Accelerating full wavefield inversion with nonstationary point-spread functions

Abstract

Method for reducing computational time in inversion of geophysical data to infer a physical property model (), especially advantageous in full wavefield inversion of seismic data. An approximate Hessian is pre-calculated by computing the product of the exact Hessian and a sampling vector composed of isolated point diffractors (), and the approximate Hessian is stored in computer hard disk or memory (). The approximate Hessian is then retrieved when needed () for computing its product with the gradient () of an objective function or other vector. Since the approximate Hessian is very sparse (diagonally dominant), its product with a vector may therefore be approximated very efficiently with good accuracy. Once the approximate Hessian is computed and stored, computing its product with a vector requires no simulator calls (wavefield propagations) at all. The pre-calculated approximate Hessian can also be reused in the subsequent steps whenever necessary.