An lp-space Matching Pursuit algorithm and its application to robust seismic data denoising via time-domain Radon transforms

Geophysics ◽  
2021 ◽  
pp. 1-90
Author(s):  
Ji Li ◽  
Mauricio D. Sacchi
Keyword(s):  
Time Domain ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Basis Functions ◽  
Inner Product ◽  
Radon Transforms ◽  
Matching Pursuit Algorithm ◽  
The Time Domain ◽  
Sparse Solutions ◽  
Linear Systems Of Equations

Sparse solutions of linear systems of equations are important in many applications of seismic data processing. These systems arise in many denoising algorithms, such as those that use Radon transforms. We propose a robust Matching Pursuit algorithm for the retrieval of sparse Radon domain coefficients. The algorithm is robust to outliers and, hence, applicable for seismic data deblending. The classical Matching Pursuit algorithm is often adopted to approximate data by a small number of basis functions. It performs effectively for data contaminated with well-behaved, typically Gaussian, random noise.On the other hand, Matching Pursuit tends to identify the wrong basis functions when erratic noise contaminates our data. Incorporating a lp space inner product into the Matching Pursuit algorithm significantly increases its robustness to erratic signals. Our work describes a Robust Matching Pursuit algorithm that includes lp space inner products. We also provide a detailed description of steps required to implement the proposed lp space Robust Matching Pursuit algorithm when the basis functions are not given in an explicit form, such as is the case with the time-domain Radon transform. Finally, we test the proposed algorithm with deblending problems. Both synthetic and field data examples show a significant denoising improvement compared to deblending via the standard Matching Pursuit algorithm.

Separating Multiple Moving Sources by Microphone Array Signals for Wayside Acoustic Fault Diagnosis

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Wei Xiong ◽  
Qingbo He ◽  
Zhike Peng
Keyword(s):  
Fault Diagnosis ◽  
Time Domain ◽  
Feature Matching ◽  
Matching Pursuit ◽  
Microphone Array ◽  
Time Frequency ◽  
Moving Sources ◽  
The Time Domain ◽  
Envelope Spectrum ◽  
Threshold Setting

Wayside acoustic defective bearing detector (ADBD) system is a potential technique in ensuring the safety of traveling vehicles. However, Doppler distortion and multiple moving sources aliasing in the acquired acoustic signals decrease the accuracy of defective bearing fault diagnosis. Currently, the method of constructing time-frequency (TF) masks for source separation was limited by an empirical threshold setting. To overcome this limitation, this study proposed a dynamic Doppler multisource separation model and constructed a time domain-separating matrix (TDSM) to realize multiple moving sources separation in the time domain. The TDSM was designed with two steps of (1) constructing separating curves and time domain remapping matrix (TDRM) and (2) remapping each element of separating curves to its corresponding time according to the TDRM. Both TDSM and TDRM were driven by geometrical and motion parameters, which would be estimated by Doppler feature matching pursuit (DFMP) algorithm. After gaining the source components from the observed signals, correlation operation was carried out to estimate source signals. Moreover, fault diagnosis could be carried out by envelope spectrum analysis. Compared with the method of constructing TF masks, the proposed strategy could avoid setting thresholds empirically. Finally, the effectiveness of the proposed technique was validated by simulation and experimental cases. Results indicated the potential of this method for improving the performance of the ADBD system.

The Shuey-Radon transform

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. V197-V206 ◽  
Author(s):  
Ali Gholami ◽  
Milad Farshad
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Real Data ◽  
Transform Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Linear System Of Equations ◽  
Matching Pursuit Algorithm ◽  
Zero Offset

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Depth-domain seismic reflectivity inversion with compressed sensing technique

2017 ◽  
Vol 5 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Rui Zhang ◽  
Kui Zhang ◽  
Jude E. Alekhue
Keyword(s):  
Compressed Sensing ◽  
Time Domain ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Depth Migration ◽  
Band Limited ◽  
The Time Domain

More and more seismic surveys produce 3D seismic images in the depth domain by using prestack depth migration methods, which can present a direct subsurface structure in the depth domain rather than in the time domain. This leads to the increasing need for applications of seismic inversion on the depth-imaged seismic data for reservoir characterization. To address this issue, we have developed a depth-domain seismic inversion method by using the compressed sensing technique with output of reflectivity and band-limited impedance without conversion to the time domain. The formulations of the seismic inversion in the depth domain are similar to time-domain methods, but they implement all the elements in depth domain, for example, a depth-domain seismic well tie. The developed method was first tested on synthetic data, showing great improvement of the resolution on inverted reflectivity. We later applied the method on a depth-migrated field data with well-log data validated, showing a great fit between them and also improved resolution on the inversion results, which demonstrates the feasibility and reliability of the proposed method on depth-domain seismic data.

Frequency‐time decomposition of seismic data using wavelet‐based methods

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1906-1916 ◽  
Author(s):  
Avijit Chakraborty ◽  
David Okaya
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Spectral Decomposition ◽  
Matching Pursuit ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Matching Pursuit Algorithm ◽  
Processing Algorithms ◽  
Short Time

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale‐translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive‐source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet‐based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

scholarly journals Matching Pursuit Algorithm for Decoding of Binary LDPC Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Jianzhong Guo ◽  
Cong Cao ◽  
Dehui Shi ◽  
Jing Chen ◽  
Shuai Zhang ◽  
...  
Keyword(s):  
Error Probability ◽  
High Efficiency ◽  
Matching Pursuit ◽  
Ldpc Codes ◽  
Inner Product ◽  
Parity Check ◽  
Decoding Algorithms ◽  
Low Density Parity Check ◽  
Matching Pursuit Algorithm ◽  
Simulation Results

This paper presents a novel hard decision decoding algorithm for low-density parity-check (LDPC) codes, in which the stand matching pursuit (MP) is adapted for error pattern recovery from syndrome over GF(2). In this algorithm, the operation of inner product can be converted into XOR and accumulation, which makes the matching pursuit work with a high efficiency. In addition, the maximum iteration is theoretically explored in relation to sparsity and error probability according to the sparse theory. To evaluate the proposed algorithm, two MP-based decoding algorithms are simulated and compared over an AWGN channel, i.e., generic MP (GMP) and syndrome MP (SMP). Simulation results show that the GMP algorithm outperforms the SMP by 0.8 dB at BER = 10 − 5 .

scholarly journals Time-Depth Curve Evaluation Method for Conversion Time to Depth at Penobscot Field, Nova-Scotia, Canada

2017 ◽  
Vol 17 (1) ◽  
pp. 25
Author(s):  
Fitri Rizqi Azizah ◽  
Puguh Hiskiawan ◽  
Sri Hartanto
Keyword(s):  
Time Domain ◽  
Seismic Data ◽  
Evaluation Method ◽  
Seismic Survey ◽  
Seismic Exploration ◽  
Reflection Seismic ◽  
Conversion Time ◽  
Well Data ◽  
The Time Domain ◽  
Depth Curve

Oil and natural gas as a fossil fuel that is essential for human civilization, and included in nonrenewable energy, making this energy source is not easy for updated availability. So that it is necessary for exploration and exploitation reliable implementation. Seismic exploration becomes the method most widely applied in the oil, in particular reflection seismic exploration. Data wells (depth domain) and seismic data (time domain) of reflection seismic survey provides information wellbore within the timescale. As for the good interpretation needed information about the state of the earth and is able to accurately describe the actual situation (scale depth). Conversion time domain into the depth domain into things that need to be done in generating qualified exploration map. Method of time-depth curve to be the method most preferred by the geophysical interpreter, in addition to a fairly short turnaround times, also do not require a large budget. Through data information check-shot consisting of the well data and seismic data, which is then exchanged plotted, forming a curve time-depth curve, has been able to produce a map domain depth fairly reliable based on the validation value obtained in the range of 54 - 176m difference compared to the time domain maps previously generated.Keywords: Energy nonrenewable, survei seismik, peta domain waktu, peta domain kedalaman, time-depth curve

Time-domain inversion of GPR data containing attenuation due to conductive losses

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. K103-K109 ◽  
Author(s):  
Qingyun Di ◽  
Meigen Zhang ◽  
Maioyue Wang
Keyword(s):  
Time Domain ◽  
Ground Penetrating Radar ◽  
Seismic Data ◽  
Random Noise ◽  
Synthetic Data ◽  
The Time Domain ◽  
Ground Penetrating ◽  
Domain Inversion ◽  
Inversion Techniques ◽  
And Inversion

Many seismic data processing and inversion techniques have been applied to ground-penetrating radar (GPR) data without including the wave field attenuation caused by conductive ground. Neglecting this attenuation often reduces inversion resolution. This paper introduces a GPR inversion technique that accounts for the effects of attenuation. The inversion is formulated in the time domain with the synthetic GPR waveforms calculated by a finite-element method (FEM). The Jacobian matrix can be computed efficiently with the same FEM forward modeling procedure. Synthetic data tests show that the inversion can generate high-resolution subsurface velocity profiles even with data containing strong random noise. The inversion can resolve small objects not readily visible in the waveforms. Further, the inversion yields a dielectric constant that can help to determine the types of material filling underground cavities.

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