The dispersive velocity of compressional waves in magmatic suspensions

Abstract

SUMMARY The geophysical detection of magma bodies and the estimation of the dimensions, physical properties and the volume fraction of each phase composing the magma is required to improve the forecasting of volcanic hazards and to understand transcrustal magmatism. We develop an analytical model to calculate P waves velocity in a three-phase magma consisting of crystals and gas bubbles suspended in a viscous melt. We apply our model to calculate the speed of sound as a function of the temperature in three magmas with different chemical compositions, representative of the diversity that is encountered in arc magmatism. The model employs the coupled phase theory that explicitly accounts for the exchanges of momentum and heat between the phases. We show that the speed of sound varies nonlinearly with the frequency of an acoustic perturbation between two theoretical bounds. The dispersion of the sound in a magma results from the exchange of heat between the melt and the dispersed phases that affects the magnitude of their thermal expansions. The lower bound of the sound speed occurs at low frequencies for which all the constituents can be considered in thermal equilibrium, whereas the upper bound occurs at high frequencies for which the exchange of heat between the phases may be neglected. The presence of gas in a magma produces a sharp decrease in the velocity of compressional waves and generates conditions in which the dispersion of the sound is significant at the frequencies usually considered in geophysics. Finally, we compare the estimates of our model with the ones from published relationships. Differences are largest at higher frequencies and are <10 per cent for typical magma.