@Article{CSIAM-AM-2-131,
author = {Gao , JinghuaiChen , HonglingWang , Lingling and Zhang , Bing},
title = {Super-Resolution Inversion of Non-Stationary Seismic Traces},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2021},
volume = {2},
number = {1},
pages = {131--161},
abstract = {<p style="text-align: justify;">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.<br/>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 $L_p (0 &lt; p &lt; 1)$ 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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.2020-0115},
url = {http://global-sci.org/intro/article_detail/csiam-am/18657.html}
}