Numerical simulation of first-order velocity-dilatation-rotation elastic wave equation with staggered grid
WANG Hui1,2, HE Bingshou1,2, SHAO Xiangqi3
1. Key Lab of Submarine Geosciences and Prospecting Techniques, MOE China, Ocean University of China, Qingdao, Shandong 266100, China; 2. Functional Laboratory of Marine Mineral Resources Evaluation and Exploration Technology, Qingdao National Laboratory of Marine Science and Technology, Qingdao, Shandong 266100, China; 3. Yantai Natural Resources and Planning Bureau, Yantai, Shandong 264003, China
Abstract：Elastic wave forward modeling plays an important role in seismic wave propagation mechanism research and the acquisition, processing, interpretation, and inversion of multi-wave seismic data. Present forward modeling of elastic wave equations often numerically solves first-order velocity-stress equation or second-order displacement equation to only obtain three particle vibration velocity components or displacement components containing P- and S-wave. The wave-field decoupling operator should be employed to separate P- and S-wave for a more intuitive recording of pure P- and S-wave components. Therefore, the accuracy of the wave records simulated by the methods is subject to the accuracy of both the simulation algorithm and the wavefield decoupling algorithm. This paper derives the higher-order finite-diffe-rence scheme of the first-order velocity-dilatation-rotation elastic wave equation in three-dimensional staggered grid space and gives the corresponding stability conditions. The PML absorbing boundary conditions adapted to the equation are derived, and the forward modeling of the first-order velocity-dilatation-rotation elastic wave equation is realized. The physical meaning of each component in the simulation results is analyzed. The equation not only contains the vibration velocity vector of the particles but also explicitly includes the P- and S-wave vibration velocity vectors. Additionally, an volumetric strain and a rotation vector are also involved. Therefore, in addition to the three particle vibration velocity components, the decoupled P- and S-wave components can be obtained directly by the equation. This avoids the influence of the decoupling algorithm on decoupling accuracy, and model trials prove he validity and superiority of the proposed method.
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