Fractal wavefield analysis to characterize geometric properties of fractured media

We have investigated wave scattering by chaotic fractured systems of fractal geometry with random spatial variation that causes energy loss of the directly propagated field. We have examined simple analytic solutions in fractal poroelastic media. These solutions may be characterized by their frequency- power- law ( FPL) signature caused by wave dispersion and attenuation. It has been proved that medium memory effects cause smoothing of the wavefield in the vicinity of the wavefront and rapid amplitude decay far from the wavefront. It appears that finite-bandwidth signals are delayed with respect to the wavefront in comparable elastic media. To examine the FPL dependence of direct body waves propagating in a homogeneous medium containing fractal inhomogeneities, we compute acoustic finite-difference snapshots in the frequency range f = 20 - 200Hz. Numerical results show that the fractal dimension can be estimated from the FPL dependence of the scattered wavefield. Applications to fracture characterization are considered. Results are important for multi- scale depth imaging, inverse Q filtering, fracture detection, and integrated geophysical reservoir monitoring.