Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

Full waveform inversion (FWI) is one of the most challenging procedures to obtain quantitative information of the subsurface. For elastic inversions, when both compressional and shear velocities have to be inverted, the algorithmic issue becomes also a computational challenge due to the high cost related to modelling elastic rather than acoustic waves. This shortcoming has been moderately mitigated by using high-performance computing to accelerate 3D elastic FWI kernels. Nevertheless, there is room in the FWI workflows for obtaining large speedups at the cost of proper grid pre-processing and data decimation techniques. In the present work, we show how by making full use of frequency-adapted grids, composite shot lists and a novel dynamic offset control strategy, we can reduce by several orders of magnitude the compute time while improving the convergence of the method in the studied cases, regardless of the forward and adjoint compute kernels used.The authors thank REPSOL for the permission to publish the present research and for funding through the AURORA project. J. Kormann also thankfully acknowledges the computer resources, technical expertise and assistance provided by the Barcelona Supercomputing Center - Centro Nacional de Supercomputacti ´on together with the Spanish Supercomputing Network (RES) through grant FI-2014-2-0009. This project has received funding from the European Union’s Horizon 2020, research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 644202. The research leading to these results has received funding from the European Union’s Horizon 2020 Programme (2014–2020) and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP) under the HPC4E Project (www.hpc4e.eu), grant agreement no. 689772.We further want to thank the Editor Clint N. Dawson for his help, and Andreas Fichtner and an anonymous reviewer for their comments and suggestions to improve the manuscript.Peer ReviewedPostprint (published version

A penalty method for PDE-constrained optimization in inverse problems

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand-sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the paramaters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the non-linearity of the problem and is less sensitive the initial iterate

Bringing modern mathematical modeling to orientation imaging for material science

The vast majority of metallic and ceramic objects have a granular microstructure, which has a direct influence on their mechanical behaviour. Understanding the microstructure of these materials is especially important for nuclear reactors and other safety-critical applications in which they are used. Modern mathematical tools and recent developments in computed tomography can be used to study the evolution of these materials when they are being deformed or heated

Frugal full-waveform inversion: From theory to a practical algorithm

As conventional oil and gas fields are maturing, our profession is challenged to come up with the next-generation of more and more sophisticated exploration tools. In exploration seismology this trend has let to the emergence of wave-equation-based inversion technologies such as reverse time migration and full-waveform inversion. While significant progress has been made in wave-equation-based inversion, major challenges remain in the development of robust and computationally feasible workflows that give reliable results in geophysically challenging areas that may include ultralow shear-velocity zones or high-velocity salt. Moreover, subsalt production carries risks that need mitigation, which raises the bar from creating subsalt images to inverting for subsalt overpressure

Computational and numerical aspects of full waveform seismic inversion

Full-waveform inversion (FWI) is a nonlinear optimisation procedure, seeking to match synthetically-generated seismograms with those observed in field data by iteratively updating a model of the subsurface seismic parameters, typically compressional wave (P-wave) velocity. Advances in high-performance computing have made FWI of 3-dimensional models feasible, but the low sensitivity of the objective function to deeper, low-wavenumber components of velocity makes these difficult to recover using FWI relative to more traditional, less automated, techniques. While the use of inadequate physics during the synthetic modelling stage is a contributing factor, I propose that this weakness is substantially one of ill-conditioning, and that efforts to remedy it should focus on the development of both more efficient seismic modelling techniques, and more sophisticated preconditioners for the optimisation iterations. I demonstrate that the problem of poor low-wavenumber velocity recovery can be reproduced in an analogous one-dimensional inversion problem, and that in this case it can be remedied by making full use of the available curvature information, in the form of the Hessian matrix. In two or three dimensions, this curvature information is prohibitively expensive to obtain and store as part of an inversion procedure. I obtain the complete Hessian matrices for a realistically-sized, two-dimensional, towed-streamer inversion problem at several stages during the inversion and link properties of these matrices to the behaviour of the inversion. Based on these observations, I propose a method for approximating the action of the Hessian and suggest it as a path forward for more sophisticated preconditioning of the inversion process.Open Acces