A thermodynamical model for paleomagnetism in Earth’s crust

Abstract

A thermodynamically consistent model for soft deformable viscoelastic magnets is formulated in actual space (Eulerian) coordinates. The possibility of a ferro-paramagnetic-type (or ferri-antiferromagnetic) transition exploiting the Landau phase-transition theory as well as mechanical melting or solidification is considered, being motivated and applicable to paleomagnetism (involving both thermo- and isothermal and viscous remanent magnetization) in rocks in Earth’s crust and to rock-magma transition. The temperature-dependent Jeffreys rheology in the deviatoric part combined with the Kelvin-Voigt rheology in the spherical (volumetric) part is used. The energy balance and the entropy imbalance behind the model are demonstrated, and its analysis is performed by time discretization, proving existence of weak solutions.

Pore Pressure Drop During Dynamic Rupture and Conditions for Dilatancy Hardening

“…We will derive an evolution equation for fluid pressure within a deforming porous medium. The evolution equation (Equation 9) has been derived in a similar form previously (Goren et al., 2011; Samuelson et al., 2009; Segall & Rice, 1995; Walder & Nur, 1984), but we re‐derive it here once again to stress it should contain a material derivative instead of a partial derivative (see also Kelka et al., 2017; Roubíček, 2022). Using the material derivative adds the convection term and allows to describe, for example, an incompressible fluid flow associated with a non‐uniform density distribution.…”