Parallel reformulation of the sequential adjoint-state method

This abstract is about reducing the total computation time to solve full-waveform inversion problems. A common problem formulation is a nonlinear least-squares problem where the gradient is computed using the adjoint-state algorithm. This formulation offers parallelism for the computation of gradients for different sources and frequencies. The adjoint-state algorithm itself is sequential however and this is a limiting factor when a lot of compute nodes are available and only a few wavefields need to be computed. This situation occurs when stochastic optimization strategies are used to minimize the objective function. We present a parallel reformulation of the sequential adjoint-state algorithm, which allows the forward- and adjoint wavefields to be computed in parallel. Both algorithms are mathematically equivalent but the parallel version is twice as fast in run time. An important characteristic of the proposed algorithm is that one wavefield needs to be computed per source and one per receiver. These fields can be used to apply the (inverse) Gauss-Newton Hessian to a vector without recomputing wavefields. A 2D example shows that good full-waveform inversion results are obtained, even when a small number of sources and receivers is used.

https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/peters2...