摘要
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.
We propose a symplectic partitioned Runge–Kutta(SPRK) method with eighthorder spatial accuracy based on the extended Hamiltonian system of the acoustic wave equation. Known as the eighth-order NSPRK method, this technique uses an eighth-order accurate nearly analytic discrete(NAD) operator to discretize high-order spatial differential operators and employs a second-order SPRK method to discretize temporal derivatives. The stability criteria and numerical dispersion relations of the eighth-order NSPRK method are given by a semi-analytical method and are tested by numerical experiments. We also show the differences of the numerical dispersions between the eighth-order NSPRK method and conventional numerical methods such as the fourth-order NSPRK method, the eighthorder Lax–Wendroff correction(LWC) method and the eighth-order staggered-grid(SG) method. The result shows that the ability of the eighth-order NSPRK method to suppress the numerical dispersion is obviously superior to that of the conventional numerical methods. In the same computational environment, to eliminate visible numerical dispersions, the eighthorder NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 times faster than the fourth-order SPRK, and the memory requirement is only approximately 47.17% of the fourth-order NSPRK method and 49.41 % of the fourth-order SPRK method, which indicates the highest computational efficiency. Modeling examples for the two-layer models such as the heterogeneous and Marmousi models show that the wavefields generated by the eighth-order NSPRK method are very clear with no visible numerical dispersion. These numerical experiments illustrate that the eighth-order NSPRK method can effectively suppress numerical dispersion when coarse grids are adopted. Therefore, this method can greatly decrease computer memory requirement and accelerate the forward modeling productivity. In general, the eighth-order NSPRK method has tremendous potential value for seismic exploration and seismology research.
基金
This research was supported by the National Natural Science Foundation of China （Nos. 41230210 and 41204074）, the Science Foundation of the Education Department of Yunnan Province （No. 2013Z152）, and Statoil Company （Contract No. 4502502663）.
