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An Objective Function Based on q-Gaussian Distribution for Full-Waveform Inversion
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, EAGE 2020 Annual Conference & Exhibition Online, Dec 2020, Volume 2020, p.1 - 5
Abstract
Summary
Full-waveform inversion (FWI) is a wave-equation-based inversion method to estimate the physical parameters of the geological structures by exploiting full-information of the seismograms. However, FWI is inherently an ill-posed problem that is sensitive to noise, especially to outliers in the dataset. Usually, this technique is formulated as a least-squares optimization problem that consists of to minimize the difference between the observed and the modelled seismic data (residuals). In this approach, the least-squares solution inversion problem determines the maximum likelihood for the residuals, where all residuals are assumed to follow a Gaussian distribution. However, the distribution of residuals is seldom Gaussian for non-linear problems. In this study, we propose an alternative objective function to mitigate FWI sensitivity to noise based on the q-Gaussian probability distribution. In contrast to Gaussian distribution, the q-Gaussian distribution has long-tails, being less sensitive to outliers. Application on acoustic synthetic noisy-data illustrates the performance between our proposal and FWI based on least-squares norm L2. In addition, we compare also with robust objective functions based on Huber criterion and least-absolute-values norm L1. Numerical experiments show that FWI based on the q-Gaussian probability distribution outperforms other approaches, especially in presence of outliers.
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