We consider first an acoustic bottom half-space characterized by a single wave speed, and a density, . The general solution in the half-space is given by,

where,

and the Pekeris branch of the square root is used to expose the leaky
modes. In order to have a bounded solution at infinity, we require
**B** to vanish. At the interface, we require continuity of pressure
and normal displacement which implies,

Thus, we obtain the bottom impedance condition,

A similar procedure yields the result for a top homogeneous half-space,

which differs by a sign change. Note that by letting we obtain the free-surface boundary condition and gives the perfectly rigid boundary condition.

Tue Oct 28 13:27:38 PST 1997