Finite Strain Analysis of Shear and Compressional Wave Velocities

Abstract

Published shear-modulus measurements for a wide variety of materials (Ar, Xe, H2, He, NaCl, H2O-VII, MgO, stishovite, bridgmanite) show that the Eulerian (spatial) description of energy vs. strain fits both finite- and infinitesimal-strain (e.g., wave velocity) elasticity data under high pressure. The Eulerian (spatial) formulations do so better than the Lagrangian (material) finite-strain description, with differences of 1% to 60% in both P- and S-wave velocities for these materials at the pressures of Earth's mantle. The results are significant in extending to shear previous findings that compressional (pressure-volume and bulk-modulus) measurements are also best fit using the spatial formulation. Our analysis empirically documents that a self-consistent Eulerian finite-strain equation of state offers a reliable means of describing the thermodynamic and elastic properties of planetary interiors.