Elastic Wavefield Simulation Based On Wavefield Vector Decomposition And Lowrank Decomposition

The seismic methods based on elastic wave theory have been played a more and more significant role in complex hydrocarbon reservoir exploration. As one of the core technologies, seismic wavefield simulation is an improtant tool to understand the wave propagation characteristics in earth medium. Therefore, the research focused on high precision elastic wave numerical modeling method has an important theory meaning and practical value. The two key issues are how to construct a dispersion-free and low computational cost elastic wavefield extrapolation operator and how to absorb boundary reflection effectively.The elastic wave numerical modeling method proposed by this paper is an extension of the recursive integral time-extrapolation(RITE) algorithms, and the key theories are wavefield vector decomposition and lowrank decomposition. To construct a high precision extrapolation operator, the elastic wavefield is decomposed into a vector P-wave and a vector S-wave based on wavefield vector decomposition, and single P- or S-wave extrapolation operator is derivated, respectively. Lowrank decomposition is introduced to approximate the extrapolation operator so as to improve the computational efficiency. The propsed operator, includeing the compensation of error caused by numerical discretization and inhomogeneous media, can be used to simulate complex variable velocity medium, even if it is essentially a spectral method.In order to weaken the artifical boundary reflection, a kind of perfectly matched layer(PML) boundary condition, which is suitable for two-order elastic wave equations, is derivated according to the method of auxiliary differential equations(ADE). In the paper, we implement the ADE-PML for the proposed extrapolation operator and the results show that the boundary reflection can be absorbed effectively by alternately solving the two-order wave equations and ADE-PML equations.The elastic wave numerical modeling method based on wavefield vector decomposition and lowrank decomposition is an extension of the RITE algorithm from acoustic equation to elastic case. Model tests show that the proposed method can simulate the elastic wavefield in variable velocity medium accurately, efficiently and robustly.