Wedge_volume_sampled

This analysis variable shows the volumes of a wedge which includes the analysis domain.

The wedge volume of a single ping within the analysis domain is calculated as:

where:

l	= the length of the analysis domain (as measured along the cruise track, see notes below) (m)
N	= The number of pings in the analysis domain being analyzed (-)
f	= the across track beam angle, specified on the Calibration page of the Variable Properties dialog box. By default the value is obtained from the MajorAxis3dBBeamAngle. However, in situations where the across track beam angle is not the same as the Major axis 3dB beam angle, the setting WedgeVolumeBeamAngle can be specified to override MajorAxis3dBBeamAngle.
Ri	= the range (measured along the beam axis of the ping) of a transition between in-domain and out-of-domain space (m)
R0	= the range (measured along the beam axis of the ping) to the start of the analysis domain (m)
Rn	= the range (measured along the beam axis of the ping) to the end of the analysis domain (m)
	=
		0 if the samples in the interval interval between Ri and Ri+1 are in the analysis domain but excluded from the analysis
		1 Otherwise

where:

N = The number of pings in the analysis domain being analyzed
Vp = The volume of ping p - as above (m3)

Notes:

Wedge_volume_sampled does not represent the sampled volume of water, but an approximation thereof with simplifying assumptions.
Calculation of Wedge_volume_sampled assumes that the variable (or echogram) contains individual pings. The results of this calculation will not be valid for resampled, integrated or otherwise reduced pings.
The calculation assumes straight line travel over the analysis domain and a uniform vessel speed and ping rate.
The distance l is estimated as the distance between two points P1 and P2 defined as follows:
- if there is a ping before the analysis domain then P1 is the position midway between the first ping in the analysis domain and the previous ping, otherwise P1 is the position calculated in this same manner assuming there is a ping before the analysis domain equally far from the first ping as is the second ping.
- if there is a ping after the analysis domain then P2 is the position midway between the last ping in the analysis domain and the next ping, otherwise P2 is the position calculated in this same manner assuming there is a ping after the analysis domain equally far from the last ping as is the second last ping.
This algorithm is taken from Kieser and Mulligan (1984)