The accuracy of an explicit traveltime-offset approximation affects the results of the velocity analysis that plays a crucial role in the seismic data processing. Seismic anisotropy is important to account for large offset and azimuth since it can provide detailed information comparing with the isotropic assumption. For the perturbation-based method, different traveltime approximation forms result in different accuracy. It is necessary to find the optimal traveltime approximation for specific signs and magnitudes of the anellipticity and different offset ranges. In this paper, a series of perturbation-based traveltime approximations from different acoustic assumptions and parameterizations are specified. The perturbation coefficients are derived from the corresponding acoustic eikonal equations. We test the accuracy of the defined perturbation approximations in four homogeneous transversely isotropic medium with vertical symmetry axis (VTI) medium with a different set of anisotropy parameters and one multilayered transversely isotropic medium with vertical symmetry axis medium. The sensitivity in anellipticity for different approximations is also analysed. We find that different approximation achieves different accuracy under the circumstance of specific offset range and the value of anellipticity. Therefore, the optimal approximation form with higher accuracy can be selected based on different offset ranges and the magnitudes of anellipticity.

中文翻译：

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具有垂直对称轴的横向各向同性介质中两个声学假设的基于扰动的走时近似

显式走时偏移近似的准确性会影响速度分析的结果，而速度分析在地震数据处理中起着至关重要的作用。地震各向异性对于解释大偏移距和方位角很重要，因为它可以提供与各向同性假设相比的详细信息。对于基于微扰的方法，不同的走时近似形式会导致不同的精度。有必要为椭圆度的特定符号和大小以及不同的偏移范围找到最佳走时近似值。在本文中，指定了来自不同声学假设和参数化的一系列基于扰动的走时近似值。扰动系数来自相应的声学特征方程。我们测试了具有不同组的各向异性参数的四种具有垂直对称轴 (VTI) 介质的均匀横向各向同性介质和一种具有垂直对称轴介质的多层横向各向同性介质中定义的扰动近似的准确性。还分析了不同近似值的椭圆率敏感性。我们发现在特定的偏移范围和椭圆率值的情况下，不同的近似达到不同的精度。因此，可以根据不同的偏移范围和椭圆率的大小选择精度更高的最优逼近形式。