ARTICLE

Simple and fast gradient-based impedance inversion using total variation regularization

DANIEL O. PÉREZ1,2 DANILO R. VELIS1
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1 Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, and CONICET; Argentina,
2 YPF Tecnología S.A., Av. Del Petroleo s/n, Berisso, Argentina,
JSE 2018, 27(5), 473–486;
Submitted: 24 October 2017 | Accepted: 20 July 2018 | Published: 1 October 2018
© 2018 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Pérez D.O. and Velis D.R., 2018. Simple and fast gradient-based impedance inversion using total variation regularization. Journal of Seismis Exploration, 27: 473-486. We present an algorithm to estimate blocky images of the subsurface acoustic impedance (AI) from poststack seismic data. We regularize the resulting inverse problem, which is inherently ill-posed and non-unique, by means of the total variation semi-norm (TV). This allows us promote stable and blocky solutions which are, by virtue of the capability of TV to handle edges properly, adequate to model layered earth models with sharp contrasts. The use of the TV leads to a convex objective function easily minimized using a gradient-based algorithm that requires, in contrast to other AI inversion methods based on TV regularization, simple matrix-vector multiplications and no direct matrix inversion. The latter makes the algorithm numerically stable, easy to apply, and economic in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional 1p- or ll-norm regularized solutions is able to provide blocky AI images that preserve the subsurface layered structure with good lateral continuity from noisy observations.

Keywords
acoustic impedance
inversion
poststack
total variation
blocky
FISTA
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing