A dynamical study of frictional effect on scaling of earthquake source displacement spectra

Jeen-Hwa Wang


The scaling of earthquake source displacement spectra is analytically studied based on the continuous form of one-dimensional dynamical spring-slider model in the presence of either linearly slip-weakening friction or linearly velocity-weakening friction. The main parameters of the model are the natural angular frequency, wo, and the (dimensionless) decreasing rate, D, of friction with slip (or the characteristic displacement) for slip-weakening friction as well as the (dimensionless) decreasing rate, u, of friction with velocity (or the characteristic velocity) for velocity-weakening friction. The analytic solution includes the complementary and particular parts. The former shows the travelling wave and the latter denotes vibrations at a site. The complementary solution exhibits w-1 scaling in the whole range of w for both friction laws. For the particular solution, slip-weakening friction results in spectral amplitudes only at three values of w. For velocity-weakening friction with u>0.5, the log-log plot of spectral amplitude versus w exhibits almost w0 scaling when w is lower than the corner angular frequency, wc, which is independent on u and increases with wo. When w>wc, the spectral amplitude monotonically decreases with w following a line with a slope value of -1, which is the scaling exponent.


Source spectrum; Spring-slider model; Weakening friction; Natural frequency

Full Text:



DOI: https://doi.org/10.4401/ag-6974
We use cookies to ensure that we give you the best experience on our website. If you continue to use this site we will assume that you are happy with it (Read more).

Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X