Seismic modeling by Gaussian beams in the global Cartesian coordinate system
Bai Min1, Wu Juan1, Sun Zhangqing2, Yang Lei3
1. School of Resources and Environment, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450046, China; 2. College of Geoexploration Science and Technology, Jilin University, Changchun, Jilin 130026, China; 3. Yellow River Institute of Hydraulic Research, Yellow River Conservancy Commission, Zhengzhou, Henan 450003, China
Abstract：For the Gaussian beam in the ray-centered coordinate system, the coordinate transformation is needed for solving wave-field values at every point in the underground.To this end, Leung et al proposed a mathematical theory method to solve Gaussian beam in a global Cartesian coordinate system using the ansatz theory, which can be understood as deriving the traveling time along the central ray and adding an imaginary part as two-order Taylor expansion of central ray in its neighborhood, to construct an approximate travel time function.The approximate travel time function of conventional Gaussian beam can be obtained from the new approximate travel time function with a local ray-centered coordinate transformation.For the first time, the mathematical theory of Gaussian beam in the global Cartesian coordinate system is applied to seismic wave propagation.One Gaussian beam, Green's function, the single-frequency wave-field of continuous medium and wave-field of complex medium are simulated respectively.And the accuracy of Gaussian beam in the ray-center coordinate system and the global Cartesian coordinate system are compared.Results show that Green's function calculated by Gaussian beams in both of the coordinate systems approximates the analytic Green's function in a homogeneous medium.For continuous medium, Gaussian beam in the global Cartesian coordinate system can handle caustics problem and simulate wavefield propagation of complex media, but the accuracy will be reduced and the lateral energy is weak.
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Bai Min, Wu Juan, Sun Zhangqing, Yang Lei. Seismic modeling by Gaussian beams in the global Cartesian coordinate system. Oil Geophysical Prospecting, 2018, 53(2): 257-265.
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