Gassmann's relations are receiving more attention as seismic data are
increasingly used for reservoir monitoring. Correct interpretation
of underground fluid migration from seismic data requires a quantitative
understanding of the relationships among the velocity data and fluid
properties in the form of fluid substitution formulas, and these
formulas are very commonly based on Gassmann's equations.
Nevertheless, confusion persists about the basic assumptions and
the derivation of Gassmann's (1951) well-known equation in poroelasticity
relating dry or drained bulk elastic constants to those for
fluid saturated and undrained conditions.
It is frequently stated, for example, but quite incorrect
to say that Gassmann *assumes* the shear modulus is
constant, *i.e.*, mechanically independent of the presence of
the saturating fluid. This note
clarifies the situation by presenting an unusually brief
derivation of Gassmann's relations that emphasizes the true origin
of the constant shear modulus *result*, while also
clarifying the role played by the shear modulus in the derivation
of the better understood result for the bulk modulus.

10/25/1999