The density perturbation is known as the * acoustic
approximation* [11].
A fluid has a pressure which is a function of density, temperature,
and gravity forces. We shall assume that the gravity forces are
relatively constant over the domain and do not
exert any differential force on the fluid.
The earth temperature field does vary as a function of
position and in time, but the temperature changes are
very small compared to the time it takes to make seismic measurements.
Hence, we will assume that only the density is important and that
the stress within the fluid is related to the strain as a function
of density.

First, is defined as the Kronecker delta function,

The stress matrix is