Transformation of seismic velocity data to extract porosity and saturationvalues for rocks

For wave propagation at low frequencies in a porous medium, the Gassmann-Do menico relations are well-established for homogeneous partial saturation by a liquid. They provide the correct relations for seismic velocities in ter ms of constituent bulk and shear moduli, solid and fluid densities, porosit y and saturation. It has not been possible. however, to invert these relati ons easily to determine porosity and saturation when the seismic velocities are known. Also, the state (or distribution) of saturation, i.e., whether or not liquid and gas are homogeneously mixed in the pore space, is another important variable for reservoir evaluation. A reliable ability to determi ne the state of saturation from velocity data continues to be problematic. It is shown how transforming compressional and shear wave velocity data to the (rho/lambda,mu/lambda)-plane (where lambda and mu are the Lame paramete rs and rho is the total density) results in a set of quasi-orthogonal coord inates for porosity and liquid saturation that greatly aids in the interpre tation of seismic data for the physical parameters of most interest. A seco nd transformation of the same data then permits isolation of the liquid sat uration value. and also provides some direct information about the state of saturation. By thus replotting the data in the (lambda/mu, rho/mu)-plane, inferences can be made concerning the degree of patchy (inhomogeneous) vers us homogeneous saturation that is present in the region of the medium sampl ed by the data. Our examples include igneous and sedimentary rocks, as well as man-made porous materials. These results have potential applications in various areas of interest, including petroleum exploration and reservoir c haracterization. geothermal resource evaluation, environmental restoration monitoring, and geotechnical site characterization. (C) 2000 Acoustical Soc iety of America. [S0001-4966(00)05306-6].