Contents I. Introduction
A vector hydrophone consists of either two or three identical but orthogonally oriented velocity hydrophones plus a pressure hydrophone, all of which are spatially co-located in a point-like geometry [1]. In practical applications, an array with vector hydrophones is located at or near a reflecting boundary. For example, a plane array with vector hydrophones is mounted on the submarine hulls [2]; or it is mounted on the seabed in shallow water. The four-component vector hydrophone, which is located at or near a reflecting boundary, produces the following 41 array manifold [3]: {\bf h}(\theta_k,\phi_k) = \left[\matrix{ (1+{\cal R}(\theta_{k})e^{-{i}\vartheta_{k}}){u}(\theta_{k},\phi_{k})\cr (1+{\cal R}(\theta_{k})e^{-{i}\vartheta_{k}}){v}(\theta_{k},\phi_{k})\cr (1-{\cal R}(\theta_{k})e^{-{i}\vartheta_{k}}){w}(\theta_{k})\cr (1+{\cal R}(\theta_{k})e^{-{i}\vartheta_{k}})}\right] \eqno{\hbox{(1)}} where is the direction cosine along the axis, is the direction cosine along the axis, is the direction cosine along the axis, denotes the th source's elevation angle measured from the vertical axis, and denotes azimuth angle. , and denotes the vertical distance between the vector hydrophone array and the reflecting boundary, and which is in the unit of wavelength. is the (complex) reflection coefficient, which specifies the attenuation and phase change of the reflected wave. By our choice of a coordinate system, the incident angle is just ; therefore, for a given frequency, is a function of but not .
