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Least‐squares reverse‐time migration in a matrix‐based formulation
Author(s) -
Yao Gang,
Jakubowicz Helmut
Publication year - 2016
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12305
Subject(s) - seismic migration , deconvolution , least squares function approximation , inversion (geology) , algorithm , inverse problem , wavelet , computer science , iterative method , geophysical imaging , mathematical optimization , mathematics , geology , mathematical analysis , geophysics , computer vision , statistics , estimator , paleontology , structural basin
This paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful.