Quasi-wavelet cascade models for intermittent random media and application to wave scattering

Terrestrial environments often possess intermittent distributions of scattering objects. Examples include atmospheric turbulence, subsurface geology, vegetation, and buildings. A quasi-wavelet (QW) cascade process model for such intermittent random media is described, and the implications for wave scattering are examined. The QW model builds the random medium from randomly positioned and oriented, wavelet-like entities, which follow prescribed distributions for number density and energy vs spatial scale. Different types of QWs, including monopole and dipole scalar fields and toroidal and poloidal vector fields, can be combined with statistically preferred orientations to create multiple field properties possessing correlated properties and anisotropy. The spatially localized nature of the QWs facilitates construction of intermittent random fields in a manner that would be extremely challenging, if not impossible, with conventional Fourier approaches. To test the QW model, we conducted a seismic propagation experiment in the vicinity of a volcanic crater in the Mojave Desert. This site was chosen for its highly inhomogeneous, intermittent distribution of basalt and sand. Propagation of impulse signals was sampled along 864 distinct paths. Statistical distributions of seismic travel times were simulated with good success using a finite-difference, time-domain method applied to a QW model for the site geology.