Modeling reflections from rough surfaces in complex spaces

Abstract

Acoustic reflections from rough surfaces occur both in indoor and outdoor environments. Detailed modeling of such reflections is possible with wave-based modeling algorithms. However, their time and resource consumption limits the applicability of such algorithms in practical modeling tasks where the modeled space is large or even unbounded. On the other hand, geometrical acoustics modeling techniques are more efficient in most cases, but they are not able to capture the wave interaction with the rough surface. The presented solution combines a geometric modeling algorithm with a theoretical model of the rough surface. The geometric algorithm is an efficient beam tracer. The theoretical model assumes long wavelength compared to the dimensions of the surface details. The model shows that the effect of the rough surface can be approximated with a exponential decay tail after an impulse in the time domain impulse response. A further approximation is to present multiple such reflections with a decay resembling a gamma distribution. Several complex example cases with a large number of reflections are shown. In addition, comparison of the theoretical model to finite-difference time-domain algorithm modeling results is given. The results support the applicability of the presented approach to practical modeling tasks.