Calculation of particle velocity

TRACEO ignores the $\omega $ and $\rho$ factors in the calculation of particle velocity (see section 2.5). Therefore, what TRACEO presents as particle velocity is nothing more than the horizontal and vertical derivatives of acoustic pressure, multiplied by the complex unit $i$. To calculate such derivatives at a given position TRACEO performs an additional set of calculations, determining the acoustic pressure above and below the given point, and also on both sides. The points aligned along the horizontal are used to calculate the horizontal derivative at the center, using a barycentric parabolic interpolator; likewise, the points aligned along the vertical are used to calculate the vertical derivative at the center. In order to obtain an accurate approximation to the real derivatives the spacing between the points is defined, arbitrarily, as being equal to $\lambda/10$, unless the hydrophones are spaced closer than such value. The advantage of such strategy, despite its computational cost, resides on its independence of the approximation used to calculate the acoustic pressure.

Orlando Camargo Rodríguez 2012-06-21