Abstract
Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records. Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem. The derivation of a Laplace mixed-domain formula of the Robinson convolution is the first step in our work. With this formula, the Laplace seismic spectrum, the wavelet spectrum and time-domain reflectivity are joined together. Next, to improve inversion stability, the object inversion function accompanied by the initial constraint of the linear increment model is launched under a Bayesian framework. The likelihood function and prior probability distribution can be combined together by Bayesian formula to calculate the posterior probability distribution of subsurface parameters. By achieving the optimal solution corresponding to maximum posterior probability distribution, the low-frequency background of subsurface parameters can be obtained successfully. Then, with the regularization constraint of estimated low frequency in the Laplace mixed domains, multi-scale Bayesian inversion in the pure frequency domain is exploited to obtain the absolute model parameters. The effectiveness, anti-noise capability and lateral continuity of Laplace mixed-domain inversion are illustrated by synthetic tests. Furthermore, one field case in the east of China is discussed carefully with different input frequency components and different inversion algorithms. This provides adequate proof to illustrate the reliability improvement in low-frequency estimation and resolution enhancement of subsurface parameters, in comparison with conventional Bayesian inversion in the frequency domain.
Highlights
There are many ill-conditioned geophysical inversion problems in geophysical prospecting due to the absence of sufficient field data
Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records
Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem
Summary
There are many ill-conditioned geophysical inversion problems in geophysical prospecting due to the absence of sufficient field data. Based on the previous research in low-frequency inversion, we propose a novel Bayesian impedance inversion method in the Laplace mixed domains, which is not dependent on the precision of the initial model. To discuss the inverse problem more clearly, Eq (4) is simplified and a constant angular frequency xj is assumed, so the discrete matrix equation of Eq (4) can be given as, Yxj 1⁄4 Wxj Á C Á Exj Á m ð5Þ where Wxj , C and Exj are the Laplace spectrum of wavelets, damping matrix of subsurface reflectivity corresponding to each sample and Fourier forwarding matrix, respectively. For the resolution enhancement and convergence precision of seismic inversion, the multi-scale inversion strategy with multicomponent successive iterations in the pure frequency domain is utilized to obtain the final subsurface parameters after low-frequency estimation in the Laplace mixed domains
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