Earthquake Forward Modeling Method Based on Vector Decomposition and Low-rank Decomposition of Elastic Wavefield

Abstract

The invention belongs to the field of exploration geophysics, and in particular relates to a forward modeling method for elastic seismic wave field. First, the method decomposes the elastic seismic wave field into a longitudinal wave field and a shear wave field based on the principle of wave field vector decomposition, and calculates the corresponding propagation matrices of the longitudinal and shear waves respectively. Parameter compensation, so it has high calculation accuracy; then, based on the principle of low-rank decomposition, the propagation matrix is ​​decomposed to obtain the propagation operators of the vector longitudinal wave and the vector shear wave, thereby reducing the calculation amount of numerical simulation and improving the calculation efficiency; finally, the The updated vector P-wave records and vector S-wave records obtained by numerical simulation are coupled to obtain the seismic wavefield forward modeling results. The seismic wave field record obtained by the forward modeling method constructed by the invention has almost no numerical dispersion and high numerical simulation stability, and is a high-precision elastic wave field numerical simulation method.

Description

technical field [0001] The invention belongs to the field of exploration geophysics, and in particular relates to a forward modeling method for elastic seismic wave field. Background technique [0002] The forward modeling method is an important means to study the law of seismic wave propagation in the earth medium, and it is also the theoretical basis for the technical research of seismic wave imaging method and wave equation inversion method. As far as the equations describing the earth's medium are concerned, the most commonly used methods at present mainly include the forward modeling of the acoustic wave equation and the forward modeling of the elastic wave equation. For a long time in the past, the forward modeling method based on the acoustic wave equation has been favored by the industry and academia due to its fast calculation speed and small computer memory requirements, and has played a huge role. But the actual earth medium is an elastic body, and the simple aco...

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Problems solved by technology

Among them, the finite difference method has the advantages of fast calculation speed and small memory requirements, but the numerical simulation accuracy of this algorithm is low, and it is increasingly difficult to meet the needs of the industry for high-precision numerical simulation algorithms; the finite element method can simulate any geometry Shaped earth medium model, the numerical simulation accuracy is very high, but the calculation amount of this kind of method is very large, and the numerical dispersion is relatively serious; the spectrum method calculates the differential through fast forward and reverse Fourier transform, which can be considered as A numerical method with an infinitely high-order approximation, but it is not suitable for complex variable-speed media, which limits the application range of this type of algorithm

In recent years, in the numerical simulation of acoustic waves, a spectral method of matrix low-rank decomposition has been newly developed. This method compensates the numerical differentiation related to the medium parameters and simulation parameters, which greatly improves the calculation accuracy. , and the amount of calculation is relatively moderate, but its propagation operator is not suitable for the elastic wave equation

[0004] This patent proposes an elastic wave field extrapolation operator based on elastic vector wave field decomposition and matrix low-rank decomposition. This method is an elastic wave recursive time integral wave field extrapolation algorithm, which maintains the high calculation accuracy of the traditional spectrum method. , while overcoming the problem that traditional spectral methods are not suitable for complex variable-speed media

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