A computational method for full waveform inversion of crosswell seismic data using automatic differentiation

Abstract

Full waveform inversion (FWI) is a model-based data-fitting technique that has been widely used to estimate model parameters in Geophysics. In this work, we propose an efficient computational approach to solve the FWI of crosswell seismic data. The FWI problem is mathematically formulated as a partial differential equation (PDE)-constrained optimization problem, which is numerically solved using a gradient-based optimization method. The efficiency and accuracy of FWI are mainly determined by the three main components: forward modeling, gradient calculation and model update which usually involves the gradient-based optimization algorithm. Given the large number of iterations needed by FWI, an accurate gradient is critical for the success of FWI, as it will not only speed up the convergence but also increase the accuracy of the solution. However computing the gradient still remains a challenging task even after the adjoint PDE has been derived. Automatic differentiation (AD) tools have been proved very effective in a variety of application areas including Geoscience. In this work we investigated the feasibility of integrating TAPENADE, a powerful AD tool into FWI, so that the FWI workflow is simplified to allow us to focus on the forward modeling and the model updating. In this paper we choose the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method due to its robustness and fast convergence. Numerical experiments have been conducted to demonstrate the effectiveness, efficiency and robustness of the new computational approach for FWI.