Statisztikai próbák sztochasztikus, közel izotróp tenzorral leírható kőzetfizikai mennyiségek vizsgálatára. Statistical tests for rock physical parameters given by near isotropic, stochastic tensors

Sipos, András Árpád (2013) Statisztikai próbák sztochasztikus, közel izotróp tenzorral leírható kőzetfizikai mennyiségek vizsgálatára. Statistical tests for rock physical parameters given by near isotropic, stochastic tensors. Magyar Geofizika, 54 (4). pp. 170-184. ISSN 0025-0120

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Abstract

Statistical hypothesis testing for the eigenvalues and eigenvectors of a stochastic tensor is not straightforward process due to the nonlinear dependence involved in the problem. For anisotropic tensors the linearized approaches of the literature are adequate, however geophysical applications require the analysis of nearly isotropic tensors, too. Our paper is devoted to introduce new statistical methods for these, seemingly rare cases which turns out to be a regular problem in practice. We point out that the well-known behavior of deterministic tensors, namely that the multiplicity of the eigenvalues unambiguously refers to the spatial distribution of the eigenvectors, does not hold for matrices with random variable elements. In this way the published methods focusing only on the eigenvalues are not satisfactory. The latter statement is also confirmed by examples from geophysics. Our method can be used to analyse closeness of tensor state parameters or directional differences between a vector and one of the eigenvectors in a statistical framework.

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