Born Scattering Integral, Scattering Radiation Pattern, and Generalized Radon Transform Inversion in Acoustic Tilted Transversely Isotropic Media

Although the pseudoacoustic wave equation has good accuracy in characterizing anisotropic wave propagation and obtaining interpretable seismic images, a high-precision multiparameter inversion accounting for anisotropy from compressional wavefields is still confronted with challenges, even in the simple transversely isotropic (TI) case, due to the complicated relationship between anisotropic properties and pressure data. To reduce difficulty in correctly inverting surface compressional data in anisotropic media, an appropriate parameterization for inversion is necessary. For acoustic TI media with a tilted symmetry axis (TTI), we describe the pseudoacoustic TTI equations with the P-wave normal moveout velocity
$v_{n}$
and anisotropic parameters
$\eta $
and
$\delta $
, and aim to invert this parameterization by the scattering integral method. Using the perturbation theory in formulating the integral solution of the singly scattered pressure wavefield allows to acquire a scattering radiation pattern that explicitly illustrates the angular effect (including migration dip and scattering angles) of the TTI perturbation parameters, in which perturbations, whether in the wavefield or anisotropic parameters, are from the elliptical anisotropic background medium. Taking advantage of a ray-theoretical approximation to the background Green’s function, we can establish a relationship between the scattering integral and a form of TTI generalized Radon transform (GRT). As a result, we develop an acoustic TTI pseudoinverse GRT operator for estimating the corresponding perturbation parameters. Numerical tests on two simple models and a part of the BP 2007 anisotropic benchmark model verify the effectiveness of the presented acoustic TTI GRT inversion/migration method and show its evident advantages over the conventional acoustic isotropic and TI with a vertical symmetry axis (VTI) approaches.