Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

Convergence acceleration in scattering series and seismic waveform inversion using nonlinear... Summary Iterative solution process is fundamental in seismic inversions, such as in full-waveform inversions and some inverse scattering methods. However, the convergence could be slow or even divergent depending on the initial model used in the iteration. We propose to apply Shanks transformation (ST for short) to accelerate the convergence of the iterative solution. ST is a local nonlinear transformation, which transforms a series locally into another series with an improved convergence property. ST works by separating the series into a smooth background trend called the secular term versus an oscillatory transient term. ST then accelerates the convergence of the secular term. Since the transformation is local, we do not need to know all the terms in the original series which is very important in the numerical implementation. The ST performance was tested numerically for both the forward Born series and the inverse scattering series (ISS). The ST has been shown to accelerate the convergence in several examples, including three examples of forward modeling using the Born series and two examples of velocity inversion based on a particular type of the ISS. We observe that ST is effective in accelerating the convergence and it can also achieve convergence even for a weakly divergent scattering series. As such, it provides a useful technique to invert for a large-contrast medium perturbation in seismic inversion. Shanks transform, scattering series, inversion Published by Oxford University Press on behalf of The Royal Astronomical Society 2018. This work is written by (a) US Government employee(s) and is in the public domain in the US. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

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Publisher
The Royal Astronomical Society
Copyright
Published by Oxford University Press on behalf of The Royal Astronomical Society 2018.
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggy228
Publisher site
See Article on Publisher Site

Abstract

Summary Iterative solution process is fundamental in seismic inversions, such as in full-waveform inversions and some inverse scattering methods. However, the convergence could be slow or even divergent depending on the initial model used in the iteration. We propose to apply Shanks transformation (ST for short) to accelerate the convergence of the iterative solution. ST is a local nonlinear transformation, which transforms a series locally into another series with an improved convergence property. ST works by separating the series into a smooth background trend called the secular term versus an oscillatory transient term. ST then accelerates the convergence of the secular term. Since the transformation is local, we do not need to know all the terms in the original series which is very important in the numerical implementation. The ST performance was tested numerically for both the forward Born series and the inverse scattering series (ISS). The ST has been shown to accelerate the convergence in several examples, including three examples of forward modeling using the Born series and two examples of velocity inversion based on a particular type of the ISS. We observe that ST is effective in accelerating the convergence and it can also achieve convergence even for a weakly divergent scattering series. As such, it provides a useful technique to invert for a large-contrast medium perturbation in seismic inversion. Shanks transform, scattering series, inversion Published by Oxford University Press on behalf of The Royal Astronomical Society 2018. This work is written by (a) US Government employee(s) and is in the public domain in the US.

Journal

Geophysical Journal InternationalOxford University Press

Published: Jun 7, 2018

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