TITLE: How to derive this equation?
QUESTION [0 upvotes]: How to derive this equation? It comes from a book named Seismic Wave Propagation in Stratified Media.

REPLY [0 votes]: There are two forces in presence and, because the system is in equilibrium (=0), the change in one will be compensated by a change in the other.
A change in this context is decoded to 'the rate of change in relation to space: $\frac{d}{dx_i}$ '
$\frac{d\sigma}{dx_i}$ is a force per unit length and
$\frac{d\psi}{dx_i}$ is an acceleration  per unit length, times mass ($\rho_0$) is also a force per unit length (recall Newton f=m.a) and thus they can be added or subtracted.
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