Anisotropic ray-Born migration/inversion: A synthetic modeling study

David W. S. Eaton, Robert R. Stewart

A least-squares migration/inversion technique is used to investigate the resolution of isotropic and anisotropic parameters for a transversely isotropic earth model. The method is based on the elastic ray-Born approximation, which linearizes the forward modeling problem using far-field, high-frequency and small-perturbation assumptions. Approximate background ray-Green's tensors comprise the kernel of the scattering integral, and are computed using a finite-difference approach. Least-squares inversion is implemented using an iterative three-step conditioned-gradient procedure. The first step for each iteration resembles prestack Kirchhoff depth migration of the current data residual, yielding a gradient subimage for each model parameter. An approximate Hessian operator is then applied to partially deconvolve parameter coupling effects, producing a set of model-perturbation images. Finally, a predicted forward model is computed by scattering from the current set of model perturbations. This scheme attempts to recover short-wavelength parameter variations relative to the reference model, rather than its slowly varying components.

The resolution of P- and S-wave velocities, density and Thomsen's anisotropy parameters is investigated for the case of a homogeneous, isotropic background model, using both surface and crosswell acquisition geometries. A third example, involving an anticline structure, composed of anisotropic, inhomogeneous layers is used to demonstrate the feasibility of these techniques for seismic imaging in structurally complex areas. Finally, a ray-traced (non-Born) dataset illustrates that superior resolution of subsurface features (in particular, slope discontinuities) can be achieved by migrating all elastic wave types simultaneously.