Abstract:
Parametric sonar is widely used for sea-floor characterization, sub-bottom object detection, or underwater communication. It takes advantage of the interaction between two primary beams transmitted at slightly different frequencies. Due to nonlinear propagation, two secondary beams at the sum and difference frequency are generated. The radiation at the difference frequency combines sub-bottom penetration due to low attenuation, and high resolution due to an acoustic beam with a narrow mainlobe and negligible sidelobes. It allows to generate directive low frequency beams with transducers of reasonable size. A method that estimates the pressure level and the beam profile of the radiation at the sum and difference frequencies is presented. It solves the Westervelt equation in the frequency domain under the quasi-linear approximation. A full three dimensional estimate of the radiated fields can be computed at any depth without the need for stepwise propagation from the source plane. The method applies to two dimensional transducers of arbitrary geometry and distribution. It does not rely on the parabolic approximation and is not limited to monochromatic radiations, thus allowing to model pulses with wide bandwidth. The limits of the method come from the assumptions of a homogeneous medium and input pressure levels sufficiently low to satisfy the quasi-linear approximation. The obtained results in the case of a flat piston transducer compare favorably to previous measurements and numerical estimates from proven methods.