Determining the effect of a variable rupture velocity on the generation of high-frequency ground motion during an earthquake

Abstract

Understanding the source of high-frequency ground motion (10-50 Hz) that occurs during an earthquake is not only important from a theoretical standpoint, but from a practical standpoint as well. From the theoretical viewpoint, it can lead to improved understanding of the earthquake-source processes, correct interpretations of seismic data, and more accurate simulations of earthquake ground motions. From the practical view, knowledge of the source of high frequencies is important for earthquake engineering and the seismic-hazard prediction. The generally accepted mechanism for producing high frequencies is any change in the rupture velocity, whether smooth and consistent or abrupt and random. Here, we aim to thoroughly test this hypothesis with numerical simulations based on both the representation integral of elasticity and near-line source approximation in order to determine the true source of high-frequency ground motion. Our simulation results, based on both the representation integral and near-line source model, show that a rupture velocity varying in a consistent, non-random way does not preferentially produce high-frequency radiation. The regularity of the rupture velocity artificially causes a destructive-interference effect to occur, which suppresses these frequencies. Our results further indicate that high frequencies are only produced when the rupture is traveling with a randomly varying velocity. The highly variable and randomized rupture velocity eliminates the destructive interference caused by assuming a regular velocity law, and removes the artificial suppression, resulting in an elevated high-frequency content. We conclude that, contrary to the common assumption, not any change in the rupture velocity leads to the generation of high frequencies during earthquakes. If the velocity law is smooth and regular, the resulting radiation is fully controlled by the artificially induced interference phenomena. In reality, earthquake ruptures will always have a random component in their velocities, eliminating the artificial factors forming the radiation. It thus should be expected that realistic ruptures will always produce an elevated high-frequency content relative to their smooth counterparts. Attributing the preferential generation of high frequencies to any change in rupture velocity is incorrect.