扩展的近似解析离散化方法及弹性波方程数值模拟

Expanded approximate analytic discretization and elastic wave numerical simulation

地震波场数值模拟是研究地震波理论、偏移成像和地震反演等工作的基础,提高数值模拟的精度具有重要意义。在前人的研究基础上,提出了一种扩展的近似解析离散化数值模拟方法,并从理论上对该方法的精度、数值频散、稳定性和计算效率进行了分析。该方法在时间差分上比扩展前提高了一阶精度、误差最大降低了88%。与其他近似解析离散化类方法一样,具有算子半径小和适应粗网格步长的优势,在最小主波长内仅需使用5.9个网格点。与四阶Lax-Wendroff修正格式和交错网格有限差分格式的频散曲线和模拟结果对比,验证了该方法能更好地压制数值频散。二维各向同性均匀介质和水平层状介质模型数值模拟的地震弹性波场特征清晰准确,说明了该方法的实用性。

The seismic wave numerical simulation is the foundation of the seismic wave theory,migration imaging and seismic inversion.The accuracy of numerical simulation has a great significance for seismic exploration.This paper discusses an expanded approximate analytic discretization method for seismic wave numerical simulation,and theoretically analyses its accuracy,dispersion relations,stability,and computational efficiency.This method is one order higher in time difference than before,thereby the calculation accuracy is improved.Simulation results demonstrate that the maximum error rate is 88% lower than before.As other approximate analytic discretization methods,the proposed method has advantages of shorter operator radius and better adaption to too-coarse grids.In the smallest main wavelength it needs only 5.9 grid points.Compared with the dispersion curves and the simulation results with the fourth-order LWC and the staggered-grid finite difference scheme,the proposed method can better suppress numericaldispersion.Finally with the proposed method we numerically simulate elastic waves in the isotropic homogeneous medium model and horizontal layered medium model.Very clear and accurate seismic characteristics demonstrate the practicability of the proposed method.