{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stochastic-seismic-waveform-inversion-using","title":"Stochastic seismic waveform inversion using generative adversarial networks as a geological prior","arxiv_id":"1806.03720","date":"2018-06-10","proceeding":null,"authors":["Lukas Mosser","Olivier Dubrule","Martin J. Blunt"],"abstract":"We present an application of deep generative models in the context of\npartial-differential equation (PDE) constrained inverse problems. We combine a\ngenerative adversarial network (GAN) representing an a priori model that\ncreates subsurface geological structures and their petrophysical properties,\nwith the numerical solution of the PDE governing the propagation of acoustic\nwaves within the earth's interior. We perform Bayesian inversion using an\napproximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the\nposterior given seismic observations. Gradients with respect to the model\nparameters governing the forward problem are obtained by solving the adjoint of\nthe acoustic wave equation. Gradients of the mismatch with respect to the\nlatent variables are obtained by leveraging the differentiable nature of the\ndeep neural network used to represent the generative model. 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