Determination of rock friction constitutive parameters using an iterative least squares inversion method

Abstract

In order to understand the behavior of slip in fault zones that can lead to earthquakes, a detailed description of the constitutive behavior of the slipping rocks is needed. Rate‐ and state‐variable constitutive laws have been very successful in describing results of laboratory studies of rock friction, but the actual determination of constitutive law parameter values has been limited to forward trial‐and‐error methods only. This paper presents a method of inverting rock friction experimental data to determine the parameters in the Dieterich‐Ruina friction constitutive model. We use an iterative least squares method to solve the inverse problem, and we describe the solutions to several difficulties that arose owing to the nonlinearity of both the model and the iterated solution. These solutions include (1) using a finite differences method to estimate the derivatives of the constitutive model, (2) incorporating a vector to weight the relative “importance” of the friction observations, (3) using singular‐value decomposition to solve the inverse problem, and (4) creating a damped version of the inverse routine to enhance the ability of the program to converge on a final solution. We explore the effects of machine stiffness and added noise on the covariances and correlations between model parameters. We find that increasing stiffness reduces parameter variances, covariances, and the strong correlations between some model parameters; increasing noise increases parameter variances and covariances without affecting the correlation between model parameters.