Clustering of fracture orientations using a mixed Bingham distribution and its application to paleostress analysis from dike or vein orientations

Abstract

The clustering and classification of fracture orientations are important in rock mechanics and in brittle tectonics, the latter of which includes the paleostress analysis of extension fractures hosting dikes or mineral veins. Here, we present an unsupervised clustering method for the orientations of extension fractures using mixed Bingham distributions. The method not only detects the elliptical clusters and girdles made by the poles to such planar features, but also determines the appropriate number of those groups by means of Bayesian information criterion (BIC) without a priori information. The method was tested with artificial data sets, and successfully detected the assumed groups, when the clusters had little overlaps. However, clusters with the common maximum concentration orientation and large aspect ratios were distinguished, provided that their minimum concentration orientations were separated by a large angle. Our method separated two stress states from natural data from a Miocene dike swarm in SW Japan. The method also evaluated the probabilities of the stresses to form each of the dike.

A middle Miocene post‐rift stress regime revealed by dikes and mesoscale faults in the Kakunodate area, NE Japan

“…The magma pressure that opened fractures in which dikes were formed can also now be estimated (Faye, Yamaji, Yonezu, Tindell, & Watanabe, ; Jolly & Sanderson, ). The latest methods can also separate stresses from dikes that were formed under different stress conditions (Yamaji, ; Yamaji & Sato, ).…”

Orientation of the Eruption Fissures Controlled by a Shallow Magma Chamber in Miyakejima

“…Therefore, the orientation of dikes has been used as an indicator of the stress field in volcanic fields (Nakamura, 1977;Yamaji and Sato, 2011). Dikes will be oriented parallel to the maximum stress axis in a homogeneous stress field.…”

Determination of structural domain boundaries in jointed rock masses: An example from the Songta dam site, China

“…It is generally recognized that joints play a pivotal role in the deformability, permeability and strength of rock masses (Goodman, 1976;Hudson and Harrison, 1997;Smith, 2004;Larsen et al, 2009;Yamaji and Sato, 2011;Ye et al, 2012a, b). Characterizing joints within a rock mass is a basic step for rock mass classification and rock engineering design (Kruhl, 2013;Stavropoulou, 2014).…”