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.
Highlights
In seismic exploration, a seismic trace y(n) can be often represented as the convolution of a wavelet w(n) with the reflectivity series r(n) plus a superposed noise n(n): (1)y (n ) = s (n ) + n(n ) = r (n ) ∗ w(n ) + n(n )Entropy 2010, 12 where * denotes the convolution, s(n) represents the clean signal
The reflectivity is simulated by a white process with generalized Gaussian distribution (GGD) distribution, the true and estimated parameters are shown in table 6 respectively
We have proposed a new approach based on the multivariate scale mixture of Gaussians (MSMG) model for estimating seismic wavelets
Summary
A seismic trace y(n) can be often represented as the convolution of a wavelet w(n) with the reflectivity series r(n) plus a superposed noise n(n):. One early technique, which assumes that the reflectivity sequence is a Gaussian white noise, supplies a minimum phase wavelet from the second-order statistical content of the trace signal [1,2]. A computationally efficient method is proposed for computing the HOS (fourth-order and sixth-order cumulants) based on the joint probability distribution function (PDF) of the output seismic signal, which is described by the multivariate scale mixture of Gaussians (MSMG) model. Using this PDF model, we can represent.
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