A fast, modified parabolic Radon transform

Abbad, Brahim; Ursin, Bjørn; Porsani, Milton J.

doi:10.1190/1.3532079

Cited by 29 publications

(8 citation statements)

References 27 publications

(24 reference statements)

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“…The number of rows and columns in the matrix L is nx and nq, with nx being the trace number of input data and nq being the sampling number of slowness in the Radon domain, respectively. Using the 1D forward Fourier transform f [•] and the inverse transform f −1 [•], Equation (3) can be written as [41]…”

Section: Sparse Radon Transform With the Elastic Half-norm Constraintmentioning

confidence: 99%

Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain

Ma,

Song,

et al. 2023

Applied Sciences

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Multiple reflection is a common interference wave in offshore petroleum and gas exploration, and the Radon-based filtering method is a frequently used approach for multiple removal. However, the filtering parameter setting is crucial in multiple suppression and relies heavily on the experience of processors. To reduce the dependence on human intervention, we introduce the geometric mode decomposition (GMD) and develop a novel processing flow that can automatically separate primaries and multiples, and then accomplish the suppression of multiples. GMD leverages the principle of the Wiener filtering to iteratively decompose the data into modes with varying curvature and intercept. By exploiting the differences in curvature, GMD can separate primary modes and multiple modes. Then, we propose a novel sparse Radon transform (RT) constrained with the elastic half (EH) norm. The EH norm contains a l1/2 norm and a scaled l2 norm, which is added to overcome the numerical oscillation problem of the l1/2 norm. With the help of the EH norm, the estimated Radon model can reach a remarkable level of sparsity. To solve the optimization problem of the proposed sparse RT, an efficient alternating multiplier iteration algorithm is employed. Leveraging the high sparsity of the Radon model obtained from the proposed transform, we improve the GMD-based multiple removal framework. The high-sparsity Radon model obtained from the proposed Radon transform can not only simplify the separation of primary and multiple modes but also accelerate the convergence of GMD, thus improving the processing efficiency of the GMD method. The performance of the proposed GMD-based framework in multiple elimination is validated through synthetic and field data tests.

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Section: Sparse Radon Transform With the Elastic Half-norm Constraintmentioning

confidence: 99%

Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain

Ma,

Song,

et al. 2023

Applied Sciences

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“…However, increasing the number of iterations also leads to lower computing efficiency. Abbad et al [6]. proposed a fast algorithm for solving the problem in frequency domain based on singular value decomposition technology.…”

Section: Introductionmentioning

confidence: 99%

Research Status and Progress of Multiples Suppression Based on Radon Transform

Wang¹

2023

IJE

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The existence of multiple waves in seismic data has a substantial impact on earthquake imaging, inversion, and interpretation results. As a result, multiples are often suppressed as noise prior to seismic data preattack processing. Currently, there are two primary methods for suppressing multiple reflections in seismic data. One is a filtering technique based on geometric differences in the seismic waves, while the other is based on wave equation methods. The Radon transform, which suppresses multiple reflections, belongs to the class of geometric seismic diffraction filtering techniques. In the process of seismic data processing, it effectively separates multiple reflections from seismic data by utilizing the characteristic differences between primary and multiple reflections, thereby achieving noise attenuation and improving the signal-to-noise ratio of the data. This article primarily investigates the current state of methods for suppressing multiple reflections based on the Radon transform, both domestically and internationally. By introducing various forms and fundamental principles of the Radon transform, this study analyzes and compares the adaptability and pros and cons of each type of Radon transform. The high-precision Radon transform can effectively address the sawtooth phenomenon and energy dispersion issues that arise in the least-squares Radon transform. It also highlights the challenges associated with suppressing multiple reflections in the Radon transform and provides a glimpse into future developments.

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“…(2019) iteratively updated the singular value decomposition of current spatial patches using the most recently added spatial sample, which can reduce the computational cost of classic singular spectrum analysis. Methods based on the sparse transform, like curvelet, seislet, τ – p , radon and wavelet, are also used for the denoising of microseismic data (Akram et al., 2018; Brahim et al., 2011; Forghani‐Arani et al., 2013; Jiang et al., 2012; Sabbione et al., 2013). However, these sparse transforms have the characteristics of close framework and fast numerical implementation, but they lack adaptability to capture the various sparse structures existing in seismic data.…”

Section: Introductionmentioning

confidence: 99%

A denoising method of microseismic data based on a single‐channel phase space reconstruction and independent component analysis algorithm

Meng,

Zeng,

et al. 2023

Geophysical Prospecting

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Estimating clean seismic signals from noisy single‐channel records is a hot research topic in the field of microseismic data processing. Due to the existence of strong random noise, the signal‐to‐noise ratio of such data is low, presenting a challenge for signal restoration In this paper, we propose a denoising method of microseismic data based on a single‐channel phase space reconstruction and independent component analysis algorithm. Specifically, we first apply the phase space reconstruction to transform the one‐dimensional seismic signal into a high‐dimensional phase space in which signal and noise have different trajectories. We then employ independent component analysis to the reconstructed data for noise separation. Experimental results on real microseismic data verifies that our proposed denoising method is useful for noise suppression and can enhance the signal‐to‐noise ratio of data, which can be further used for signal identification and event positioning in microseismic monitoring.This article is protected by copyright. All rights reserved

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A fast, modified parabolic Radon transform

Cited by 29 publications

References 27 publications

Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain

Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain

Research Status and Progress of Multiples Suppression Based on Radon Transform

A denoising method of microseismic data based on a single‐channel phase space reconstruction and independent component analysis algorithm

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