Hierarchical model for the scale-dependent velocity of seismic waves

Details Hierarchical model for the scale-dependent velocity of seismic waves Hierarchical model for the scale-dependent velocity of seismic waves

1999-11-05

arxiv.org/abs/cond-mat/9911075v1

Phys.Rev.Lett. 85, 674 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages including 3 figures

Scientific paper

10.1103/PhysRevLett.85.674

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.

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