The parameterization of anisotropic models is very important when focusing on specific signatures of seismic waves and reducing the parameter crosstalk involved in inverting seismic data. The parameterization is strongly dependent on the problem at hand. We have developed a new parameterization for an elastic orthorhombic (ORT) model with on-axes compressional wave (P-wave) and shear wave (S-wave) velocities and new symmetric anelliptic parameters. The perturbation approach is well defined for P-waves in acoustic ORT media. In the elastic ORT media, the P-wave perturbation coefficients are very similar to their acoustic counterparts. However, the S-wave perturbation coefficients are still unknown. The perturbation coefficients can be interpreted as sensitivity coefficients, and they are important in many applications. We apply the second-order perturbation in anelliptic parameters for P-, S1-, and S2-wave phase velocities in the elastic ORT model. We find that when using the conventional method some perturbation coefficients for S-waves are not defined in the vicinity of the singularity point in an elliptical background model. Thus, we adopt an alternative perturbation approach that overcomes this problem. We compute the first- and second-order perturbation coefficients for P- and S-waves. The perturbation-based approximations are very accurate for P- and S-waves compared with the exact solutions, based on a numerical example. The reductions to transversely isotropic and acoustic ORT models are also considered for analysis. We also determine how perturbations in anelliptic parameters affect S-wave triplications in an elastic ORT model.

中文翻译：

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弹性正交介质中相速度的扰动

在关注地震波的特定特征和减少地震数据反演中涉及的参数串扰时，各向异性模型的参数化非常重要。参数化在很大程度上取决于手头的问题。我们已经为具有轴上压缩波 (P 波) 和剪切波 (S 波) 速度和新对称非椭圆参数的弹性正交 (ORT) 模型开发了新的参数化。对于声学 ORT 介质中的 P 波，微扰方法是明确定义的。在弹性 ORT 介质中，P 波扰动系数与其声学对应物非常相似。然而，S波扰动系数仍然未知。扰动系数可以解释为灵敏度系数，它们在许多应用中都很重要。我们在弹性 ORT 模型中的 P 波、S1 波和 S2 波相速度的椭圆参数中应用二阶微扰。我们发现，当使用传统方法时，在椭圆背景模型的奇异点附近没有定义一些 S 波的扰动系数。因此，我们采用了一种替代的扰动方法来克服这个问题。我们计算 P 波和 S 波的一阶和二阶扰动系数。基于数值示例，与精确解相比，基于扰动的近似对于 P 波和 S 波非常准确。还考虑对横向各向同性和声学 ORT 模型的简化进行分析。我们还确定了椭圆参数的扰动如何影响弹性 ORT 模型中的 S 波三次。