3D acoustic frequency-domain full-waveform inversion

We present one of the first attempt at implementing a massively parallel frequency-domain full-waveform inversion algorithm for imaging 3D acoustic media. The inverse method is based on a classic steepest-descent algorithm. The algorithm was designed so that one or several frequencies are inverted at a time. Wave propagation modeling, a key component of the inversion algorithm, is performed with a finite-difference frequency-domain method which requires 4 grid points per wavelength. Frequency-domain methods for wave propagation modeling requires to solve a huge sparse system of linear equations whose solutions are the computed wavefields and right-hand side (RHS) terms are the sources. We solve this system with a massively parallel direct solver in order to compute efficiently multiple-source solutions. The massively parallel direct solver leaves the multiple solutions distributed over the processors. We take advantage of this distributed storage to compute in parallel the gradient of the cost function in the inversion. The algorithm was validated with preliminary synthetic examples of limited dimensions.