We have shown that seismic/sonic velocity data can be transformed to polar coordinates that have quasi-orthogonal dependence on saturation and porosity. This observation is based on the Gassmann-Domenico relations, which are known to be valid at low frequencies. The transformation loses its effectiveness at high frequencies whenever dispersion becomes significant, because then Biot theory and/or other effects play important roles in determining the velocities. So, the simple relations between vp, vs, and , , ,and S break down at high frequencies. Our results are, nevertheless, quite encouraging because the predicted relationships seem to work in many cases up to frequencies of 1 kHz, and in a few special cases to still higher frequencies. These results present a straightforward method for obtaining porosity, saturation, and some information about spatial distribution of fluid (i.e., patchy versus homogeneous) in porous rocks and sediments, from compressional and shear wave velocity data alone. These results have potential applications in various areas of interest, including petroleum exploration and reservoir characterization, geothermal resource evaluation, environmental restoration monitoring, and geotechnical site characterization. The methods may also provide physical insight suggesting new approaches to AVO data analysis.