Effective seismic wave velocities and attenuation in partially molten rocks

Abstract

Significant reduction in mechanical properties, i.e., elastic moduli and seismic wave velocities, as well as enhanced inelastic attenuation is often associated with areas of partially molten rocks. In this paper we suggest a new mechanism responsible for significant reduction of wave velocity and enhanced attenuation. The suggested mechanism considers solid-melt phase transition at thermodynamic equilibrium. Any pressure change, that takes the system out of thermodynamic equilibrium, causes solidification or melting which modifies the heat balance according to the Clausius-Clapeyron equation. The latent heat (sink or source) is transferred away or towards the interface by conductive-advective mechanism, heating or cooling the entire rock mass, and leading to energy loss and dissipation of the mechanical energy and to seismic wave attenuation. We use simplified geometry and derive analytical solutions for wave velocity reduction and attenuation associated with a moving solid-melt interface (Stefan problem). We demonstrate that the latent heat generation due to wave-induced pressure oscillations around thermodynamic equilibrium is an efficient mechanism for energy dissipation and leads to significant reduction in mechanical properties (seismic velocities and attenuation). The highest attenuation occurs when the period of oscillation is close to the heat transfer time-scale associated with the size of melt inclusions. The predicted values are approximately in agreement with large scale seismological observations, showing that seismic waves are mostly attenuated within the shallow parts of Earth's crust and mantle, and are associated with possible presence of melt.