Estimating statistical parameters of an elastic random medium from traveltime fluctuations of refracted waves

Traveltime fluctuations of diving-type refracted waves are studied in the framework of geometrical optics in order to estimate the statistical parameters of an elastic random medium. A stratified background medium is considered in which the velocity increases linearly with depth. Smooth and strongly anisomeric (statistically anisotropic) inhomogeneities are embedded in this medium. The covariance and the variance of traveltime fluctuations are derived and subsequently used to estimate the standard deviation of the medium fluctuations and the inhomogeneity scale lengths in horizontal and vertical directions. The theoretical estimation procedure is verified by performing numerical calculations and it is observed that, under the considered conditions, the traveltime variance decreases at large offsets. This new phenomenon has not been observed before either in acoustics and optics, or in radio wave propagation.

[1]  Bertrand Iooss.  Seismic reflection traveltimes in two-dimensional statistically anisotropic random media , 1998 .

[2]  R. A. Silverman,et al.  Wave Propagation in a Turbulent Medium , 1961 .

[3]  Guust Nolet,et al.  Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana–doughnut paradox , 1999 .

[4]  B. Iooss,et al.  Statistical moments of travel times at second order in isotropic and anisotropic random media , 2000 .

[5]  R. Snieder,et al.  The effect of small-scale heterogeneity on the arrival time of waves , 2001 .

[6]  Robert W. Clayton,et al.  Finite difference simulations of seismic scattering: Implications for the propagation of short‐period seismic waves in the crust and models of crustal heterogeneity , 1986 .

[7]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[8]  Guust Nolet,et al.  Wave front healing and the evolution of seismic delay times , 2000 .

[9]  Statistical interpretation of traveltime fluctuations , 1997 .

[10]  G. Müller,et al.  Seismic-wave traveltimes in random media , 1992 .

[11]  F. Dahlen,et al.  Traveltimes of waves in three-dimensional random media , 2003 .

[12]  H. Marquering,et al.  Diffraction effects upon finite‐frequency travel times: A simple 2‐D example , 1998 .

[13]  Olafur Gudmundsson,et al.  Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data , 1990 .

[14]  Stefan Buske,et al.  Statistical properties of reflection traveltimes in 3-D randomly inhomogeneous and anisomeric media , 2003 .

[15]  O. Witte,et al.  Ray tracing in random media , 1996 .

[16]  Richard A. Silverman,et al.  Wave Propagation in a Random Medium , 1960 .

[17]  V. I. Tatarskii.  The effects of the turbulent atmosphere on wave propagation , 1971 .