VTI介质弹性体波模式解耦高效算法

Efficient algorithms for mode decoupling of elastic wavefield in transversely isotropic media with a vertical symmetry axis

对于各向异性波场模式解耦来说,常规的散度与旋度运算存在明显误差,而理论上精确的偏振投影算子受介质参数和传播方向共同控制,导致相应的模式解耦算法成本难以承受。在前人研究基础上,开发面向带有垂直对称轴的横向各向同性(VTI)介质的弹性体波模式解耦高效算法。首先,针对依据主能量传播与偏振方向偏差角设计的伪散度/伪旋度算子,借助波场方向分解,考虑偏差角随传播方向的变化,构造出更精确的qP/qS波分离算法。然后,针对理论更完备、适用性更强的偏振投影低秩近似算法,借助模型分区和GPU加速策略,达到了精度与成本的相对平衡。SEG Hess VTI二维模型数值试验揭示了改进的伪散度/伪旋度算法、分区低秩分解GPU算法的特点,同时验证了方法的可靠性。

For the elastic wave mode decoupling in anisotropic media,conventional approaches with divergence and curl operations lead significant errors.The accurate mode decomposition algorithm,however,is prohibitively expensive because the polarization projection operators are model-and direction-dependent.Based on previous work,we focus on developing efficient algorithms for mode decoupling in heterogeneous medium with vertically transverse isotropy(VTI).First,for the pseudo-divergence or pseudo-curl operators constructed by the deviation of propagation and polarization direction of the dominant energy,we improve the accuracy of qP/qS separation by taking into account the variations of the deviation angle with the propagation direction.This improvement is very important when different wave modes overlap in the same spatial zone at the same time.Then,for the accurate but prohibitively expensive algorithm of mode decoupling through polarization projection,based on the existing low-rank approximation of the projection operator,we achieve a balance between the accuracy and computational cost using the strategies of model partitioning and graph processing unit(GPU)acceleration.The example on the SEG Hess VTI model demonstrates the features and validities of the improved pseudo-divergence/pseudo-rotation algorithm and the GPUbased low-rank approximate polarization projection algorithm.