Staggered-Grid Finite Difference Method with Variable-Order Accuracy for Porous Media

The numerical modeling of wave field in porous media generally requires more computation time than that of acoustic or elastic media. Usually used finite difference methods adopt finite difference operators with fixed-order accuracy to calculate space derivatives for a heterogeneous medium. A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. In this paper, we develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD) method. High-order finite difference operators are adopted for low-velocity regions, and low-order finite difference operators are adopted for high-velocity regions. Dispersion analysis and modeling results demonstrate that the proposed SFD method can decrease computational costs without reducing accuracy

A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical tests are presented to illustrate the effectiveness and stability of our proposed method

Automatic events extraction in pre-stack seismic data based on edge detection in slant-stacked peak amplitude profiles

Events picking is one of the fundamental tasks in interpreting seismic data. To extract the correct travel-time of reflected waves, picking events in a wide range of source-receiver offsets is needed. Compared to post-stack seismic data, pre-stack seismic data has an accurate horizon and abundant travel-time, amplitude, and frequency while the waveform of post-stack data is damaged by normal move-out (NMO) applications. In this paper, we focus on automatic event extraction from pre-stack reflection seismic data. With the deep development of oil-gas exploration, the difficulty of petroleum exploration is being increased. Auto recognition and picking of seismic horizon is presented as the basis for oil-gas detection. There is a correspondence between the real geology horizon and events of seismic profiles. As a result, firstly, recognizing and tracing continuous events from real seismic records are needed to acquire significant horizon locations. Picking events is in this context the recognition and tracing of waves reflected from the same interfaces according to kinematics and dynamic characteristics of seismic waves. Current extraction algorithms are well able to trace these events of the seismic profile and are undergoing great development and utilization. In this paper, a method is proposed to pick travel-time and local continuous events based on edges obtained by slant-stacked peak amplitude section (SSPA). How to calculate the SSPA section is discussed in detail. The new method can improve the efficiency and accuracy without windowing and manual picking of seed points. The event curves obtained from both the synthetic layered model and field record have validated the high accuracy and efficiency of the proposed methodology

Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

We have developed a new sparse-spike deconvolution (SSD) method based on Toeplitz-sparse matrix factorization (TSMF), a bilinear decomposition of a matrix into the product of a Toeplitz matrix and a sparse matrix, to address the problems of lateral continuity, effects of noise, and wavelet estimation error in SSD. Assuming the convolution model, a constant source wavelet, and the sparse reflectivity, a seismic profile can be considered as a matrix that is the product of a Toeplitz wavelet matrix and a sparse reflectivity matrix. Thus, we have developed an algorithm of TSMF to simultaneously deconvolve the seismic matrix into a wavelet matrix and a reflectivity matrix by alternatively solving two inversion subproblems related to the Toeplitz wavelet matrix and sparse reflectivity matrix, respectively. Because the seismic wavelet is usually compact and smooth, the fused Lasso was used to constrain the elements in the Toeplitz wavelet matrix. Moreover, due to the limitations of computer memory, large seismic data sets were divided into blocks, and the average of the source wavelets deconvolved from these blocks via TSMF-based SSD was used as the final estimation of the source wavelet for all blocks to deconvolve the reflectivity; thus, the lateral continuity of the seismic data can be maintained. The advantages of the proposed deconvolution method include using multiple traces to reduce the effect of random noise, tolerance to errors in the initial wavelet estimation, and the ability to preserve the complex structure of the seismic data without using any lateral constraints. Our tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the wavelet and reflectivity simultaneously from band-limited data with appropriate lateral coherence, even when the seismic data are contaminated by noise and the initial wavelet estimation is inaccurate

Cognitive seismic data modelling based successive differential evolution algorithm for effective exploration of oil-gas reservoirs

A cognitive modelling based new inversion method, the successive differential evolution (DE-S) algorithm, is proposed to estimate the Q factor and velocity from the zero-offset vertical seismic profile (VSP) record for oil-gas reservoir exploration. The DE algorithm seeks optimal solutions by simulating the natural species evolution processes and makes the individuals become optimal. This algorithm is suitable for the high-dimensional nonseparable model space where the inversion leads to recognition and prediction of hydrocarbon reservoirs. The viscoelastic medium is split into layers whose thicknesses equal to the space between two successive VSP geophones, and the estimated parameters of each layer span the related subspace. All estimated parameters span to a high dimensional nonseparable model space. We develop bottom-up workflow, in which the Q factor and the velocity are estimated using the DE algorithm layer by layer. In order to improve the inversion precision, the crossover strategy is discarded and we derive the weighted mutation strategy. Additionally, two kinds of stopping criteria for effective iteration are proposed to speed up the computation. The new method has fast speed, good convergence and is no longer dependent on the initial values of model parameters. Experimental results on both synthetic and real zero-offset VSP data indicate that this method is noise robust and has great potential to derive reliable seismic attenuation and velocity, which is an important diagnostic tool for reservoir characterization