INFERRING THE RELATIVE MEASURE OF PRINCIPAL STRESS COMPONENTS

The relative measure R of principal stress components has been of spec ial interest in Earth Sciences, since its variation may indicate the r edistribution of stress. The purpose of this paper is to investigate i ts statistical aspects. Given a probability density function of a rand om 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 seco nd-order approximation. Theoretical examples have shown that the estim ate of R can be seriously biased and its accuracy poorly determined if linear approximation is used. Analysis of real data sets might show t hat the linear approximation is not enough for the estimation of R and the computation of its accuracy.