Year: 2021
Author: Jinghuai Gao, Hongling Chen, Lingling Wang, Bing Zhang
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 131–161
Abstract
In reflection seismology, the inversion of subsurface reflectivity from the observed seismic traces (super-resolution inversion) plays a crucial role in target detection. Since the seismic wavelet in reflection seismic data varies with the travel time, the
reflection seismic trace is non-stationary. In this case, a relative amplitude-preserving
super-resolution inversion has been a challenging problem. In this paper, we propose
a super-resolution inversion method for the non-stationary reflection seismic traces.
We assume that the amplitude spectrum of seismic wavelet is a smooth and unimodal
function, and the reflection coefficient is an arbitrary random sequence with sparsity.
The proposed method can obtain not only the relative amplitude-preserving reflectivity but also the seismic wavelet. In addition, as a by-product, a special $Q$ field can be
obtained.
The proposed method consists of two steps. The first step devotes to making an
approximate stabilization of non-stationary seismic traces. The key points include:
firstly, dividing non-stationary seismic traces into several stationary segments, then
extracting wavelet amplitude spectrum from each segment and calculating $Q$ value by
the wavelet amplitude spectrum between adjacent segments; secondly, using the estimated $Q$ field to compensate for the attenuation of seismic signals in sparse domain to
obtain approximate stationary seismic traces. The second step is the super-resolution
inversion of stationary seismic traces. The key points include: firstly, constructing
the objective function, where the approximation error is measured in $L_2$ space, and
adding some constraints into reflectivity and seismic wavelet to solve ill-conditioned
problems; secondly, applying a Hadamard product parametrization (HPP) to transform the non-convex problem based on the $L_p (0 < p < 1)$ constraint into a series of
convex optimization problems in $L_2$ space, where the convex optimization problems
are solved by the singular value decomposition (SVD) method and the regularization
parameters are determined by the L-curve method in the case of single-variable inversion. In this paper, the effectiveness of the proposed method is demonstrated by both
synthetic data and field data.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0115
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 131–161
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Non-stationary seismic trace reflectivity inversion super-resolution attenuation compensation $L_p$ regularization.