Title: Frequency-domain full-waveform inversion with non-linear descent directions

Abstract

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. In this study, we examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss–Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s₀ is, in our scheme, proportional to at most (Δs/s₀)³ in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss–Newton FWI update is proportional to (Δs/s₀)². For numerical implementation of more complex cases, we introduce a non-linearmore » frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. Lastly, the inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.« less

Authors:

Geng, Yu ^[1]; Pan, Wenyong  ^[2];

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• Search DOE PAGES for ORCID "0000-0002-3870-5247"

Innanen, Kristopher ^[1]

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+ Show Author Affiliations

1. Univ. of Calgary, AB (Canada)
2. Los Alamos National Laboratory

Publication Date:

Tue Jan 09 00:00:00 EST 2018

Research Org.:

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1506000

Report Number(s):

LA-UR-18-20412
Journal ID: ISSN 0956-540X

Grant/Contract Number:  

89233218CNA000001

Resource Type:

Accepted Manuscript

Journal Name:

Geophysical Journal International

Additional Journal Information:

Journal Volume: 213; Journal Issue: 2; Journal ID: ISSN 0956-540X

Publisher:

Oxford University Press

Country of Publication:

United States

Language:

English

Subject:

58 GEOSCIENCES; Inverse theory; Waveform inversion; Theoretical seismology; Wave scattering and diffraction