Parametric and non-parametric statistical approaches to the determination of paleostress from dilatant fractures: Application to an Early Miocene dike swarm in central Japan

Abstract

Several methods have been proposed for determining paleostress states from orientations of dilatant fractures such as dikes and veins. Recently a stochastic inversion method was invented to objectively estimate the principal stress axes and the stress ratio. Whether a fracture is dilated or not is controlled by the balance of the fluid pressure and the normal stress acting on it. The magnitude of normal stress depends on the fracture orientation, which causes anisotropic orientation distribution of dilatant fractures. The inversion method assumes that the orientation distribution of fractures can be approximated by a Bingham distribution, an exponential probability distribution on the unit sphere, of which symmetric axes are interpreted as the principal stress axes. However, it is unknown if the exponential type of distribution function is suitable or not. Here, we examine the distribution functions and propose two improved methods. One method uses the shifted power-law function as the shape of probability distribution, which is more

Variations in stress and driving pore fluid pressure ratio using vein orientations along megasplay faults : Example from the Nobeoka Thrust, Southwest Japan

“…; Sato et al . ). The principal axes and the concentration parameters of the optimized Bingham distribution give the principal stress axes and the stress ratio, respectively.…”

“…We applied the inversion method of Sato et al . () to estimate the stress conditions from mineral vein orientations. The stereogram in Figure illustrates the procedure.…”

Mechanical models to estimate the paleostress state from igneous intrusions

“…Jolly and Sanderson, 1997;Yamaji et al, 2010;Sato et al, 2013). Whether this is a tight cluster or a distributed set of poles, the pattern is usually interpreted to represent a single event, governed by one fluid pressure (e.g.…”

“…These mechanical models have been adopted for statistical constraints on paleostress axes, and the paleostress state, from vein or dike data (e.g. Sato et al, 2013;Yamaji, 2016). Although several methods exist to determine paleostress axes and a state of paleostress via fault, fracture, or dike data, subhorizontal sheet intrusions (sills) are typically omitted from such…”

Genetic algorithm for fitting a mixed Bingham distribution to 3D orientations: a tool for the statistical and paleostress analyses of fracture orientations

“…Fracture orientations are important to predict the leakage of geofluid from reservoirs (e.g., Bigi et al ) and to estimate the stability of open pit and tunnel walls (Priest ; Peel et al ). The orientations of dilational fractures such as dikes and mineral veins are clues to paleostresses (Stevens ; Anderson ; McHone ; Delaney et al ; Baer et al ; Jolly & Sanderson ; Yamaji et al ; Sato et al ; Kanai et al ). Since the poles to natural fractures often show multimodal distribution, the clustering of the fracture orientations is essential for the description and paleostress analysis of the fractures.…”