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http://dx.doi.org/10.7582/GGE.2019.22.4.195

Laplace-domain Waveform Inversion using the Pseudo-Hessian of the Logarithmic Objective Function and the Levenberg-Marquardt Algorithm  

Ha, Wansoo (Department of Energy Resources Engineering, Pukyong National University)
Publication Information
Geophysics and Geophysical Exploration / v.22, no.4, 2019 , pp. 195-201 More about this Journal
Abstract
The logarithmic objective function used in waveform inversion minimizes the logarithmic differences between the observed and modeled data. Laplace-domain waveform inversions usually adopt the logarithmic objective function and the diagonal elements of the pseudo-Hessian for optimization. In this case, we apply the Levenberg-Marquardt algorithm to prevent the diagonal elements of the pseudo-Hessian from being zero or near-zero values. In this study, we analyzed the diagonal elements of the pseudo-Hessian of the logarithmic objective function and showed that there is no zero or near-zero value in the diagonal elements of the pseudo-Hessian for acoustic waveform inversion in the Laplace domain. Accordingly, we do not need to apply the Levenberg-Marquardt algorithm when we regularize the gradient direction using the pseudo-Hessian of the logarithmic objective function. Numerical examples using synthetic and field datasets demonstrate that we can obtain inversion results without applying the Levenberg-Marquardt method.
Keywords
Laplace-domain waveform inversion; logarithmic objective function; pseudo-Hessian; Levenberg-Marquardt method;
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