GEOMETRICAL OPTICS OF ACOUSTIC MEDIA WITH ANISOMETRIC RANDOM HETEROGENEITIES: TRAVEL-TIME STATISTICS OF REFLECTED AND REFRACTED WAVES


Kaslilar A. , KRAVTSOV Y. A. , SHAPIRO S. A.

ADVANCES IN GEOPHYSICS, VOL 50, cilt.50, ss.95-121, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 50
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/s0065-2687(08)00004-6
  • Dergi Adı: ADVANCES IN GEOPHYSICS, VOL 50
  • Sayfa Sayıları: ss.95-121

Özet

When deterministic methods become insufficient to resolve the complexity of a medium, Statistical investigation becomes necessary. This helps to characterize the medium by its statistical parameters such as mean value, standard deviation, correlation function, and correlation distance. In this chapter, we develop a Formalism based on geometrical optics (GO), which allows its to estimate the statistical parameters (the standard deviation and the inhomogeneity scale lengths in vertical and horizontal directions) from travel-time fluctuations of reflected and refracted seismic waves. We consider a three-dimensional random clastic medium with quasi-homogeneous statistics and anisometric (statistically anisotropic) inhomogeneities. We derive the covariance and the variance functions which are fundamental to estimate the statistical parameters. For the reflection geometry, we reconfirm the double passage effect (DPE) of the travel-lime variance quadruplicating at zero offsets, For the refraction geometry, we observe a closely related but a new phenomenon - the reduction of travel-time variance in large offsets, which lilts not yet been described before. We propose it procedure for estimating the statistical parameters of the medium from travel-time fluctuations of refracted waves. The procedure is illustrated by the numerical simulations of the random refractive medium.