Abstract

Rock-physics models are often needed to interpret fluid signatures from subsurface seismic data. Over the last decade or so, generalized fluid- and solid-substitution equations have been derived for estimating the exact change in seismic velocity or rock moduli upon changes in properties of quasisolids (e.g., heavy oil, bitumen, kerogen, ice, and salt) for the specified model conditions. However, these exact and mathematically elegant substitution equations fundamentally require details of rock microstructure, which are seldom known. Still, for problems involving solid or fluid substitution in rocks with heterogeneous pores, a rigorous solution range can be predicted using recently derived substitution bounds. These bounds only require total rock porosity, which can be inferred easily from geophysical data. In fact, Gassmann's equations are one of the lower bounds on the change in rock moduli upon fluid substitution, but, for solid substitution, Gassmann's predictions can be outside the bounds. Thus, for solid substitution, the lower bound itself is a better model than Gassmann. If additional microstructural parameters are known, it is possible to further constrain solid substitution or fluid substitution for heterogeneous rocks using the solid-squirt models. The solution range can be further constrained using additional effective moduli measurements of the same rock but filled with materials of varied elastic properties.

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