Open AccessInferring the relative measure of principal stress components
Author(s) -
Xu Peiliang,
Shimada Seiichi
Publication year - 1997
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1997.tb00982.x
Subject(s) - measure (data warehouse) , mathematics , principal component analysis , computation , approximation error , stress (linguistics) , cauchy stress tensor , statistics , statistical physics , mathematical analysis , computer science , algorithm , physics , data mining , linguistics , philosophy
SUMMARY The relative measure R of principal stress components has been of special interest in Earth Sciences, since its variation may indicate the redistribution of stress. The purpose of this paper is to investigate its statistical aspects. Given a probability density function of a random stress tensor, we derive the pdf of R , which can be very different from normal, give its bias estimate and compute the error using a second‐order approximation. Theoretical examples have shown that the estimate of R can be seriously biased and its accuracy poorly determined if linear approximation is used. Analysis of real data sets might show that the linear approximation is not enough for the estimation of R and the computation of its accuracy.