Multi-Parameter True-Amplitude Generalized Radon Transform Inversion for Acoustic Transversely Isotropic Media With a Vertical Symmetry Axis

Abstract

In anisotropic media, the compressional wave scattering phenomena is governed by several parameters and can be simulated using a good kinematic approximation. How to retrieve anisotropic properties from recorded seismic data free of shear waves for exploration geophysics is interesting and challenging. We present an approach to infer the material properties in acoustic transversely isotropic (TI) media with a vertical axis of symmetry (VTI) described by a combination of the normal-moveout velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{n}$ </tex-math></inline-formula> and anisotropic parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> . The method we consider is based on the true-amplitude generalized Radon transform (GRT) inversion strategy. Because the scattering integral is at the kernel of the inversion engine, we start our investigation from a fourth-order pseudo-acoustic VTI equation instead of the conventionally coupled system of second-order wave equations. With the single-scattering approximation and high-frequency asymptotic analysis, the integral representation of P-wave scattered wavefield is incorporated into a weighted GRT operator that contains VTI scattering patterns of each parameter perturbation, which leads the way in constructing an acoustic VTI amplitude-preserving GRT pseudo-inverse operator. We describe an appropriate survey design by shooting a fan of rays from the target area toward the acquisition system, which is necessary when calculating the pseudo-inverse operator. Numerical test results from 2-D synthetic data verify the effectiveness of our method.