In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.

中文翻译：

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修正的最短路径法在2D / 3D粘弹性各向异性介质中进行地震复射线追踪

在粘弹性各向异性介质中，会发生速度各向异性和波能衰减，并且经常在地震数据应用中观察到。复杂黏弹性各向异性介质中地震波传播的数值研究对于理解地震数据和重建地下结构非常有帮助。地震射线追踪是研究高频地震波传播特性的有效手段。不幸的是，大多数地震射线追踪方法和行进时间层析反演算法仅处理弹性介质，而忽略了粘弹性对地震射线路径的影响。我们已经开发出一种方法，可以找到在任意粘弹性各向异性介质中能给出地震射线速度和衰减的复射线速度，然后将它们与改进的最短路径方法结合在一起，以确定射线路径，并同时计算实际和假想的传播时间（波能衰减）。我们确定在复杂的地质模型中，复杂的射线追踪方法适用于任意2D / 3D粘弹性各向异性介质，实际和假想旅行时间的计算误差分别小于0.36％和0.59％。数值算例验证了该方法是一种在异质粘弹性各向异性介质中完成地震复射线追踪的有效和强大的工具。我们确定在复杂的地质模型中，复杂的射线追踪方法适用于任意2D / 3D粘弹性各向异性介质，实际和假想旅行时间的计算误差分别小于0.36％和0.59％。数值算例验证了该方法是一种在异质粘弹性各向异性介质中完成地震复射线追踪的有效和强大的工具。我们确定在复杂的地质模型中，复杂的射线追踪方法适用于任意2D / 3D粘弹性各向异性介质，实际和假想旅行时间的计算误差分别小于0.36％和0.59％。数值算例验证了该方法是一种在异质粘弹性各向异性介质中完成地震复射线追踪的有效和强大的工具。