Acoustic particle velocity and intensity calculations from tri-axial pressure gradient measurements

Abstract

In July 2004 Fisheries and Oceans Canada supported a study to investigate effects of seismic airgun signals on hearing organs of freshwater fish in the Mackenzie River at Inuvik, NWT Canada. The study required particle velocity measurements for correlation with observed biological effects. JASCO Research built a pressure gradient measurement apparatus consisting of four hydrophones mounted at the vertices of a triangular-pyramid frame. The system was used to measure differential pressure from the airgun events simultaneously in three perpendicular axial directions. An attached depth-compass sensor monitored the depth and orientation of the system. Hydrophone separations were chosen to be small relative to the acoustic wavelength so that measured differential pressures correctly approximated the pressure gradients along each axis. Particle accelerations were computed directly from pressure gradients following Euler’s linearized momentum equation, and particle velocities were computed by integrating particle accelerations. Acoustic intensity was computed from the product of acoustic pressure and particle velocity. The hydrophone precision imposed a limit on accuracy of particle velocity measurements at low frequencies. Likewise the fixed hydrophone spacings defined an upper frequency limit for applicability of this method.