A wave field extrapolation approach to acoustical modeling in enclosed spaces

In practice, impulse responses in enclosed spaces are calculated with algor ithms that are based on the ray tracing model, the mirror image source mode l, or a mixture of both. Using those algorithms. however, the wave characte r of sound propagation is not properly taken into account and complex bound aries cannot be included. This paper presents an alternative approach adopt ed from the seismic imaging field. The proposed model is based on the conce pt of wave field extrapolation. Absorption properties of the boundaries can be specified in detail by means of reflection matrices. Propagation betwee n boundaries is formulated by propagation matrices. Impulse responses along an array of receivers are numerically simulated by executing a sequence of matrix multiplications that can be interpreted as generalized spatial conv olutions. Diffraction phenomena due to the finiteness and irregularity of t he boundaries are correctly taken into account. The proposed algorithm is i llustrated on a two-dimensional configuration. Results are compared with th ose of conventional models and with measured data. A discussion on computin g time is included. In addition, the proposed algorithm leads to new direct ions in the analysis of measurements in enclosed spaces. The proposed algor ithm implies a new concept for dereverberation of recordings that are made in complex acoustic surroundings, using microphone arrays. (C) 1999 Acousti cal Society of America. [S0001-4966(99)03203-8].