This is the second part of a three-part tutorial series on full-waveform inversion (FWI) in which we provide a step-by-step walk through of setting up forward and adjoint wave equation solvers and an optimization framework for inversion. In Part 1 ( Louboutin et al., 2017 ), we showed how to use Devito ( http://www.opesci.org/devito-public ) to set up and solve acoustic wave equations with (impulsive) seismic sources and sample wavefields at the receiver locations to forward model shot records. Here in Part 2, we will discuss how to set up and solve adjoint wave equations with Devito and, from that, how we can calculate gradients and function values of the FWI objective function.
Full-waveform inversion, Part 2: Adjoint modeling