### Acoustic Calculations

*Propagation*

A ray-theoretic code has been developed for the calculation of the acoustic field, in particular transmission loss versus range and depth, and intensity of the scattered field at the bottom versus range. 3D coverage is obtained by solving the propagation problem along 36 vertical range-dependent sections extending radially around the source location in angle steps of 10°, as well as 36 similar sections around the receiver location .

*Reverberation*

The bistatic reverberation is calculated by combining the transmission loss and scattered field intensity results provided by the propagation code. The contributions of the scattered field at the bottom are integrated along ellipses having the source and receiver locations as focal points, taking into account the directional characteristics (directivity pattern, steering angle) of the receiver.

*Directivity*

In the current version of the system the acoustic source is assumed to be omnidirectional while the reception is considered to be directional, and subject to beam steering. The directivity pattern and the resulting directivity index is calculated at any steering angle of the array by applying spatial filtering – beamforming.

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*Probability of
Detection*

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Using the results of the above calculations and the operational characteristics of the involved platforms (source, target, receiver) the signal-to-noise and signal-to-reverberation ratios at the beamformer output are calculated for each target location. Then the probability of detection is calculated using receiver operating characteristics (ROC curves) for energy or matched-filter detection.