## Plane-wave orthogonal polynomial transform

March 27, 2020 Documentation No comments

Amplitude-preserving data processing is an important and challenging topic in many scientific fields. The amplitude-variation details in seismic data are especially important because the amplitude variation is directly related with the subsurface wave impedance and fluid characteristics. We propose a novel seismic noise attenuation approach that is based on local plane-wave assumption of seismic events and the amplitude preserving capability of the orthogonal polynomial transform (OPT). The OPT is a way for representing spatially correlative seismic data as a superposition of polynomial basis functions, by which the random noise is distinguished from the useful energy by the high orthogonal polynomial coefficients. The seismic energy is the most correlative along the structural direction and thus the OPT is optimally performed in a flattened gather. We introduce in detail the flattening operator for creating the flattened dimension, where the OPT can be applied subsequently. The flattening operator is created by deriving a plane-wave trace continuation relation following the plane-wave equation. We demonstrate that both plane-wave trace continuation and OPT can well preserve the strong amplitude variation existing in seismic data. In order to obtain a robust slope estimation performance in the presence of noise, a robust slope estimation approach is introduced to substitute the traditional method. A group of synthetic, pre-stack and post-stack field seismic data are used to demonstrate the potential of the proposed framework in realistic applications.

## Time-frequency decomposition

March 18, 2020 Documentation No comments

A new paper is added to the collection of reproducible documents: Probing the subsurface karst features using time-frequency decomposition

The high-resolution mapping of karst features is of great importance to hydrocarbon discovery and recovery in the resource exploration field. However, currently, there are few effective methods specifically tailored for such mission. The 3D seismic data can reveal the existence of karsts to some extent but cannot obtain a precise characterization. I propose an effective framework for accurately probing the subsurface karst features using a well-developed time-frequency decomposition algorithm. More specifically, I introduce a frequency interval analysis approach for obtaining the best karsts detection result using an optimal frequency interval. A high resolution time-frequency transform is preferred in the proposed framework to capture the inherent frequency components hidden behind the amplitude map. Although the single frequency slice cannot provide a reliable karst depiction result, the summation over the selected frequency interval can obtain a high-resolution and high-fidelity delineation of subsurface karsts. I use a publicly available 3D field seismic dataset as an example to show the performance of the proposed method.

## Spectral decomposition using regularized non-stationary autoregression

March 11, 2020 Documentation No comments

We propose an application of spectral decomposition using regularized non-stationary autoregression (SDRNAR) to random noise attenuation. SDRNAR is a recently proposed signal-analysis method, which aims at decomposing the seismic signal into several spectral components, each of which has a smoothly variable frequency and smoothly variable amplitude. In the proposed novel denoising approach, random noise is deemed to be the residual part of decomposed spectral components because it is unpredictable. One unique property of this novel denoising approach is that the amplitude maps for different frequency components can also be obtained during the denoising process, which can be valuable for some interpretation tasks. Compared with spectral decomposition algorithm by empirical mode decomposition (EMD), SDRNAR has higher efficiency and better decomposition performance. Compared with $f$-$x$ deconvolution and mean filter, the proposed denoising approach can obtain higher signal-to-noise ratio (SNR) and preserve more useful energy. The proposed approach can only be applied to seismic profiles with relatively flat events, which becomes its main limitation. However, because it is applied trace by trace, it can preserve spatial discontinuities. We use both synthetic and field data examples to demonstrate the performance of the proposed method.

## Rank-reduction 3D seismic data denoising and reconstruction

March 11, 2020 Documentation No comments

Simultaneous seismic data denoising and reconstruction is a currently popular research subject in modern reflection seismology. Traditional rank-reduction based 3D seismic data denoising and reconstruction algorithm will cause strong residual noise in the reconstructed data and thus affect the following processing and interpretation tasks. In this paper, we propose an improved rank reduction method by modifying the truncated singular value decomposition (TSVD) formula used in the traditional method. The proposed approach can help us obtain nearly perfect reconstruction performance even in the case of low signal-to-noise ratio (SNR). The proposed algorithm is tested via one synthetic and field data examples. Considering that seismic data interpolation and denoising source packages are seldom in the public domain, we also provide a program template for the rank reduction based simultaneous denoising and reconstruction algorithm by providing an open-source Matlab package.

## Structure-oriented singular value decomposition

March 11, 2020 Documentation No comments

Singular value decomposition (SVD) can be used both globally and locally to remove random noise in order to improve the signal-to-noise ratio (SNR) of seismic data. However, they can only be applied to seismic data with simple structure such that there is only one dip component in each processing window. We introduce a novel denoising approach that utilizes a structure-oriented SVD and this approach can enhance seismic reflections with continuous slopes. We create a third dimension for a 2D seismic profile by using the plane-wave prediction operator to predict each trace from its neighbour traces and apply SVD along this dimension. The added dimension is equal to flattening the seismic reflections within a neighbouring window. The third dimension is then averaged to decrease the dimension. We use two synthetic examples with different complexities and one field data example to demonstrate the performance of the proposed structure-oriented SVD. Compared with global and local SVDs, and $f-x$ deconvolution, the structure-oriented SVD can obtain much clearer reflections and preserve more useful energy.