Journal ArticleDOI
Which data residual norm for robust elastic frequency-domain full waveform inversion?
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In this paper, the performance of different minimization functionals such as the least squares norm 2, the least absolute values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to two offshore and onshore Valhallmodelandonshore overthrust model synthetic data sets were investigated in 2D elastic frequency-domain fullwaveform inversion FWI.Abstract:
Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model,definitionofmultiparameterclasses,andinaccuratemodeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm 2, the least-absolute-values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to twonoisyoffshoreValhallmodelandonshoreoverthrustmodel synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion FWI, where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the 1-norm provided the most reliable models for P- and S-wave velocities VP and VS, even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data. The 2-norm can provide reliable results in the presence of uniform white noise for VP and VS if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency. The 1-norm and the Huber and hybrid criteria, unlike the 2-norm, allowforsuccessfulimagingoftheVSmodelfromnoisydataina soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The 1-norm provides a robust alternativetothe2-normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency-domainFWI.read more
Citations
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Book
Full Seismic Waveform Modelling and Inversion
TL;DR: In this article, the authors proposed a numerical solution of the Elastic Wave Equation and computing sensitivity kernel for full waveform tomography for upper-mantle structure in Australasian Region.
Journal ArticleDOI
Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion
TL;DR: In this study, a measure of the misfit computed with an optimal transport distance allows to account for the lateral coherency of events within the seismograms, instead of considering each seismic trace independently, as is done generally in full waveform inversion.
Journal ArticleDOI
Multiscale full waveform inversion
Andreas Fichtner,Jeannot Trampert,Paul Cupillard,Erdinc Saygin,Tuncay Taymaz,Yann Capdeville,Antonio Villaseñor +6 more
TL;DR: In this article, a multigrid approach based on the decomposition of a multiscale earth model with widely varying grid spacings into a family of single-scale models where the grid spacing is approximately uniform.
Journal ArticleDOI
Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field. Part 1: imaging compressional wave speed, density and attenuation
TL;DR: In this article, the authors assess frequency-domain visco-acoustic FWI to reconstruct the compressive velocity (VP), the density (ρ) or the impedance (IP) and the quality factor (QP), from the hydrophone component, using a synthetic data set that is representative of the Valhall oil field in the North Sea.
Journal ArticleDOI
Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
TL;DR: In this paper, the quadratic Wasserstein metric is used to measure amplitude differences and global phase shifts, which helps to avoid cycle-skipping issues in full waveform inversion.
References
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TL;DR: In this paper, the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation, which is based on the generalized least squares criterion, and it can handle errors in the data set and a priori information on the model.
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TL;DR: In this paper, the least-squares (l 2 -norm) and the Minimax (l #-norm) Criterion are introduced. But they do not cover the general discrete inverse problem.
Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
TL;DR: In this article, a general definition of the nonlinear least squares inverse problem is given, where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations).
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