none 10.1190/tle37010069.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 95529794 5980 2025120815060174700 10.1190 2025-12-08T20:06:06Z 2017-12-29T13:08:03Z 18 The Leading Edge 1070-485X 01 2018 01 01 2018 37 1 Mathias Louboutin 1 The University of British Columbia, Seismic Laboratory for Imaging and Modeling (SLIM). Philipp Witte 1 The University of British Columbia, Seismic Laboratory for Imaging and Modeling (SLIM). Michael Lange 2 Imperial College London. Navjot Kukreja 2 Imperial College London. Fabio Luporini 2 Imperial College London. Gerard Gorman 2 Imperial College London. Felix J. Herrmann 1 The University of British Columbia, Seismic Laboratory for Imaging and Modeling (SLIM). 3 Georgia Institute of Technology. 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. 01 2018 01 01 2018 69 72 https://creativecommons.org/licenses/by-sa/3.0/ 1 10.1190/crossmark-policy library.seg.org true 2017-12-29 10.1190/tle37010069.1 https://pubs.geoscienceworld.org/tle/article/37/1/69/525689/Full-waveform-inversion-Part-2-Adjoint-modeling https://pubs.geoscienceworld.org/seg/tle/article-pdf/37/1/69/7433275/tle37010069.1.pdf https://pubs.geoscienceworld.org/seg/tle/article-pdf/37/1/69/7433275/tle37010069.1.pdf https://pubs.geoscienceworld.org/tle/article/37/1/69/525689/full-waveform-inversion-part-2-adjoint-modeling Optimal control of systems governed by partial differential equations 1971 The Leading Edge 36 12 1033 2017 10.1190/tle36121033.1 Full-waveform inversion, part 1: Forward modeling Geophysical Journal International 167 2 495 2006 10.1111/j.1365-246X.2006.02978.x A review of the adjoint-state method for computing the gradient of a functional with geophysical applications Geophysics 49 8 1259 1984 10.1190/1.1441754 Inversion of seismic reflection data in the acoustic approximation Geophysics 74 6 WCC1 2009 10.1190/1.3238367 An overview of full-waveform inversion in exploration geophysics Geophysics 76 3 WA3 2011 10.1190/1.3554411 A stable TTI reverse time migration and its implementation