b-value and kinematic parameters from 3D focal mechanisms distributions in Southern California

Abstract

<p><span>The frequency-magnitude relation of earthquakes, with particular attention to the <em>b</em>-value of Gutenberg-Richter law, is computed in Southern California. A three-dimensional grid is employed to sample relocated focal mechanisms and determine both the magnitude of completeness and the <em>b</em>-value for each node. Sampling radius and grid size are appropriately chosen accordingly to seismogenic source dimensions. The SCEC Community Fault Model is used for comparison of the main fault systems along with the calculated 3D distributions. </span></p><p><span>The <em>b-</em>values are compared to <em>A<sub>λ</sub></em>, a streamlined kinematic fault quantification, which does not use inversion processes since directly depends on individual rakes of focal mechanisms. Potential relationships between the two quantities are then computed through multiple regressions at increasing depth ranges: they may help to evaluate seismic hazard assessment in relating the frequency and size of earthquakes to kinematic features. The rheological transition from elastic to plastic conditions is computed, assuming different physical constraints, and its influence on <em>b-</em>value and <em>A<sub>λ</sub></em> is also analyzed. Among proposed linear, polynomial, and harmonic equations, the linear model is statistically valued as the most probable one to relate the two parameters at different depth ranges. <em>b</em>-values against <em>A<sub>λ</sub></em> results are implemented into a 3D figure, where point data are interpolated by “Lowess Smoothing” surfaces to visually check the constancy depending on depth.</span></p>