Finite strain theories and comparisons with seismological data

@article{Stacey1981FiniteST,
  title={Finite strain theories and comparisons with seismological data},
  author={Frank D. Stacey and B. J. Brennan and R. D. Irvine},
  journal={Geophysical surveys},
  year={1981},
  volume={4},
  pages={189-232}
}
All the finite strain equations that we are aware of that are worth considering in connection with the interior of the Earth are given, with the assumptions on which they are based and corresponding relationships for incompressibility and its pressure derivatives in terms of density. In several cases, equations which have been presented as new or independent are shown to be particular examples of more general equations that are already familiar. Relationships for deriving finite strain… Expand
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References

SHOWING 1-10 OF 52 REFERENCES
A Seismic Equation of State
Birch's hypothesis of a close relationship between seismic velocity and density is extended and modified so as to be in accord with theoretical predictions concerning the form of the equation ofExpand
Equation of state fits to the lower mantle and outer core
The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data.Expand
Elasticity and constitution of the Earth's interior
The observed variation of the seismic velocities with depth, below the crust, is examined with reference to the variation to be expected in a homogeneous medium. A general equation is derived for theExpand
Application of the equation of state to the Earth's lower mantle
Abstract For the Earth's lower mantle an empirical expression of the Poisson ratio is newly developed to supplement “Model 1” which consists of a set of three-parameter approximating functions forExpand
Parametrically simple earth models consistent with geophysical data
Abstract We present a set of three parametric earth models (PEM) in which radial variations of the density and velocities are represented by piecewise continuous analytical functions of radiusExpand
Evidence supporting the approximation γρ = const for the Grüneisen parameter of the Earth's lower mantle
There has been no uniform acceptance of one theoretical formulation of the Gruneisen parameter formula over another. The application of a Gruneisen function to the earth's interior for temperatureExpand
Homogeneity and Constitution of the Earth's Lower Mantle and Outer Core
The lower mantle and outer core of the recent “parametric earth model” (PEM), in which the velocity and density distributions in these regions are both smooth and consistent with the Adams-WilliamsonExpand
Applications of thermodynamics to fundamental earth physics
New fundamental thermodynamic relationships of complete generality and absolute rigour of derivation are not to be expected, because the subject has such a secure and complete basis in classicalExpand
A thermodynamically based equation of state for the lower mantle
An observation by O. L. Anderson that for close-packed minerals, (∂KT/∂T)V = 0, approximately, implies without further assumption the Birch relationship (αKT)T = const, to a similar approximation. AtExpand
Application of isotropic finite strain theory to ultrasonic and seismological data
The finite strain expressions, originally derived by F. Birch (1938), for the compressional and shear velocities in an isotropic solid under hydrostatic pressure, when rederived to be complete toExpand
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2
3
4
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...