Accelerated Source-Encoding Full-Waveform Inversion with Additional Constraints

Abstract:

We present a flexible framework of Newton-type methods for constrained full-waveform inversion in the time domain. Our main goal is (1) to incorporate additional prior knowledge by using general constraints on the model parameters and (2) to reduce the computational costs of solving the inverse problem by tailoring source-encoding strategies to Newton-type methods.

In particular, we apply the Moreau-Yosida regularization to handle the constraints and use a continuation strategy to adjust the regularization parameter. Furthermore, we propose a semismooth Newton method with a trust-region globalization that relies on second-order adjoints to compute the Newton system with a matrix-free preconditioned conjugate gradient solver.

The costs of conventional FWI approaches scale proportionally with the number of seismic sources. Here, source-encoding strategies that trigger different sources simultaneously have been proven to be a successful tool to trade a small loss of information for huge savings of computational time to solve the inverse problem. This is particularly interesting for our setting as one iteration of Newton's methods using the full Hessian is considerably more expensive than quasi-Newton methods like L-BFGS. To this end, we discuss a sample average approximation model that is accelerated by using inexact Hessian information based on mini-batches of the samples. Furthermore, we compare its performance with stochastic descent schemes. Here, the classical stochastic gradient method is accelerated by an L-BFGS preconditioner and moreover, the stability of this stochastic preconditioner is enhanced by using the Hessian instead of only gradient information.

Numerical results are presented for problems in geophysical exploration on reservoir-scale.