Velocities of water-saturated isotropic sandstones under low frequency can be modeled using the Biot-Gassmann theory if the moduli of
dry rocks are known. On the basis of effective medium theory by Kuster
and Toksöz, bulk and shear moduli of dry sandstone are proposed. These
moduli are related to each other through a consolidation parameter and
provide a new way to calculate elastic velocities. Because this parameter
depends on differential pressure and the degree of consolidation, the
proposed moduli can be used to calculate elastic velocities of sedimentary
rocks under different in-place conditions by varying the consolidation
parameter. This theory predicts that the ratio of P-wave to S-wave velocity
(Vp/Vs) of a dry rock decreases as differential pressure increases and porosity decreases.
This pattern of behavior is similar to that of water-saturated sedimentary
rocks. If microcracks are present in sandstones, the velocity ratio usually
increases as differential pressure increases. This implies that this
theory is optimal for sandstones having intergranular porosities. Even
though the accurate behavior of the consolidation parameter with respect
to differential pressure or the degree of consolidation is not known,
this theory presents a new way to predict S-wave velocity from P-wave
velocity and porosity and to calculate elastic velocities of gas-hydrate-bearing
sediments. For given properties of sandstones such as bulk and shear
moduli of matrix, only the consolidation parameter affects velocities,
and this parameter can be estimated directly from the measurements; thus,
the prediction of S-wave velocity is accurate, reflecting in-place conditions.
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