时间域广义2.5D一阶波动方程曲网格有限差分法数值模拟

2.5D地震波场数值模拟通过在2D地质模型中施加点源从而计算得到3D地震波场。首先通过傅里叶变换得到了一种适用于混合（声波、弹性各向同性、弹性各向异性）介质和各种边界条件（声波自由地表、固体自由地表和固—液边界）的2.5D时域广义一阶波动方程，并采用曲线网格有限差分法求解该波动方程。在各种均匀介质模型（声波、弹性各向同性和弹性各向异性）中，通过对比2.5D数值解与3D解析解和3D数值解，不仅验证了推导的方程和数值求解方法的正确性，而且验证了2.5D数值方法相比3D数值方法在计算效率和内存占用方面有很大的优势。2D数值方法由于线源假设，其解与2.5D数值解相比存在较大的振幅误差和相移，难以直接应用。数值实验结果表明，该2.5D数值模拟方法适用于含各种边界（声波自由地表、固体自由地表和固—液边界）的地质模型。不同于2D波场数值模拟方法，2.5D波场数值模拟方法可直接应用于实际的点源观测数据处理，如2.5D逆时偏移成像。

Curvilinear-grid finite-difference numerical simulation method for generalized first-order 2.5D time-domain wave equation

The 2.5D seismic wavefield numerical stimulation employs the point source in 2D geological models to calculate 3D seismic wavefields. In this paper, we present a generalized 2.5D first-order time-domain wave equation that can be applied to different media (acoustic isotropic, elastic isotropic, and elastic anisotropic) and various boundary conditions (acoustic free-surface, solid free-surface, and solid-liquid boundary). The wave equation is solved by a curvilinear-grid finite-difference method. A comparison of 2.5D numerical solutions, 3D analytic solutions, and 3D numerical solutions in different homogeneous medium models (acoustic isotropic, elastic isotropic, and elastic anisotropic) verifies the correctness of the derived equation and the numerical solution method. It also demonstrates that compared with the 3D nume-rical method, the 2.5D numerical method has great advantages in calculation efficiency and memory footprint. The 2D numerical solutions cannot be applied directly in that they suffer significant amplitude distortion and phase shifts due to an artificial line source applied in this method. The results of numerical experiments show that the proposed 2.5D numerical simulation method can be applied to geological models with different boundary conditions (acoustic free-surface, solid free-surface, and solid-liquid boundary). In addition, unlike the 2D wavefield numerical simulation method, the 2.5D method can be directly employed to process actual point source observation data such as 2.5D reverse-time migration.