p‐ and SV‐wave transversely isotropic phase velocities analysis from VSP data

Abstract

The purpose of this paper is to obtain some measurements of the seismic anisotropy from VSP data independently of the complexity of the medium between source and receiver locations. The anisotropy at receiver locations is studied by analysing P‐and SV‐wave phase velocities as well as polarization directions under the hypothesis of a transversely isotropic (TI) medium with a vertical axis of symmetry. Multiple‐source offset VSPs provide generally direct P‐ and SV‐waves for different incident angles. In this study, the data pairs used are the interval apparent vertical velocities and the polarization directions related to both P‐ and SV‐waves. These directions are given, in the vertical plane, by the angle γ from the vertical axis. Apparent vertical velocities are computed from the delays for a constant phase which travels in the interval between two receivers. This interval has to be smaller than the seismic wavelength in order to consider these velocities as P‐ and SV‐wave phase velocities. The forward problem is defined by the exact equations of P‐ and SV‐wave velocities as a function of four parameters (α, β, η, τ) and of the polarization angle γ. Parameters α and β are tied to the P‐ and SV‐wave vertical velocities, and parameters η and τ explain phase velocity variations with incidence. With this model, these four parameters can be inverted by a least‐squares method. This method has been applied to the Pierre Shale data (White, Martineau‐Nicoletis & Monash 1983). Inverted parameters have been compared with results obtained by White et al. (1983). The parameter η (which explains velocity variations for small incidences) is accurately recovered because data (in particular phase velocities) are reliable at incident angles lower than 45d̀. The parameter τ (which explains velocity variations for high incidence) is less accurately recovered because there are not enough reliable data for incident angles higher than 45d̀. The lack of data (only 8 P shots and 8 S shots) and uncertainties in data provide a large a posteriori error in inverted parameters. However, it is hoped that this method can provide accurate recovery of anisotropy parameters if there is a large number of shot locations (case of a walkaway). Copyright © 1991, Wiley Blackwell. All rights reserved