A small resistive axisymmetric object in the presence of an underwater point-source field

A small, acoustically resistive and axisymmetric object is placed in a deep homogeneous sea environment with a hard plane bottom. The size of the object is small when compared to the depth of the water channel. The free surface of the sea is assumed to be soft. The source and the receiver are placed on the same vertical line and far away from the object. Given the positions of the source and the receiver, two problems are solved: The determination of the pressure field at the receiver from the position and the shape of the object and the determination of the position and the shape of the object from the pressure field at the receiver. The special case of smooth axisymmetric objects, i.e. objects generated by the rotation of differentiable curves, is studied. I provide results for the case of a floating object and for the case of an object or a “hillock” at the bottom of the sea.