Wavelet estimation and deconvolution of seismic data through phase retrieval method

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Vafaei Shoushtari Sepideh; GHOLAMI ALI

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Journal: JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS Year:2020 | Volume:5 | Issue:2 Page(s): 193-205

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Title

Wavelet estimation and deconvolution of seismic data through phase retrieval method

Author(s)

Vafaei Shoushtari Sepideh | GHOLAMI ALI | Issue Writer Certificate

Keywords

Phase Retrieval

Blind Deconvolution

Seismic Wavelet

Complex Phase

Fourier Amplitude Spectrum

Impulse Response

Wavelet Estimation

Abstract

Summary Seismic data can present a remarkably good image of the subsurface, and therefore, seismic methods have found considerable attention in oil and gas exploration industry. Wavelet or source deconvolution is one of the most important procedures in seismic processing used to increase the time resolution of the seismic sections while requires a reliable wavelet. The accuracy of the wavelet depends severely on the complexity of the wavelet phase. In this paper, through a smooth estimation of the wavelet amplitude spectrum, we go for obtaining the Impulse Response of the earth via a Phase Retrieval algorithm. Despite the conventional deconvolution methods, here just the Fourier Amplitude Spectrum information of the data is inverted as a Phase Retrieval problem. In the next step, deconvolution of the recorded Impulse Response from the data leads to a better estimation of the wavelet with any desired phase spectrum. Therefore, the presented algorithm is considered as a ''Blind Deconvolution'' method. Introduction In statistical seismic deconvolution, the wavelet is estimated from the data; however, it is easier to estimate its amplitude spectrum, and the phase is usually missed or is very inaccurate. This makes deconvolution of mixed-phase wavelets more problematic. It has still remained a challenge among geophysicists to estimate a reasonable Seismic Wavelet from the data to perform deconvolution efficiently. In this paper, as it is going to be illustrated, the proposed Phase Retrieval algorithm can be used for deconvolution of mixed-phase wavelets. Methodology and Approaches A reflection seismogram, after some specified processing steps, can be regarded as a convolution of the source wavelet with the reflectivity series and some additive noise. For obtaining the reflectivity series describing the earth, an appropriate wavelet is needed for deconvolution. The reflectivity model is obtained only by the amplitude spectrum of the observed data, looking for a solution whose predicted amplitude spectrum matches the observations of amplitude spectrum, up to a constant considered for errors in the data. Actually, it refers to an amplitude-only inversion problem, which reconstructs the Fourier phase of a signal from the Fourier amplitude. Obtaining the reflectivity model through the Phase Retrieval algorithm is an ill-posed inverse problem and has to be solved through regularization method. The problem is solved for a reflectivity series based on the fast iterative shrinkage/thresholding algorithm (FISTA) allowing extra constraints while preserving the computational simplicity. In multichannel deconvolution for improving temporal sparsity while preserving the lateral continuity of the estimation, we define a combined regularization function based on sparsity and second-order total variation. Split Bregman algorithm is used to solve the corresponding proximity function. Then, a wavelet with any desired phase spectrum is estimated using the obtained reflectivity. Results and Conclusions In this paper, we proposed a deconvolution algorithm which just needed a smooth approximation of the source wavelet amplitude spectrum. The desired performance of the proposed Phase Retrieval method on the numerical and field seismic examples confirmed its efficiency by enhancing the resolution of the seismic section and obtaining the accurate reflectivity model. The approach for solving deconvolution discussed here had no limitations for the phase of the extracted wavelet and could obtain wavelets having complex structures with an acceptable accuracy.

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APA: Copy

Vafaei Shoushtari, Sepideh, & GHOLAMI, ALI. (2020). Wavelet estimation and deconvolution of seismic data through phase retrieval method. JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS, 5(2 ), 193-205. SID. https://sid.ir/paper/268618/en

Vancouver: Copy

Vafaei Shoushtari Sepideh, GHOLAMI ALI. Wavelet estimation and deconvolution of seismic data through phase retrieval method. JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS[Internet]. 2020;5(2 ):193-205. Available from: https://sid.ir/paper/268618/en

IEEE: Copy

Sepideh Vafaei Shoushtari, and ALI GHOLAMI, “Wavelet estimation and deconvolution of seismic data through phase retrieval method,” JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS, vol. 5, no. 2 , pp. 193–205, 2020, [Online]. Available: https://sid.ir/paper/268618/en

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