A Statistical Framework for Calculating and Assessing Compositional Linear Trends Within Fault Zones: A Case Study of the NE Block of the Clark Segment, San Jacinto Fault, California, USA

Utilizing chemical data derived from the various fault zone architectural components of the Clark strand of the San Jacinto fault, southern California, USA, we apply for the first time non-central principal component analysis to calculate a compositional linear trend within molar A–CN–K space. In this procedure A–CN–K are calculated as the molar proportions of Al2O3 (A), CaO* + Na2O (CN), and K2O (K) in the sum of molar Al2O3, Na2O, CaO*, and K2O. CaO* is the molar CaO after correction for apatite. We then derive translational invariant chemical alteration intensity factors, t, for each architectural component through orthogonal projection of analyzed samples onto the compositional linear trend. The chemical alteration intensity factor t determines the relative change in composition compared to the original state (i.e., the composition of the altered wall rocks). It is dependent on the degree of intensity to which the process or processes responsible for the change in composition of each architectural component has been active. These processes include shearing, fragmentation, fluid flow, and generation of frictional heat. Non-central principal component analysis indicates that principal component 1 explains 99.7 % of the spread of A–CN–K data about the calculated compositional linear trend (i.e., the variance). The significance level for the overall one-way analysis of variance (ANOVA) is 0.0001. Such a result indicates that at least one significant difference across the group of means of t values is different at the 95 % confidence level. Following completion of the overall one-way ANOVA, the difference in means t test indicated that the mean of the t values for the fault core are different than the means obtained from the transition and damage zones. In contrast, at the 95 % confidence level, the means of the t values for the transition and damage zones are not statistically distinguishable. The results of XRD work completed during this study revealed that the <2 µm fraction is composed primarily of illite/smectite with ~15 % illite in the damage zone, of illite/smectite with ~30 % illite in the transition zone, and of discreet illite with very minor smectite in the fault core. These changes parallel the increasing values of the chemical alteration intensity factors (i.e., t). Based on the above results, it is speculated that when fault zones are derived from tonalitic wall rocks at depths of ~400 ± 100 m, the onset of the illite/smectite to illite conversion will occur when t values exceed 0.20 ± 0.12, the average chemical alteration intensity factor calculated for the transition zone. Under such conditions during repeated rupturing events, frictional heat is produced and acidic fluids with elevated temperatures (≥ ~125 °C) are flushed through the fault core. Over time, the combination of shearing, fragmentation, and frictionally elevated temperatures eventually overcomes the kinetic barrier for the illite/smectite to illite transition. Such settings and processes are unique to fault zones, and as a result, they represent an underappreciated setting for the development of illite from illite/smectite. The success of non-central principal component analysis in this environment offers the first statistically rigorous methodology for establishing the existence of compositional linear trends in fault zones. This method also derives quantifiable alteration intensity factors that could potentially be used to compare the intensity of alteration at different segments of a fault, as well as offer a foundation to interpret the potential driving forces for said alteration and differences therein.