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Finite Strain Analysis of Shear and Compressional Wave Velocities
Author(s) -
MelingerCohen Ariel,
Jeanloz Raymond
Publication year - 2019
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1029/2019jb017868
Subject(s) - eulerian path , finite strain theory , shear (geology) , shear modulus , bulk modulus , mechanics , elasticity (physics) , geology , classical mechanics , materials science , physics , thermodynamics , finite element method , mathematics , mathematical analysis , lagrangian , composite material
Published shear‐modulus measurements for a wide variety of materials (Ar, Xe, H 2 , He, NaCl, H 2 O‐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.