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The Santa Barbara Channel Experiment (SBCX)

Deep Water KRAKEN-RAM Comparison

Peter Daly
MIT Ocean Acoustics
December 22, 1999

This is the third in a series of papers on comparison between RAM and KRAKEN. The focus of this paper is which depth gridding parameter (dz) should be used with RAM in a deep water environment. Both magnitude and phase of the pressure field generated by RAM and KRAKEN are compared. The results are similar to those for the shallow water case: a z gridding of 0.125 meters or less is required to match normal mode results at 70 Hz.

Deep Water Environment

A 4000 meter water column was used for this simulation, with a Munk profile,

with the axis depth, z0 set to 1000 meters, and the speed at the axis depth, c0 is 1480 m/sec. The last 100 meters of the sound velocity profile departed from the equation above; from 3900 < z < 3950 meters, the sound speed was linear from c(z = 3900) to c(z = 3950) = 1600. From 3950 < z < 4000 meters, c(z) = 1600 m/sec. The bottom properties are very simple; with a halfspace compressional speed of 1700 m/sec, a halfspace density of 1.5 g/cm3. The attenuation varies linearly from 4000 to 4500 meters depth; at 4000 meters, it is 0.5 dB/, while at 4500 meters, 10 dB/. Tables 1 and 2 are annotated input files for RAM and KRAKEN, respectively. Each provides the same input environment, with typical propagation parameters.

Table 1: Annotated RAM input file

RAM input line Comments
RAM.IN TITLE Title line
70.0 100.0 1000.0
  • Frequency: 70 Hz
  • Source depth: 100 m
  • Receiver depth: 1000 m
200000.0 5.0 80
  • Maximum Range Calculation: 200000 m
  • Range step: 5 m
  • Output Range decimation: 80
4500.0 1.0 4 4500.0
  • Maximum Depth Calculation: 4500 m
  • Depth step: 1 m
  • Depth decimation: 4
  • Output depth maximum: 4500 m
1480.0 10 1.0 100000.0
  • Reference Sound Speed (c0): 1480 m/sec
  • Number of Pade coefficients: 10
  • Number of stability constraints: 1
  • Maximum range of stability constraints: 0
0 No starter field file
1 2 0 0 0 Output flags:
  • Output complex pressure field instead of TL
  • Output is not scaled for carrier or spreading
  • Output has no TL line
  • Output is not restricted to a specific range
  • No ``on the fly'' range step changes
0.0 4000.0 Bathymetric parameters:
  • 4000 meters water column depth starting at range 0.
-1 -1 End of Bathymetric parameters
0.0 1503.238000
(through)
4000.0 1700.0
 SVP block:
  • depth (m), speed (m/sec) pairs
-1 -1 End of SVP block
0.0 1700.0 Bottom compressional speed:
  • 1700 m/sec from the water column bottom down.
-1 -1 End of bottom compressional speed block
0.0 1.5 Bottom density:
  • 1.5 g/cm3, starting at range 0, from the bottom of the water column down.
-1 -1 End of bottom density block
4000.0 0.5
4500.0 10.0
 Attenuation block:
  • 0.5 dB/ at 4000 meters depth, linearly increasing to 10 dB/ at 4500 meters depth.
-1 -1 End of bottom attenuation block (end of input file)

Table 2: Annotated KRAKEN input file

KRAKEN input line Comments
RAM.IN TITLE Title line
70.0 Frequency: 70 Hz
2 Number of layers: 2
CVW Options:
  • C: C-linear interpolation
  • V: Vacuum half-space above water column
  • W: Attenuation in dB/
0 0 4000.0 Layer 1 block:
  • Number of mesh points: 0 (autocompute)
  • RMS Roughness: 0
  • Bottom depth of layer: 4000 m
0.0 1503.238000
(through)
4000.0 1600.0
Layer 1 block:
depth dependent parameters;
depth, sound speed pairs
0 0 4500.0 Layer 2 block:
  • Number of mesh points: 0 (autocompute)
  • RMS Roughness: 0
  • Bottom depth of layer: 4500 m
4000.0 1700.0 0.0 1.5 0.5 0.0
4500.0 1700.0 0.0 1.5 10.0 0.0
Layer 2 block:
  • 4000-4500 meter depth
  • 1700 m/sec compressional sound speed
  • 0.0 m/sec shear sound speed
  • Density: 1.5 g/cm3
  • Attenuation: linearly progressing from 0.5 dB/ to 10.0 dB/.
A 0.0 Bottom Boundary Condition:
  • A: Acousto-Elastic half space
  • 0.0: Interface roughness (m)
4500.0 1700.0 0.0 1.5 10.0 0.0 Bottom halfspace properties (same as Layer 2 block)
1480.0 1700.0 Phase speed limits (c0 and cmax)
200.0 Maximum Range (km)
1 100.0 Source information:
  • Number of sources: 1
  • Source Depth: 100 m
1126 1.0 4500.0 / Receiver information:
  • Number of receivers: 1126 (linearly spaced)
  • Top receiver: 1 m
  • Bottom receiver: 4500 m

Results

RAM was configured to output the pressure envelope from 0 to 4500 meters in depth, and 0 to 200 km range. The envelope, differs from the pressure field p(r,z) in that the carrier and attenuation due to spreading have both been removed,

where c0 is a reference sound speed, and k0 is a reference wavenumber.

KRAKEN outputs both mode numbers, kn, and mode shapes, , which can be reconstructed using Green's function,


One does not directly compare pr and pk to determine the agreement between the two models, since the carrier term ejkr induces oscillations which increase with range. Instead, the average carrier term is removed, and the result is then compared:

Following are a series of plots which show the magnitude and phase differences between gr and gk. The upper plot shows the logarithmic difference in magnitude between the two:

while the lower plot shows the linear phase difference (in degrees). Only the dz parameter is varied, starting at 1.0 meter and ending at 0.0625 meters.

In all cases of dz, the magnitude difference is -40 dB or less; which is adequate for this case. The phase difference, however, is substantial in the 1.0 case (Figure 1): greater than 60 degrees, except for the primary ray path. Only when dz falls below 0.5 meters does the phase error fall below 20 degrees in the water column. At 0.125 meters (Figure 4), the phase error is 10 degrees or less for the majority of the water column. Note, however, that even for the most conservative dz = 0.0625m case (Figure 5), there is a substantial phase error at short ranges (less than 20 km). This is most likely due to KRAKEN incorporating evanescent wave numbers into Green's function, which attenuate quickly with range.

dz = 1.0 m dz = 0.5 m dz = 0.25 m dz = 0.125 m dz = 0.0625 m

Caveats

KRAKEN and RAM use different phase conventions (+/- complex exponential). This is reflected in the equations above.

The Code

Instructions for use:

A .pdf version of this document can be found here.

Last updated: 000107 change log
Comments/Questions: pmd@mit.edu
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