A Comparative Study of Three Hessian Approximations in Wave-Equation Migration

Abstract

Enhanced pre-stack depth migration, characterized by improved resolution and amplitudes, ensures a more accurate representation of the subsurface, proving essential for reducing the likelihood of geological misinterpretations and facilitating informed decision-making in seismic exploration. However, obtaining high-resolution images with preserved amplitudes through standard depth migration could face several hurdles known as migration artifacts. Iterative least-squares migration (LSM) was developed to address these migration artifacts. However, the convergence rate of LSM using a gradient descent approach tends to be slow. Several researchers have attempted to achieve computational efficiency in linearized LSM through gradient preconditioning. In the context of iterative least-squares wave-equation migration, this extended abstract compares three minimization approaches that differ in error functions and gradient preconditioning—including the depth-dependent Hessian approximation inverse—through two numerical examples, one with an inverse-crime scenario and the other with a non-inverse-crime scenario.