Seismic attenuation in a phase change coexistence loop

Most phase transformations in the mantle occur across regions of multi-phase coexistence. Inside these regions, the long-term incompressibility becomes very low because the density can increase both by compression and by changing phase. This difference between long-term and elastic incompressibilities is a typical situation where seismic attenuation may happen. In this paper, we discuss the various differences between the classical theory of sound attenuation in a reacting fluid and the case of seismic propagation in a two-phase loop. We derive a simple analytical model of a two-phase loop to show that the phase change should affect both the bulk and the shear attenuation and in rather similar proportion. We show that attenuation occurs over two different frequency ranges. For the olivine–wadsleyite phase change, the low frequency attenuation occurs for periods larger than hundreds of years but the high frequency band occurs between 1 min and 1 h (from 16 to 0.27 mHz) in the domain of surface waves and seismic modes. We predict both bulk and shear quality factors between 1 and 10 in the middle of the 410 km phase loop.