  A model for terrestrial planets, inclusive of viscous fluid behavior and
featuring finite normal stress differences, is developed. This work offers new
insights for the interpretation of planetary survey data. Evolution equations
for poloidal and toroidal motions include gradients of density, viscosity, and
two normal stress moduli. The poloidal field exhibits gradients in the cubic
dilation, which couple non-isotropic pressures to the combined deformation
field. In contrast, the toroidal field exhibits vorticity gradients with
magnitudes proportional to the natural time. This holds even in the absence of
material gradients. Consequently, viscosity gradients are not required to drive
toroidal motions. The toroidal field is governed by an inhomogeneous diharmonic
equation, exhibiting dynamic shear localization. The strain-energy density for
this model, as a function of temperature, is found via thermodynamics. Assuming
heat transfer with characteristic diffusivity, a radial model parameterized by
thermomechanical competence is found. Shear dislocations, admissible for
thermomechanical competence greater than 1/2, are found to coincide with
supershear rupture speeds for in-plane (Mode II) cracks. This range of
thermomechanical competence coincides with depths in the crust, upper mantle
and transition zone where earthquake foci are observed. Consequently, all
seismic sources must exhibit some supershearing component. Observed variations
in Earth's gravity-topography admittance and correlation spectra, and
earthquake moment-depth release are interpreted in light of this hypothetical
structure.
