Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

Wang, Lingling; Zhao, Qian; Gao, Jinghuai; Zhao, Xu; Fehler, Michael; Jiang, Xiudi

doi:10.1190/geo2015-0151.1

Cited by 60 publications

(27 citation statements)

References 40 publications

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“…which is discretization of 1D convolution operator [53]. We also consider a partial Toeplitz matrix by random sampling some rows to have a matrix with Ψ ∈ R n×p (n ≤ p).…”

Section: Data Generation Firstly We Describe the Data Generation Process In Detailmentioning

confidence: 99%

Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem

Li¹,

Lu²,

Xiao³

2022

IPI

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<p style='text-indent:20px;'>Sparse regression plays a very important role in statistics, machine learning, image and signal processing. In this paper, we consider a high-dimensional linear inverse problem with <inline-formula><tex-math id="M3">\begin{document}$ \ell^0 $\end{document}</tex-math></inline-formula>-<inline-formula><tex-math id="M4">\begin{document}$ \ell^2 $\end{document}</tex-math></inline-formula> penalty to stably reconstruct the sparse signals. Based on the sufficient and necessary condition of the coordinate-wise minimizers, we design a smoothing Newton method with continuation strategy on the regularization parameter. We prove the global convergence of the proposed algorithm. Several numerical examples are provided, and the comparisons with the state-of-the-art algorithms verify the effectiveness and superiority of the proposed method.</p>

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“…which is discretization of 1D convolution operator [53]. We also consider a partial Toeplitz matrix by random sampling some rows to have a matrix with Ψ ∈ R n×p (n ≤ p).…”

Section: Data Generation Firstly We Describe the Data Generation Process In Detailmentioning

confidence: 99%

Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem

Li¹,

Lu²,

Xiao³

2022

IPI

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“…The deconvolution was performed by computing the Toeplitz auto-correlation matrix of the source (Wang et al, 2016), then inverting it, adding noise, and multiplying with the crosscorrelation vector of response and source (Arushanian et al, 1983). To increase the signal-noise ratio, we stacked, for each station, all the RFs computed from the teleseismic earthquakes available for such station.…”

Section: Data and Resources)mentioning

confidence: 99%

Moho Depth of Northern Baja California, Mexico, From Teleseismic Receiver Functions

Ramirez¹,

Bataille

Vidal‐Villegas

et al. 2020

Preprint

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We estimated Moho depth from data recorded by permanent and temporary broadband seismic stations deployed in northern Baja California, Mexico using the receiver function technique. This region is composed, mainly, of two subregions of contrasting geological and topographical characteristics: The Peninsular Ranges of Baja California (PRBC), a batholith with high elevations (up to 2600 m above mean sea level); and the Mexicali Valley (MV) region, a sedimentary environment at around the mean sea level. Crustal thickness derived from the P-to-S converted phases at 29 seismic stations were analyzed in 3 profiles: two that cross the two subregions, in a ~W-E direction, and the third one that runs over the PRBC in a N-S direction. For the PRBC region, Moho depths vary from 35 to 45 km, from 33ºN to 32ºN; and from 30 to 46 km depth from 32ºN to 30.5ºN. From a profile that crosses the subregions in the WE direction; Moho depths vary from 45 to ~34 km under the PRBC; with an abrupt change of depth under the Main Gulf Escarpment, from ~32 to 30 km; and depths of 17-20 km under the MV region. Moho depths of the profile that runs, of an almost WE direction at ~31.5º N, follow the eltimetry from 0 to 2600 m: from ~30 to 40 km; and became shallower (16 km depth) as the profile reaches the Gulf of California. These results show that deeper Moho is related to higher

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“…In addition, most researchers apply L 1 regularization to implement the reflectivity inversion. For instance, [23] proposed a seismic sparse-spike deconvolution method to simultaneously recover wavelet and reflectivity, where authors imposed L 1 regularization to constrain the reflectivity.…”

Section: Introductionmentioning

confidence: 99%

“…(1.1) is only applicable to the case of known wavelet. If the wavelet is unknown, the alternating iterative inversion method is considered [7,23], because of the challenges to estimate an accurate seismic wavelet. According to the commutative law of convolution, the wavelet and reflectivity can be exchanged into the form of the forward matrix.…”

Section: Introductionmentioning

confidence: 99%

Super-Resolution Inversion of Non-Stationary Seismic Traces

Gao¹

2021

CSIAM-AM

Self Cite

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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.

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Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

Cited by 60 publications

References 40 publications

Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem

Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem

Moho Depth of Northern Baja California, Mexico, From Teleseismic Receiver Functions

Super-Resolution Inversion of Non-Stationary Seismic Traces

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