A discontinuous Galerkin method for P-wave modeling in tilted TI media
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Earth Fluid Modeling and Prediction Group
Earth Science and Engineering Program
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AbstractThe acoustic approximation is an efficient alternative to the equations of elastodynamics for modeling Pwave propagation in weakly anisotropic media. We present a stable discontinuous Galerkin (DG) method for solving the acoustic approximation in tilted TI media (acoustic TI approximation). The acoustic TI approximation is considered as a modification of the equations of elastodynamics from which a modified energy is derived. The modified energy is obtained by eliminating the shear stress in the coordinates determined by the tilt angle and finding an energy for the remaining unknowns. This construction is valid if the medium is not elliptically anisotropic, a requirement frequently found in the literature. In the fully discrete setting, the modified energy is also conserved in time the presence of sharp contrasts in material parameters. By construction, the scheme can be coupled to the (fully) acoustic wave equation in the same way as the equations of elastodynamics. Hence, the number of unknowns can be reduced in acoustic regions. Our numerical examples confirm the conservation of energy in the discrete setting and the stability of the scheme.
Conference/Event name76th European Association of Geoscientists and Engineers Conference and Exhibition 2014: Experience the Energy - Incorporating SPE EUROPEC 2014