Euclid and the art of wavelet estimation, Part I: Basic algorithm for noise‐free data

Rietsch, E.

doi:10.1190/1.1444293

Cited by 18 publications

(13 citation statements)

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“…The common wavelet for all channels is estimated using the reflectivity estimates from the previous iteration. A minimumenergy wavelet is found subject to matching the data as in the convolution model (1). In the frequency domain, the seismic trace is a product of Fourier transforms of the wavelet and reflectivity series…”

Section: Proposed Blind Deconvolution Algorithmmentioning

confidence: 99%

“…For this test, 20 traces are generated with a sampling frequency of 500 Hz using the reflectivity shown in Figure 1b, which can be downloaded from [29]. The received data 1 In equation (16) of [17] there is a typo for the k-th component of ∇L, which should be in Figure 1c is the convolution of the reflectivity with a Ricker wavelet of center frequency 40 Hz with 50 degrees of phase shift (see Figure 1a) plus additive white Gaussian noise (AWGN) of SNR = 10 dB. The SNR adopted in this work for the signal-plus-noise model, i.e., x = s + n is defined as SNR = 10 log 10 s 2…”

Section: Synthetic Data Testmentioning

confidence: 99%

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Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

et al. 2019

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In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with two steps: first, wavelet estimation across all channels and second, refinement of the reflectivity estimate simultaneously in all channels using sparse deconvolution. The reflectivity update step is formulated as a basis pursuit denoising problem and a sparse solution is obtained with the spectral projected-gradient algorithm -faithfulness to the recorded traces is constrained by the measured noise level. Wavelet re-estimation has a closed form solution when performed in the frequency domain by finding the minimum energy wavelet common to all channels. Nothing is assumed known about the wavelet apart from its time duration. In tests with both synthetic and real data, the method yields sparse reflectivity series and stable wavelet estimates results compared to existing methods with significantly less computational effort.

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Section: Proposed Blind Deconvolution Algorithmmentioning

confidence: 99%

Section: Synthetic Data Testmentioning

confidence: 99%

Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

et al. 2019

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“…In contrast, SMBD and other multichannel approaches seek to directly determine the reflectivity (Rietsch, 1997a(Rietsch, , 1997bKaaresen and Taxt, 1998;Kazemi and Sacchi, 2014). As we will see, this difference also helps to explain the reduced computational complexity of our approach.…”

Section: Introductionmentioning

confidence: 76%

“…Of particular interest to this paper are the so-called multichannel blind deconvolution methods (Wiggins, 1978;Xu et al, 1995;Inouye and Sato, 1996;Rietsch, 1997aRietsch, , 1997bKaaresen and Taxt, 1998;Ding and Li, 2001;Ram et al, 2010). The term multichannel comes from the fact that these methods are applied when we have several observations of a certain signal, and each observation goes through a different channel.…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm for sparse multichannel blind deconvolution

et al. 2016

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We have addressed blind deconvolution in a multichannel framework. Recently, a robust solution to this problem based on a Bayesian approach called sparse multichannel blind deconvolution (SMBD) was proposed in the literature with interesting results. However, its computational complexity can be high. We have proposed a fast algorithm based on the minimum entropy deconvolution, which is considerably less expensive. We designed the deconvolution filter to minimize a normalized version of the hybrid l 1 ∕l 2 -norm loss function. This is in contrast to the SMBD, in which the hybrid l 1 ∕l 2 -norm function is used as a regularization term to directly determine the deconvolved signal. Results with synthetic data determined that the performance of the obtained deconvolution filter was similar to the one obtained in a supervised framework. Similar results were also obtained in a real marine data set for both techniques.

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“…They use an equation that directly relates P component records to the corresponding SV record for a model subsurface structure. The equation is similar to the concept of multichannel deconvolution proposed in the field of geophysical exploration (Kazemi & Sacchi, 2014;Rietsch, 1997aRietsch, , 1997b. Using this equation, they invert for subsurface seismic velocity structure by performing a direct search over many models.…”

Section: Introductionmentioning

confidence: 99%

Beyond Receiver Functions: Green's Function Estimation by Transdimensional Inversion and Its Application to OBS Data

et al. 2019

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Receiver functions, calculated by deconvolving P (or vertical) component records of teleseismic waveforms from the corresponding SV (or radial) components, have been widely used to obtain receiver‐side Green's functions in an approximate form. Conventional receiver function methods, however, often fail due to numerical instability of the deconvolution and strong multiples on the P components. These problems become severe when analyzing in high frequency and using data from ocean bottom seismometers (OBSs). We present a novel technique to estimate Green's functions of receiver‐side structure from teleseismic P waveforms. In this method, two components of Green's functions, which are assumed to form a series of pulses, are directly related in a single equation without explicit deconvolution. Based on the equation, we construct posterior probability distributions regarding the number of pulses, their timing, and amplitudes within a transdimensional Bayesian framework. A reversible‐jump Markov chain Monte Carlo method is used for this purpose, and we further utilize a parallel tempering method to achieve rapid convergence. Synthetic tests and application to an OBS installed at the Yamato Basin, the Sea of Japan, show that the proposed method can estimate radial‐component Green's functions more accurately than conventional receiver function methods. We suggest that the high‐frequency Green's functions estimated by the new method can be used to reveal fine‐scale (in order ~100 m) structure of the seafloor sediment.

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Euclid and the art of wavelet estimation, Part I: Basic algorithm for noise‐free data

Cited by 18 publications

References 0 publications

Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

A fast algorithm for sparse multichannel blind deconvolution

Beyond Receiver Functions: Green's Function Estimation by Transdimensional Inversion and Its Application to OBS Data

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