Modeling 3-D anisotropic fractal media

CONCLUSIONS

In this initial study I have tackled the forward problem for modeling anisotropic fractal media using second-order statistics. The method has close analogy with the two-dimensional Goff and Jordan model for seafloor morphology. The generation of synthetic models is done in the Fourier domain and the algorithms are similar for the one- two- and three-dimensional problems. The von Karman functions are presented as a generalization of the exponential correlation function associated with the Markov process in modeling seismic impedances. The von Karman functions can be used for better description of statistic lithology of stratigraphic columns and understanding their depositional pattern. I have also computed a two-state model (i.e., rock/pore or sandstone/shale) by mapping the random field from continuous realizations into a binary field. Comparisons of the autocorrelation functions of the continuous and binary fields show that the fractal dimension (i.e, the roughness of the medium) increases through the ``binarization'' process.