A Model to Study the Bias on Q Estimates Obtained by Applying the Rise Time Method to Earthquake Data

Among Q-estimation methods a simple linear technique consists of the evaluation of the increasing rise time of body waves with the increase of their travel time. This method, known as the rise time method, was theoretically justified for an impulsive source time function (Dirac delta function). WU and LEES (1996), throughout finite difference calculations, showed that, when considering finite source time functions, characterized by a cut-off frequency around 20 Hz, the rise time method can be satisfactorily applied to invert earthquake data. In order to establish the applicability of the rise time method to an arbitrary earthquake source we analytically solved the problem of the propagation, throughout an anelastic medium, of a signal generated by a finite dimensions seismic source: the shear dislocation fault of BRUNE (1970). Analyzing theoretical rise time vs. travel-time curves, we were able to distinguish two different corner frequency ranges in which the trend is different. When corner frequency is below 10 Hz the discrepancies with the rise time method increase with a decrease of the corner frequency. When corner frequency is above 10 Hz no meaningful differences are observed. The application of the model to a synthetic data set, based on the sources-receivers configuration of the 15 November 1995 Border Town, Nevada, earthquake sequence, shows that a significant bias affects Q estimates obtained with the rise time method, for seismic events characterized by a Brune corner frequency less than 5 Hz.