Applying and validating Coulomb rate-and-state seismicity models in acoustic emission experiments

Abstract

A central goal of laboratory seismology is to infer large-scale seismic processes from small-scale experiments, with acoustic emissions (AE) being a common observable. These signals, indicative of microfracturing, slip localization, and damage evolution, are often paralleled with earthquakes to understand seismic behaviors. This study challenges traditional perspectives by applying Coulomb rate-and-state seismicity theory, originally developed for earthquake clustering, to AE experiments. This theory maps stressing history to seismicity rates using rate-and-state friction, however, its validity under controlled experimental conditions remains an open question. We conducted four experiments on a sawcut sample of red felser sandstone, representing a fault under variable stress conditions. Adjustments in loading rates and initial conditions revealed that, while a single free parameter $A$—related to the direct effect—should suffice, a rescaling of the model by 1.5 to 2.2 was necessary for fitting the data. Differences in values across experiments appeared mostly non-systematic, and partial data usage did not yield consistently systematic parameter migrations. These findings suggest that fault microstructure may complexly alter parameter values during loading beyond what is accounted for in the Coulomb rate-and-state theory. Nonetheless, with the introduction of the scaling parameter, the Coulomb rate-and-state theory effectively captures the fundamental aspects of AE responses to complex controlled loading histories.