Self-affine fractal distributions of the bulk density, elastic moduli, and seismic wave velocities of rock

The scale dependence of the bulk density rho and seismic wave velocities V-p and V-s and the possibility of the existence of long-range correlations in such properties in field-scale porous media (FSPM) are investigated. We analyze measured data for rho, V-p, and V-s for nine FSPM, using the maximum entropy method and the wavelet decomposition technique. The analysis indicates the existence of long-range correlations in the data, characterized by self-affine fractal distributions that follow the statistics of the fractional Brownian motion. Therefore, the elastic moduli of the FSPM should also be fractally distributed and contain long-range correlations; our analysis confirms this. The implications of the results for modeling elastic moduli of porous rock, fracture propagation in FSPM, and the interpretation of seismic wave recordings of FSPM are discussed, and the possible deviations from the classical analysis of such phenomena are pointed out.