A general analytical expression for thetime-dependentmean-square incoherent field scatteredfromorthrough(penetrating) a 2-D fluid–fluid rough interface for a narrow-band incident plane-wave source is derived and expressed in terms of the second moment of the rough interfaceT-matrix. This analytical expression is independent of the scattering solution technique, and for distances greater than only a few wavelengths from the interface, is equivalently expressed in terms of the bistatic scattering cross section per unit area per unit solid angle (differential cross section) of the rough interface. Using this rigorously derived result, the scattered field for a narrow-band point source is heuristically derived. This derivation leads to the usual sonar equation in the limit as the narrow-band signal approaches the cw (continuous wave) case. First-order perturbation calculations for the case of a baseband Gaussian shaped source pulse illustrate narrow-band pulse dispersion effects of the incoherent field for forward scattering into a lossy sediment. For the case of incidence below the critical grazing angle, first-order perturbation computations also show that the incoherent field scattered through a rough interface can be much greater than the zeroth-order field (coherent) transmitted below the corresponding flat-surface depending on loss and receiver depth. These computations for the first-order mean square incoherent field penetrating the rough interface are compared to the results for the flat-surface case, for both plane-wave and point sources.