole in a vertically transversely isotropic subsurface, such data are governed by the P-wave vertical velocity [Formula: see text] and two quantities, [Formula: see text] and [Formula: see text], that describe the influence of anisotropy. These quantities depend on conventional anisotropic coefficients [Formula: see text] and [Formula: see text] and absorb the S-wave velocity. We apply the developed theory to a 2D walkaway VSP acquired over a subsalt prospect in the Gulf of Mexico. Our data set contains geophones placed both inside the salt and beneath it, allowing us to estimate the anisotropy of different rock formations. We find the salt to be nearly isotropic in the examined [Formula: see text] [Formula: see text] depth interval. In contrast, the sediments below the salt exhibit substantial anisotropy. While the physical origins of subsalt anisotropy are still to be fully understood, we observe a clear correlation between lithology and the values of [Formula: see text] and [Formula: see text]: both anisotropic coefficients are greater in shales and smaller in the sandier portion of the well.