Synthesizing coherence loss by atmospheric turbulence in virtual microphone array signals

Phased microphone array methods are increasingly used to localize and quantify noise sources of aircraft under flight condition. However, beamforming results suffer from loss of image resolution and corruption of sound levels due to atmospheric turbulence causing coherence loss between microphones. A synthesis method is presented that reproduces these effects in a virtual environment. Sound propagation through turbulent atmosphere is described by models by Ostashev and Wilson and by von Kármán turbulence spectra. Spatial coherence is calculated based on the parabolic equation for statistically inhomogeneous, isotropic turbulence. Decorrelation of signals is achieved by time-varying mixing of mutually independent signals with identical PSD based on coherence factors. The concept of auralization is employed to account for propagation delay, geometrical spreading, Doppler effect, air absorption, and ground effect. The application is demonstrated for a virtual 56 m aperture microphone array. The impact of different meteorological conditions on the beamforming and deconvoluted results are presented. For increasing turbulence strength, the results show decreasing sound levels and increasingly blurred images. The proposed method allows us to reproduce the effects of turbulence-induced coherence loss in phased microphone array measurements and to optimize array designs and algorithms in a virtual, controllable environment.