The spatial distribution of deep earthquakes remains elusive, as the earthquakes below 30 km depth cannot be explained using the brittle frictional processes due to the fluid behavior of rocks under high pressure and temperature conditions. Several models that have been developed to identify the source distribution fall largely into categories like negative buoyancy and viscous friction to the flow, anti-crack faulting due to metastable olivine, volume reductions from phase transformations etc. Still none of them were able to satisfactorily explain the spatial distribution of deep earthquakes. We propose a new method using the visco-elastic nature of the earth material to model the deformation, stress, and elastic energy of the subducting lithosphere using “Marker in cell method” in combination with a conservative finite difference scheme. The software is written in Python and NumPy. We have tested this code for the known results of a Rayleigh–Taylor instability of solid-fluid interaction, and for a general subduction benchmark (Schmeling et al., 2008). We show a large set of numerical models in which we investigate the role of volatiles in the transition zone by varying the viscosity of the lithosphere and the presence of a high viscosity zone below the upper-lower mantle transition zone. Finally, we compare the rate of inner energy dissipation and the stored elastic energy in the subducting lithosphere with deep earthquake spatial distribution and discuss which constrains geodynamic models offer to deep earthquake location.
Schmeling, H., Babeyko, A.Y., Enns, A., Faccenna, C., Funiciell, F., Gerya, T. V., Golabek, G.J., Grigull, S., Kaus, B.J.P., Morra, G., Schmalholz, S.M., van Hunen, J., 2008. A benchmark comparison of spontaneous subduction models – Towards a free surface. Physics of the Earth and Planetary Interiors, 171, 198–223.