Traveltime tomography in anisotropic media—I. Theory
Traveltime tomography in anisotropic media—I. Theory
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DOI：
10.1111/j.1365-246x.1992.tb00075.x
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发表时间：
1992-04
影响因子：
2.8
通讯作者：
C. Chapman;R. Pratt
中科院分区：
文献类型：
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作者：
C. Chapman;R. Pratt
从原理上讲，井间走时层析成像是直接探测和测量地震各向异性的理想方法。具有宽角覆盖的多条射线的旅行时对不均匀性和各向异性都是敏感的。实际上，走时仅取决于有限数量的各向异性速度参数，甚至可能不足以唯一地确定这些参数。此外，各向异性和非均质性之间可能存在权衡。本文利用一般弱各向异性介质走时的线性摄动理论，讨论了二维井间层析成像实验中走时对各向异性参数的依赖关系。在另一篇文章中，我们将结果应用于合成数据和真实数据实例。我们表明，当测量限于二维平面时，QP和QS旅行时取决于21个各向异性速度参数的完整集合的子集。在分段齐次模型和线性内插模型中，导出了旅行时相对于这些参数的微分系数的公式。文中展示了在面向一般的模型元素中，局部参数如何与全局模型中的相同参数相关联。可以从2-D层析数据确定的参数通常不能确定各向异性的全部性质。相反，这些参数仅用于描述慢度表与2-D平面的交点。由于许多模型可能符合这一描述，因此需要有关对称属性和取向的附加信息。例如，如果先验信息表明各向异性是横观各向同性的，那么我们可以确定一些横观各向同性参数和一些关于对称轴取向的信息。给出了一般参数与对称轴一般取向的TI系统的一般参数之间的关系。QS走时的一般公式本质上比QP的公式复杂。在QS情况下，旅行时微扰取决于偏振，而偏振又取决于微扰。这使得即使对于小的扰动，一般问题也是非线性的。然而，平均QS旅行时和旅行时对不同参数子集的依赖关系是线性的。虽然线性微扰理论对QS射线是无效的，但简并微扰理论对于旅行时的计算是有效的，并且可以用于非线性反演方案。
SUMMARY In principle, crosshole, traveltime tomography is ideal for directly detecting and measuring seismic anisotropy. The traveltimes of multiple rays with wide angular coverage will be sensitive both to inhomogeneities and to anisotropy. In practice, the traveltimes will depend only on a limited number of the anisotropic velocity parameters, and the data may not be adequate even to determine these parameters uniquely. In addition, trade-offs may exist between anisotropy and inhomogeneities. In this paper, we use the linear perturbation theory for traveltimes in general, weakly anisotropic media to discuss the dependence of traveltimes in 2-D crosshole tomographic experiments on the anisotropic parameters. In a companion paper, we apply the results to synthetic and real data examples. We show that when measurements are restricted to a 2-D plane, the qP and qS traveltimes depend on subsets of the complete set of 21 anisotropic velocity parameters. Formulae are developed for the differential coefficients of the traveltimes with respect to these parameters in piecewise homogeneous and in linearly interpolated models. It is shown how in a generally oriented model element, the local parameters are related to the same parameters in the global model. The parameters that can be determined from 2-D tomographic data do not in general determine the full nature of the anisotropy. Rather, these parameters serve only to describe the intersection of the slowness sheet with the 2-D plane. Since many models may fit this description, additional information on symmetry properties and orientations is required. For example, if a priori information suggests that the anisotropy is transversely isotropic (TI), then we can determine some of the TI parameters and some information on the orientation of the axis of symmetry. Formulae are given relating the general parameters to those of a TI system with general orientation of the symmetry axis. The general formulae for qS traveltimes are intrinsically more complicated than those for qP. In the qS case, the traveltime perturbation depends on the polarization, which in turn depends on the perturbation. This makes the general problem non-linear even for small perturbations. However, the mean qS traveltime and the traveltime dependence on various subsets of parameters are linear. Although linear perturbation theory is invalid for qS rays, degenerate perturbation theory is valid for the calculation of the traveltimes and could be used in a non-linear inversion scheme.