Modeling acoustic vector fields for inverse problems

Acoustic vector sensors that measure pressure and orthogonal particle velocity are gaining widespread interest. Predicting their performance requires calculating the pressure field and the velocity fields, which require spatial gradients of the pressure field. In typical hydrophone applications, significant computational savings are realized by using reciprocity to generate the pressure field as a function of source position rather than receive position. However, the presence of the spatial gradients in the velocity fields means that reciprocity cannot be used to model the vector field for inverse problems. Instead, the inverse vector velocity field must be computed point by point, even for the simplest environments. Examples of this effect are demonstrated by the derivation of analytic expressions for pressure and particle velocity in a Pekeris waveguide. These simple waveguide results are extended to arbitrary, range-dependent, environment parameters using a parabolic equation model.