Study On Seismic Wave Simulations In Orthogonally Curvilinear Coordinate System

With its advantage of high-efficiency, flexibility and high-adaptation, finite differnce method is widely used to simulate seismic wave propagation in various complex medium. This method has played an important role in the study of properties of seismic wave propagation in both exploration seismology and earthquake seismology. However, when irregularly topographic free surface exists, most of the current finite-differnce approaches can not achieve good results in implementing the free-surface boundary conditions and always involve complicated coordinate rotations and interpolations, which may not only affect the numerical accuracy of simulations, but make the forward modeling more complicated and low-efficient.At present, all finite difference methods used to synthetize seismic wave propagation in the presence of topography are limited to the coordinate system chosen. The discrete free surface conditions are not so well suited to model seismic waves when dealing with irregular surface. In this study, several efforts are made to improve the algorithm:(1) We introduced the orthogonally curvilinear grids to discretize the irregular physical domain. This coordinate system is body-conformal and much more accurate than staircased discretization to topography. Thus, corner wave scatterings and diffractions are avoided as a result;(2) Tensorial wave equations are introduced to simulate wave propagation as the control equation, which is well suited to arbitraryly curvilinear coordinate system;(3) We used selective filtering non-staggered finite difference method, which is commonly used in aeroacoustics, to solve tensorial wave equations. This algorithm is adaptive to complex heterogeneous medium and complicated interpolations are avoided which is the drawback of staggered-grid finite difference method;(4) In orthogonally curvilinear coordinate system, the free-surface boundary conditions are imposed by stress imaging method, which makes the boundary condtions simply to implement and has the similar form of that in Cartesian coordinate system;(5) An unsplit ADE-PML absorbing boundary condtion is utilized to attenuate reflected energy from artifical boundaries in curvilinear coordinate system.In the present study, orthogonally curvilinear grids, selective filtering non-staggered finite-difference method, stress imaging free-surface boundary condition as well as ADE-PML absorbing boundary condition are integrated to simulate seismic wave propagation in the presence of topographic free surface. Validations are made and results showed that the proposed algorithm can be a good alternative in modeling seimic wave in the case of arbitrary topography.Finally, simulation results are provided for hill and canyon models as well as for sine curve model to study the properties of wave propagation in topographic surface.