Seismic numerical modeling in the presence of surface topography has become a valuable tool to characterize seismic wave propagation in basin or mountain areas. Regarding advantages of frequency-domain seismic wavefield simulations (e.g., easy implementation of multiple sources and straightforward extension of adding attenuation factors), we propose a frequency-domain finite-difference seismic wavefield simulation in 2D elastic media with an irregular free surface. In the frequency domain, we first transform second-order elastic wave equations and first-order free surface boundary conditions from the Cartesian coordinate system to the curvilinear coordinate system. Then we apply complex frequency-shifted perfectly matched layer (CFS-PML) absorbing boundary condition to second-order elastic wave equations in the curvilinear coordinate. To better couple free surface boundary conditions and CFS-PML absorbing boundary condition, we also apply the complex coordinate stretching method used in CFS-PML to free surface boundary conditions in the curvilinear coordinate. In the first numerical test, the comparison of the seismograms calculated by our algorithm with an analytical solution indicates that our algorithm can accurately simulate seismic wavefield in the frequency domain. Finally, we choose three more elastic models with different types of surface topographies to further characterize seismic wave propagation.

中文翻译：

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存在表面形貌的频域有限差分弹性波建模

存在地表地形的地震数值模拟已成为表征盆地或山区地震波传播的重要工具。关于频域地震波场模拟的优点（例如，易于实现多源和直接扩展添加衰减因子），我们提出了在具有不规则自由表面的二维弹性介质中的频域有限差分地震波场模拟。在频域中，我们首先将二阶弹性波方程和一阶自由表面边界条件从笛卡尔坐标系转换为曲线坐标系。然后我们将复杂的频移完美匹配层（CFS-PML）吸收边界条件应用于曲线坐标中的二阶弹性波方程。为了更好地耦合自由表面边界条件和 CFS-PML 吸收边界条件，我们还将 CFS-PML 中使用的复坐标拉伸方法应用于曲线坐标中的自由表面边界条件。在第一次数值试验中，我们的算法计算的地震图与解析解的比较表明我们的算法可以准确地模拟频域的地震波场。最后，我们选择了另外三个具有不同类型表面地形的弹性模型来进一步表征地震波的传播。将我们的算法计算的地震图与解析解的比较表明我们的算法可以准确地模拟频域中的地震波场。最后，我们选择了另外三个具有不同类型表面地形的弹性模型来进一步表征地震波的传播。将我们的算法计算的地震图与解析解的比较表明我们的算法可以准确地模拟频域中的地震波场。最后，我们选择了另外三个具有不同类型表面地形的弹性模型来进一步表征地震波的传播。