Coupled Time-lapse Full Waveform Inversion for Subsurface Flow Problems using Intrusive Automatic Differentiation

Abstract

We assimilate seismic waveform data to directly invert for intrinsic parameters of subsurface flow (e.g., permeability).• We adopt an intelligent automatic differentiation strategy with customized operators for high computational efficiency and scalability.

Physics constrained learning for data-driven inverse modeling from sparse observations

“…We adopt a nonlinear implicit scheme for solving the PDE system since it is unconditionally stable. We refer readers to [43] for the numerical scheme and implementation details. The nonlinear implicit step involves solving where n stands for the time step n and ∆t is the time step.…”

A General Approach to Seismic Inversion with Automatic Differentiation

“…For implicit schemes it is challenging to apply reverse-mode AD techniques since most AD frameworks only provide explicit differentiable operators. Li et al (2019) introduce the intelligent automatic differentiation method that implements AD for implicit numerical schemes. This approach could be used for augmenting ADSeismic for implicit schemes.…”

“…Both deep neural networks and PDE simulations can be viewed as a series of linear or nonlinear operators (Hughes et al, 2019). Moreover, reverse-mode automatic differentiation has been shown to be equivalent to the adjoint-state method mathematically (Li et al, 2019). This correspondence allows us to develop a flexible and general seismic inversion framework, ADSeismic, based on current deep learning frameworks such as TensorFlow (Abadi et al, 2016) and PyTorch (Paszke et al, 2019).…”

Numerical analysis of a deep learning formulation of elastic full waveform inversion with high order total variation regularization in different parameterization

“…In addition to providing a framework for inversion methods which mixes the features of FWI with the training capacity of a deep learning network, this approach also allows for efficient calculation of the derivatives of the residual through automatic differential (AD) methods (e.g., Li et al, 2019b;Sambridge et al, 2007), an engine for which is provided by the open-source machine learning library Pytorch (Paszke et al, 2017). Our recurrent neural network is designed using this library.…”