• Geophysics and Geophysical Exploration
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• v.22 no.4
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• pp.195-201
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• 2019

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.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1096-1099
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• 2000

A method to analyze the high speed inter-connects that are composed of frequency dependent lossy distributed lines is presented. Network modeling of hybrid systems is implemented by using the modified nodal admittance matrix in the Laplace transformation domain. The network response is computed by different two methods. One method Is the asymptotic waveform evaluation (AWE) method and other is numerical Laplace inversion method. The merits and demerits of two methods are discussed by applying to several concrete illustrative networks.