Seismic Full Waveform Inversion With Shot-Encoding Using an Improved L-BFGS Method

In seismic full waveform inversion (FWI), the shot-encoding technique can reduce computational costs. It randomly encodes all individual shot gathers and combines them into a super shot gather. This allows the number of wavefield simulations to be reduced. To mitigate crosstalk noise caused by interference between different shots, shot-encoded FWI requires the shot encoding to be sufficiently random. However, this may destabilize the standard limited memory BFGS (L-BFGS) algorithm and lead to instability and nonconvergence in the interactive inversion of FWI. In this article, we propose the improved L-BFSG (iL-BFGS) method, which uses the formula of the outer product of the Hessian matrix to calculate the gradient difference for the recursive L-BFSG computation. We also redesigned the workflow for shot-encoded FWI to increase the randomness within the shot encoding. We have shown that the proposed method improves the image quality of shot-encoded FWI, especially for intermediate and deep formations, accelerates the convergence of iterative inversion, and improves the ability of FWI to suppress crosstalk effects.