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Full waveform inversion with an auxiliary bump functional. / Bharadwaj, Pawan; Mulder, Wim; Drijkoningen, Guy.

In: Geophysical Journal International, Vol. 206, No. 2, 06.04.2016, p. 1076-1092.

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Harvard

Bharadwaj, P, Mulder, W & Drijkoningen, G 2016, 'Full waveform inversion with an auxiliary bump functional' Geophysical Journal International, vol. 206, no. 2, pp. 1076-1092. https://doi.org/10.1093/gji/ggw129

APA

Vancouver

Bharadwaj P, Mulder W, Drijkoningen G. Full waveform inversion with an auxiliary bump functional. Geophysical Journal International. 2016 Apr 6;206(2):1076-1092. https://doi.org/10.1093/gji/ggw129

Author

Bharadwaj, Pawan ; Mulder, Wim ; Drijkoningen, Guy. / Full waveform inversion with an auxiliary bump functional. In: Geophysical Journal International. 2016 ; Vol. 206, No. 2. pp. 1076-1092.

BibTeX

@article{e1cbe76e3dae4c95b9150927e914ddf9,
title = "Full waveform inversion with an auxiliary bump functional",
abstract = "Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.",
keywords = "Numerical solutions, Inverse theory, Tomography, Non-linear differential equations, Seismic tomography",
author = "Pawan Bharadwaj and Wim Mulder and Guy Drijkoningen",
year = "2016",
month = "4",
day = "6",
doi = "10.1093/gji/ggw129",
language = "English",
volume = "206",
pages = "1076--1092",
journal = "Geophysical Journal International",
issn = "0956-540X",
publisher = "Blackwell",
number = "2",

}

RIS

TY - JOUR

T1 - Full waveform inversion with an auxiliary bump functional

AU - Bharadwaj, Pawan

AU - Mulder, Wim

AU - Drijkoningen, Guy

PY - 2016/4/6

Y1 - 2016/4/6

N2 - Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.

AB - Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.

KW - Numerical solutions

KW - Inverse theory

KW - Tomography

KW - Non-linear differential equations

KW - Seismic tomography

UR - http://resolver.tudelft.nl/uuid:e1cbe76e-3dae-4c95-b915-0927e914ddf9

U2 - 10.1093/gji/ggw129

DO - 10.1093/gji/ggw129

M3 - Article

VL - 206

SP - 1076

EP - 1092

JO - Geophysical Journal International

T2 - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 2

ER -

ID: 4691302