True-Amplitude Gaussian-Beam Migration for Acoustic Transversely Isotropic Media With a Vertical Symmetry Axis

The extension of Gaussian-beam migration (GBM) from isotropic media to anisotropic media is a straightforward process that involves adapting the existing framework to incorporate anisotropic effects. However, the true challenge for GBM lies in simultaneously performing geometric structure imaging and accurately restoring medium properties in the presence of anisotropy. In this article, we propose a novel approach for true-amplitude GBM in acoustic transversely isotropic (TI) media with a vertical axis of symmetry (VTI). The recovered parameters include the normal moveout (NMO) velocity parameter
$v_{n}$
, the anelliptic parameter
$\eta $
, and Thomsen’s parameter
$\delta $
. We employ Gaussian-beam expansions for the acoustic VTI Green’s function to represent the forward single scattering integral for a single-beam-center component of the common-offset scattered pressure wavefield. Based on this representation and estimation of the kernel of the single-scattering Hessian operator, we construct an acoustic VTI Gaussian-beam pseudoinverse operator. This operator includes a Beylkin determinant and a normal matrix integral over the local dip vectors chosen from the local slant stacks of the common-offset data. By utilizing this derived pseudoinverse operator, we can improve the accuracy of subsurface structure imaging and preserve the amplitude response information of material parameters during the acoustic VTI migration process. We apply the present approach to synthetic data examples and demonstrate its effectiveness in terms of imaging accuracy and amplitude fidelity.