An efficient waveform inversion using the common mid-point gather in the wavenumber-space-time domain

Abstract

As full waveform inversion (FWI) requires large computation time, a variety of techniques have been suggested to reduce the computational burden. In this study, we use wavenumber-space-time domain modelling, which directly generates common mid-point (CMP) gathers, to implement the FWI algorithm. The modelling technique, which is suitable for laterally invariant velocity models, synthesises CMP gathers efficiently by using limited wavenumber components, and therefore allows reduced computation time for FWI. To consider the accuracy as well as the efficiency of FWI, the Gauss-Newton method using the approximate Hessian matrix is chosen in this study. Rather than using all of the wavenumber components, our FWI algorithm can be accelerated by using only a few components. The wavenumber components can be chosen through an analysis of the residual wavefields. To validate the usefulness of our method, we first use a one-dimensional (1D) velocity model. From the 1D model example, we note that our FWI algorithm can be successful if given a reliable initial velocity model and sufficient data with a long offset distance. Even though our algorithm is valid for only horizontally layered velocity models, we apply our algorithm to a two-dimensional (2D) velocity model with lateral velocity variations. Through the 2D velocity example, we confirm that our FWI can be used to estimate subsurface structures with dipping interfaces if the dips are moderate and the structures can thus be considered to be locally flat.