Аннотация
For wave propagation at low frequencies in a porous medium, the Gassmann-Domenico
relations are well-established for homogeneous partial saturation
by a liquid. They provide the correct relations for seismic velocities
in terms of constituent bulk and shear moduli, solid and fluid densities,
porosity and saturation. It has not been possible, however, to invert
these relations 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 determine 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 Lamé parameters and rho is the total
density) results in a set of quasi-orthogonal coordinates for porosity
and liquid saturation that greatly aids in the interpretation of
seismic data for the physical parameters of most interest. A second
transformation of the same data then permits isolation of the liquid
saturation 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) versus homogeneous saturation that is present in
the region of the medium sampled 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 characterization, geothermal
resource evaluation, environmental restoration monitoring, and geotechnical
site characterization.
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