We developed an algorithm to simulate two-dimensional frequency domain acoustic-wave response in a transversely isotropic medium with a tilted symmetry axis. The algorithm employs a support operator finite-difference method for modelling. This method constructs a nine-point stencil finite-difference scheme for second-order elliptic equations for generalized anisotropic physical properties. The medium's properties are described as P-wave velocity on the symmetric axis, density, Thomsen's anisotropic parameters (epsilon and delta) and the tilt angle. The benchmarking analysis of the modelled amplitude is illustrated using an isotropic whole-space model. Several synthetic experiments are conducted to evaluate the accuracy of the scheme for anisotropic models. The results suggest that the developed algorithm simulates the P-wave solution and the fictitious S-wave mode as reported in the literature. Simulation for a heterogeneous model with a spatially varying tilt angle of the medium symmetry axis is performed to ascertain the algorithm's robustness. The outcomes of the numerical experiments demonstrate that the developed algorithm can accurately simulate the frequency domain response of acoustic waves in the tilted anisotropic media.

中文翻译：

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使用支持算子方法进行二维各向异性声波建模

我们开发了一种算法来模拟具有倾斜对称轴的横向各向同性介质中的二维频域声波响应。该算法采用支持算子有限差分法进行建模。该方法为广义各向异性物理性质的二阶椭圆方程构造了九点模板有限差分格式。介质的属性被描述为对称轴上的纵波速度、密度、汤姆森各向异性参数（ε 和 δ）以及倾斜角。使用各向同性全空间模型说明了建模幅度的基准分析。进行了几次综合实验来评估各向异性模型方案的准确性。结果表明，所开发的算法模拟了文献中报道的 P 波解和虚拟 S 波模式。对具有空间变化的介质对称轴倾斜角的异构模型进行仿真，以确定算法的鲁棒性。数值实验结果表明，所开发的算法可以准确模拟倾斜各向异性介质中声波的频域响应。