The variation of seismic velocities within a simplified earth model, in accordance with the theory of finite strain*

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Abstract
Murnaghan's theory of finite strain has been applied in an approximate form to a study of the density and velocity variations in a simplified model of the earth outside the core, the model consisting of two homogeneous layers, each at a uniform temperature. Following Jeffreys, the layers are separated by a first-order discontinuity at a depth of 474 km. Above 474 km., the variations of the velocities in this model are shown to be practically the same as Jeffreys' “observed” values. The main features of the velocity-depth curves are represented with fair precision down to the core. This is of course no longer true if the velocities are supposed to vary continuously through the 474-km. level. Whichever supposition be held, if the rate of change of velocity immediately below 474 km. is to be reproduced closely, a gradual change of composition must be introduced. The variation of density upon the two-layer supposition is very close to that derived by Jeffreys and by Bullen by numerical integration of the “observed” velocities, on the supposition of adiabatic compression of homogeneous layers. The validity of their method is shown to depend upon the existence of a small temperature gradient, or of compensating factors which cannot be evaluated. It is suggested that a more rigorous solution of the equations of motion derived from the theory of finite strain might prove of value in interpreting the oscillatory character of seismic records, as well as the direction of the ground motion associated with various wave types.

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