IDENTIFYING A TI MEDIUM WITH ARBITRARY ORIENTATION BY USING THE ANALYTIC EXPRESSION OF ITS ELASTIC TENSOR

doi:10.3969/j.issn.0253-4967.2011.03.017

Abstract

Abstract:

Transverse isotropy(TI)symmetry is widely applied to the study of seismic anisotropy.It can model almost all kinds of observed anisotropy,including stress-aligned cracks in the crust,a variety of sedimentary rocks and anisotropic minerals such as olivine in the uppermost mantle.TI anisotropy represents the main characteristics of different kinds of anisotropy media at various depths.TI media are not always horizontal(HTI)or vertical(VTI),but could be with an arbitrary orientation of symmetry axis.Cracks may be vertical or nearly vertical,but they could also be tilted; sedimentary rocks that underwent tectonic deformation may not retain vertical axis; the lattice preferred orientation of upper mantle olivine could also differ from horizontal.These ask for the breaking of usual hypothesis of VTI or HTI,and solving the problems concerning wave propagation and data interpretation through a TI medium with arbitrary orientation(ATI).In terms of elasticity matrix,the ATI medium is similar to the triclinic medium,both of which have 21 nonzero and distinct components.Given the elastic matrix of the medium,it’s important to determine the symmetric system it belongs to.Considering the prevalence of TI symmetry in the study of anisotropy,it’s especially important to decide whether the medium is an ATI one.Due to the rotational invariance of the TI medium about its axis,the 21 components of the ATI elastic coefficient matrix are not mutually independent at all.In fact,they can be expressed by five mutually independent elasticity constants measured in its innate symmetric coordinate system and the orientation of the symmetry axis.In light of the analytical expression for the ATI elastic tensor,it is possible to analyze the relations between the ATI elastic coefficients and find a way to identify ATI elastic matrix.

Key words: transverse isotropy, ATI, elastic tensor, symmetry axis

摘要：

利用任意空间取向横向各向同性介质(ATI)的弹性张量解析表达式,分析ATI弹性常数之间的内在关系,得到一个判断ATI介质的必要条件。假若介质弹性矩阵满足这个ATI必要条件,可做ATI假设,确定可能的ATI对称轴空间取向。此时,如果通过坐标变换得到的是VTI弹性矩阵,就说明介质确实是ATI介质,这就完整地解决了从包含21个非零元素的弹性矩阵判断介质是否ATI的问题。数值算例验证了这种方法在剔除非ATI弹性矩阵时的便捷与识别ATI介质时的可靠。

关键词: 横向各向同性, ATI, 弹性张量, 对称轴

CLC Number:

P315.72

CHEN Wen-kang, YAO Chen, HAO Chong-tao. IDENTIFYING A TI MEDIUM WITH ARBITRARY ORIENTATION BY USING THE ANALYTIC EXPRESSION OF ITS ELASTIC TENSOR[J]. SEISMOLOGY AND GEOLOGY, 2011, 33(3): 684-692.

陈文康, 姚陈, 郝重涛. 利用弹性张量解析表达式识别任意空间取向TI介质[J]. 地震地质, 2011, 33(3): 684-692.

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