Entropy 2010, 12(1), 14-33; doi:10.3390/e12010014
Article

Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model

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Received: 9 October 2009; Accepted: 11 December 2009 / Published: 28 December 2009
(This article belongs to the Special Issue Maximum Entropy)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: This paper proposes a new method for estimating seismic wavelets. Suppose a seismic wavelet can be modeled by a formula with three free parameters (scale, frequency and phase). We can transform the estimation of the wavelet into determining these three parameters. The phase of the wavelet is estimated by constant-phase rotation to the seismic signal, while the other two parameters are obtained by the Higher-order Statistics (HOS) (fourth-order cumulant) matching method. In order to derive the estimator of the Higher-order Statistics (HOS), the multivariate scale mixture of Gaussians (MSMG) model is applied to formulating the multivariate joint probability density function (PDF) of the seismic signal. By this way, we can represent HOS as a polynomial function of second-order statistics to improve the anti-noise performance and accuracy. In addition, the proposed method can work well for short time series.
Keywords: seismic wavelet; estimation; cumulant; MSMG model
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MDPI and ACS Style

Gao, J.-H.; Zhang, B. Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model. Entropy 2010, 12, 14-33.

AMA Style

Gao J-H, Zhang B. Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model. Entropy. 2010; 12(1):14-33.

Chicago/Turabian Style

Gao, Jing-Huai; Zhang, Bing. 2010. "Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model." Entropy 12, no. 1: 14-33.

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