Block VII: Wavenumber integration

This block specifies the wavenumber sampling in the standard SAFARI format, with the significance of the parameters being as follows:

CMIN:

Minimum phase velocity in m/s. Determines the upper limit of the truncated horizontal wavenumber 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, OASP allows for complex contour integration (option J) in this case.

NW:

Number of sampling points in wavenumber space. In contrast to what is the case for OAST, NW does here not have to be an integer power of 2. The sampling points are placed equidistantly in the truncated wavenumber space determined by CMIN and CMAX. If CMAX<0, i.e. the inclusion of the negative spectrum is enabled, then the NW sample points will be distributed along the positive wavenumber axis only, with the negative components obtained by symmetry.

IC1:

Number of the first sampling point where the calculation is to be performed. If IC1>1, then the Hankel transform is Hanning-windowed in the interval 1,2IC1-1 before integration.

IC2:

Number of the last sampling point where the calculation is to be performed. If IC2<NWN, then the Hankel transform is Hanning windowed in the interval IC2+1,NW before integration.

IF:

Frequency increment for plotting of integration kernels. A value of 0 disables the plotting.

Automatic wavenumber sampling

OASP Version 1.4 and higher have 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 to -1 and it automatically activates the complex frequency integration contour even though option O 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-FIPP case 2 problem with automatic sampling, change the data file as follows:

SAFARI-FIPP case 2. Auto sampling.
V H f                         # Bessel integration.
5 0
4
  0    0     0 0   0   0   0
  0 1500     0 0   0   1   0
100 1600   400 0.2 0.5 1.8 0
120 1800   600 0.1 0.2 2.0 0
95
100 100 1 
 300 1E8                      
-1 0 0                         # NW   =   -1
2048 0.0 12.5 0.006 0.5 0.5 5