Stress‐Dependent <i>b</i> Value Variations in a Heterogeneous Rate‐and‐State Fault Model
Pierre Dublanchet
Abstract
Abstract The magnitudes of earthquakes are known to follow a power law distribution referred to as the Gutenberg‐Richter empirical law. Seismological observations and laboratory experiments suggest a decrease of the decay exponent ( b value) with differential stress. The physical mechanism controlling this decrease, however, remains unclear. The present study is dedicated to the origin of relative b value variations with stress obtained in a 2‐D rate‐and‐state planar fault model considering a population of asperities with size‐dependent fracture energy. The simulations show that both b value in the intermediate magnitude range and mainshock magnitude increase with normal stress. Analytical relationships are derived, showing that the increase of b value is related to the decrease of critical nucleation length with normal stress, enhancing the productivity of small‐magnitude events and partial ruptures. The theoretical formulas also show how the increase of mainshock magnitude is a consequence of normal stress dependence of stress drop.