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WITHDRAWN Volume Collapse Instabilities in a Phase Transformation Under High Pressure Yield a Double Couple Deep Earthquake Driven by the Pressure

Description: 

W/D The deep-focus earthquakes(DFEs) (400-700kms) are events involving the nucleation and growth of phase transformations under high pressure for which instabilities occur as to minimize the energy spent to move the boundary of phase discontinuity. While in the problem of Randall (Bull Seism. Soc. Am., 1964) a sudden volume change preserves symmetry, expands spherically emitting pressure waves, under high pressure also exists a symmetry-breaking unstable solution. It was shown (Markenscoff, J. Mech. Phys. Sol.(2021),152,104379) that high-pressure phase transformations can emit the elastic waves of a shear source with little or no volumetric component, even under conditions of material and pre-stress isotropy. Due to instability at a critical nucleation pressure, an arbitrarily small densified region generated in the shape of a pancake-like flattened ellipsoid nucleates and grows, expanding self-similarly at constant potential energy, while driven by the pressure acting on the change in volume. Deviatoric stresses are developed to maintain material continuity, as the large volume collapse is accommodated in the thin inclusion, and the energy can radiate out in the only possible way as a Double Couple (DC). The DC radiation is consistent with the vast majority of observations of DFEs and the radiated energy entailing a “pressure drop” explains their large energies, while the model explains the range of appearance of the DFEs with depth in the Mantle. The mathematical modeling is based on properties of the self-similarly expanding ellipsoidal inclusion with transformation strain (dynamic Eshelby problem), which possesses the lacuna property of zero particle velocity in the interior domain allowing the phase transformation to take place under equilibrium conditions, while the growth energetics are derived through Noether’s theorem (M integral). The Eshelby solution and lacuna property are also valid for Newtonian fluids and the analysis of the instabilities could be extended to account also for coupling with dehydration. The instabilities are applicable to other phenomena, e.g., amorphization, planetary impacts, etc.

Session: Structure and Properties of Subducting Slabs and Deep Earthquakes [Poster]

Type: Poster

Date: 4/19/2023

Presentation Time: 08:00 AM (local time)

Presenting Author: Xanthippi Markenscoff

Student Presenter: No

Invited Presentation: 

Authors