Signal and reverberation formulae including refraction
Because reverberation is an incoherent process it is possible to base realistic solutions on very simple flux theory. This report extends the closed-form signal and reverberation formulae of an earlier report [SACLANTCEN SR-356] to include upward or downward refraction with potentially different scattering properties and boundary losses at each boundary. The inclusion of refraction is important for the credibility of these formulae although the additional effects are considered to be minor. This report covers two-way propagation, target echoes and reverberation in a range-independent environment, giving explicit closed-form solutions for signal-to-background. Typically these formulae can be evaluated in one line of computer code, and example plots are given. The solutions are given in two forms, one incorporating true focusing effects, the other simplified by merely adding one spherical spreading term for each eigenray. In all circumstances the simple solution performs very well, and in most itobviates the need for consideration of focusing.
Harrison, Chris H.