Block VII: Wavenumber Integration

This block specifies the wavenumber sampling in the standard SAFARI format. The critical issues involved in selecting the wavenumber sampling is described in the SAFARI manual [4], but even more detailed in Computational Ocean Acoustics [3]. The structure of this input block is as follows:

CMIN:

Minimum phase velocity in m/s. Determines the upper limit of the truncated horizontal wave- number space:

CMAX:

Maximum phase velocity in m/s. Determines the lower limit of the truncated horizontal wave- number space:

In plane geometry ( option P ) CMAX may be specified as negative. In this case, the negative wavenumber spectrum will be included with k_min=-k_max, yielding correct solution also at zero range. In contrast to SAFARI, OAST allows for complex contour integration (option J) in this case.

NW:

Number of sampling points in wavenumber space. Should be an integer power of 2, i.e. NWN=2^m. The sampling points are placed equidistantly in the truncated wavenumber space determined by CMIN and CMAX.

IC1:

Number of the first sampling point, where the calculation is to be performed. If IC1>1, then the Hankel transform is zeroed for sampling points 1,2IC1-1, and the discontinuity is smoothed.

IC2:

Number of the last sampling point where the calculation is to be performed. If IC2<NWN, then the Hankel transform is zeroed for sampling points IC2+1,NW, and the discontinuity is smoothed by Hermite polynomial extrapolation.

Automatic wavenumber sampling

OAST Version 1.5 has been supplied with an automatic sampling feature, making it possible for inexperienced users to obtain correct answers in the first attempt without the usual convergence testing. The automatic sampling is activated by specifying the parameter NW = -1 and it automatically activates the complex wavenumber integration contour even though option J may not have been specified. The parameters IC1 and IC2 have no effect if the automatic sampling is selected.

As an example, to run the SAFARI-FIP case 2 problem with automatic sampling, change the data file as follows:

SAFARI-FIP case 2. Auto sampling.
N I T J Z
30 30 1 0
5
  0    0     0 0   0   0   0
  0 1500 -1480 0   0   1   0
 30 1480 -1490 0   0   1   0
100 1600   400 0.2 0.5 1.8 0
120 1800   600 0.1 0.2 2.0 0
50
100 100 1 1
1300 1E8                       # CMIN = 1300
-1 0 0                         # NW   =   -1
 0  5 20  1
20 80 12 10
1450 1550 10 25
   0  100 10 20