# KRAKEN

##

## Overview

## Example Environmental File

##

## Description of Inputs

## How to Run Kraken

## Sample Print Out

## Overview

KRAKEN is a normal mode program for range-varying environments in either cartesian (line sources) or cylindrical coordinates (point sources). The basic method is described in

Porter, Michael B. and Reiss, Edward L., "A numerical method for ocean-acoustic normal modes", JASA 76, 244-252 (1984).

Porter, Michael B. and Reiss, Edward L., "A numerical method for bottom interacting ocean acoustic normal modes", JASA 77, 1760-1767 (1985).

Range-dependent solutions are obtained by using optionally adiabatic or coupled mode theory.

KRAKEN is the main program. It takes an environmental file, computes the modes, and writes them to disk for use by other modules. A print file is also produced, echoing the user input.

KRAKENC is a complex arithmetic version (hence the C in KRAKENC) of KRAKEN. By working in the complex domain, loss mechanisms such as ice scatter and material absorption may be included 'exactly' rather than perturbatively. In addition, leaky modes may be computed. The price of this non-perturbative treatment is a slowdown in speed by approximately a factor of 4. This factor principally represents the difference between complex and real arithmetic.

KRAKEN does not at allow for losses in elastic media due to material attenuation. Thus, for attenuating elastic media, KRAKENC should be used.

Files:

Name Description

Input

*.ENV ENVironmental data

*.BRC Bottom Refl. Coef. (optl)

*.TRC Top Refl. Coef. (optl)

*.IRC Internal Refl. Coef. (optl)

Output

*.PRT PRinT file

*.MOD MODe file

## Example Environmental File

'FRAMIV' ! TITLE

50.0 ! FREQ (Hz)

4 ! NMEDIA

'NVF' ! OPTIONS

750 0.0 3750.0 ! NMESH SIGMA (m) Z(NSSP)

0.0 1436.0 0.0 1.03/ ! Z(m) CP CS(m/s) RHO(gm/cm3)

30.0 1437.4 /

50.0 1437.7 /

80.0 1439.5 /

100.0 1441.9 /

125.0 1444.6 /

150.0 1450.0 /

175.0 1456.1 /

200.0 1458.4 /

250.0 1460.0 /

300.0 1460.5 /

350.0 1460.6 /

400.0 1461.0 /

450.0 1461.5 /

500.0 1462.0 /

600.0 1462.9 /

700.0 1463.9 /

800.0 1464.8 /

900.0 1465.8 /

1000.0 1466.7 /

1100.0 1467.0 /

1200.0 1469.0 /

1300.0 1469.5 /

1400.0 1471.8 /

1600.0 1474.5 /

1800.0 1477.0 /

2000.0 1479.6 /

2500.0 1487.9 /

3750.0 1510.4 /

35 0.0 3808.33

3750.0 1504.6 0.0 1.50 .15 0.0

3808.33 1603.07 /

35 0.0 3866.66

3808.33 1603.07 0.0 1.533 .15 0.0

3866.66 1701.53 /

35 0.0 3925.0

3866.66 1701.53 0.0 1.566 .15 0.0

3925.0 1800.0 /

'A' 0.0 ! BOTOPT SIGMA (m)

3925.0 1800.0 0.0 1.60 .15 0.0

0.0 1504.0 ! CLow CHigh (m/s)

300.0 ! RMax (km)

1 ! NSz

100.0 / ! Sz( 1 : NSz ) (m)

1 ! NRz

200.0 / ! Rz( 1 : NRz ) (m)

## Description of Environmental File

The first 6 blocks in the ENVFIL are common to all the programs in the Acoustics Toolbox. The following blocks should be appended for KRAKEN:

### (7) - Phase Speed Limits

Syntax:

CLOW CHIGH

Description:

CLOW: Lower phase speed limit (m/s).

CLOW will be computed automatically if you set it to zero. However, by using a nonzero CLOW you can skip the computation of slower modes. Mainly this is used to exclude interfacial modes (e.g.a Scholte wave). The root finder is especially slow in converging to these interfacial modes and when the source and receiver are sufficiently are far from the interface the interfacial modes are negligible.

CHIGH: Upper phase speed limit (m/s).

The larger CHIGH is, the more modes are calculated and the longer the execution time. Therefore CHIGH should be set as small aspossible to minimize execution time.

On the other hand, CHIGH controls the maximumray angle included in a subsequent field calculation-- ray paths are included which turn at the depth corresponding to CHIGH in the SSP. Thus a larger CHIGH means more deeply penetrating rays are included.

Choice of CHIGH then becomes a matter of experience. In the far-field and at high-frequencies, rays travelling in the ocean bottom are severely attenuated and one may set CHIGH to the sound speed at the ocean bottom. Inthe near-field, low-frequency case, rays refracted in the bottom may contribute significantly to the field and CHIGH should be chosen to include such ray paths.

KRAKEN will (if necessary) reduce CHIGH so that only trapped (non-leaky) modes are computed.

KRAKENC will attempt to compute leaky modes if CHIGH exceeds the phase velocity of either the S-wave or P-wave speed in the half-space. Leaky mode computations are somewhat experimental at this time.

### (8) - Maximum Range

Syntax:

RMax

Description:

RMax: Maximum range (km).

This parameter should be set to the largest range for which a field calculation will be desired.

During the mode calculation the mesh is doubled successively until the eigenvalues are sufficiently accurate at this range. If you set it to zero, then no mesh doublings will be performed. You don't need to worry too much about this parameter-- even if you set it to zero the results will usually be reasonable.

### (9) - Source/Receiver Depths

Syntax:

NSz

Sz( 1 : NSz )

NRz

Rz( 1 : NRz )

Description:

NSz: Number of source depths.

Sz(): Source depths (m).

NRz: Number of receiver depths.

Rz(): Receiver depths (m).

This data is read in using list-directed I/O so you can type it just about any way you want, e.g. on one line or split onto several lines. Also if your depths are equally spaced then you can type just the first and last depths followed by a '/' and the intermediate depths will be generated automatically.

CPU time is essentially independent of the number of sources and receivers so that you can freely ask for thousands of depths. However, for high-frequencies the storage for the mode files can be excessive.

The source/rcvr depths are sorted and merged and then the modes are calculated at the union of the two sets of depths. Thus, it doesn't matter if you mix up source and receiver depths. Furthermore, you can leave out either the source or receiver specification (but not both simultaneously) simply by using a '/' for that line.

Sources and receivers cannot be placed in a half-space.

If you are going to be doing a coupled-mode calculation then you must specify a large number of receiver depths spanning the entire column (down to the half-space). Fine sampling (about 10 points/wavelength) is needed to calculate the coupling integrals accurately.

## How to run KRAKEN

Starting out for the first time? If the distribution does not have precompiled executables for your hardware, run the 'makefiles' to compile and link of the whole package.

1. Create the environmental file for your problem, following the directions in KRAKEN.HLP.
2. Run KRAKEN (or KRAKENC) by typing

> KRAKEN filename

where "filename" is the environmental file. (The process is the same under DOS or Linux.) The KRAKEN.HLP file details the differences between the KRAKEN and KRAKENC.

1. Run FIELD to sum the modes and compute the complex pressure field:

FIELD filename

1. You now have several choices (all the GROUP II programs). These are run from inside MATLAB:

> a. PLOTMODE to plot the modes.

> b. PLOTSSP to plot the sound speed profile.

> c. PLOTSHD to plot the pressure field as a function of range and depth.

Once the modes are created by KRAKEN or KRAKENC you can run the above plot programs in any sequence or as often as you like.

## Sample Print Out

The print-out for this input is shown below.

`KRAKEN- FRAMIV`

`Frequency = 20.00 NMedia = 4`

``

``

`N2-LINEAR approximation to SSP`

`Attenuation units: dB/mkHz`

`VACUUM
`

``

``

`Z AlphaR BetaR Rho AlphaI BetaI`

``

``

`( Number of pts = 750 RMS roughness = 0.00 )`

`0.00 1436.00 0.00 1.03 0.0000 0.0000`

`30.00 1437.40 0.00 1.03 0.0000 0.0000`

`50.00 1437.70 0.00 1.03 0.0000 0.0000`

`80.00 1439.50 0.00 1.03 0.0000 0.0000`

`100.00 1441.90 0.00 1.03 0.0000 0.0000`

`125.00 1444.60 0.00 1.03 0.0000 0.0000`

`150.00 1450.00 0.00 1.03 0.0000 0.0000`

`175.00 1456.10 0.00 1.03 0.0000 0.0000`

`200.00 1458.40 0.00 1.03 0.0000 0.0000`

`250.00 1460.00 0.00 1.03 0.0000 0.0000`

`300.00 1460.50 0.00 1.03 0.0000 0.0000`

`350.00 1460.60 0.00 1.03 0.0000 0.0000`

`400.00 1461.00 0.00 1.03 0.0000 0.0000`

`450.00 1461.50 0.00 1.03 0.0000 0.0000`

`500.00 1462.00 0.00 1.03 0.0000 0.0000`

`600.00 1462.90 0.00 1.03 0.0000 0.0000`

`700.00 1463.90 0.00 1.03 0.0000 0.0000`

`800.00 1464.80 0.00 1.03 0.0000 0.0000`

`900.00 1465.80 0.00 1.03 0.0000 0.0000`

`1000.00 1466.70 0.00 1.03 0.0000 0.0000`

`1100.00 1467.00 0.00 1.03 0.0000 0.0000`

`1200.00 1469.00 0.00 1.03 0.0000 0.0000`

`1300.00 1469.50 0.00 1.03 0.0000 0.0000`

`1400.00 1471.80 0.00 1.03 0.0000 0.0000`

`1600.00 1474.50 0.00 1.03 0.0000 0.0000`

`1800.00 1477.00 0.00 1.03 0.0000 0.0000`

`2000.00 1479.60 0.00 1.03 0.0000 0.0000`

`2500.00 1487.90 0.00 1.03 0.0000 0.0000`

`3750.00 1510.40 0.00 1.03 0.0000 0.0000`

``

`( Number of pts = 35 RMS roughness = 0.00 )`

`3750.00 1504.60 0.00 1.50 0.1500 0.0000`

`3808.33 1603.07 0.00 1.50 0.1500 0.0000`

``

`( Number of pts = 35 RMS roughness = 0.00 )`

`3808.33 1603.07 0.00 1.53 0.1500 0.0000`

`3866.66 1701.53 0.00 1.53 0.1500 0.0000`

``

`( Number of pts = 35 RMS roughness = 0.00 )`

`3866.66 1701.53 0.00 1.57 0.1500 0.0000`

`3925.00 1800.00 0.00 1.57 0.1500 0.0000`

``

`( RMS roughness = 0.00 )`

`ACOUSTO-ELASTIC half-space`

`3925.00 1800.00 0.00 1.60 0.1500 0.0000`

``

`CLOW = 0.0000 CHIGH = 1504.0`

`RMAX = 300.0000000000000`

``

`Number of sources = 1`

`100.000`

``

`Number of receivers = 501`

`0.00000 7.85000 15.7000 23.5500 31.4000`

`39.2500 47.1000 54.9500 62.8000 70.6500`

`78.5000 86.3500 94.2000 102.050 109.900`

`117.750 125.600 133.450 141.300 149.150`

`157.000 164.850 172.700 180.550 188.400`

`196.250 204.100 211.950 219.800 227.650`

`235.500 243.350 251.200 259.050 266.900`

`274.750 282.600 290.450 298.300 306.150`

`314.000 321.850 329.700 337.550 345.400`

`353.250 361.100 368.950 376.800 384.650`

`392.500`

`... 3925.00000`

``

`Mesh multiplier CPU seconds`

`--- Number of modes = 16`

`1 0.200E-01`

`--- Number of modes = 16`

`2 0.100E-01`

``

`I K ALPHA PHASE SPEED GROUP SPEED`

`1 0.8624469531E-01 -0.3393680437E-33 1457.060120 1442.191128`

`2 0.8582756287E-01 -0.2258264739E-34 1464.141611 1458.363347`

`3 0.8562779133E-01 -0.7903258864E-35 1467.557486 1459.982403`

`4 0.8545321184E-01 -0.2063707986E-29 1470.555681 1459.772119`

`5 0.8527102515E-01 -0.3869615292E-29 1473.697612 1460.007439`

`6 0.8510362497E-01 -0.3647388043E-26 1476.596399 1461.303669`

`7 0.8495175125E-01 -0.1793622439E-23 1479.236205 1462.170030`

`8 0.8479899358E-01 -0.3873153170E-21 1481.900915 1462.347048`

`9 0.8465055475E-01 -0.4836458160E-19 1484.499499 1461.666057`

`10 0.8450362764E-01 -0.4794435113E-17 1487.080610 1462.889869`

`11 0.8435766539E-01 -0.3328862832E-15 1489.653674 1463.381675`

`12 0.8421539792E-01 -0.1526837394E-13 1492.170188 1463.060233`

`13 0.8407682246E-01 -0.5076531997E-12 1494.629584 1463.714231`

`14 0.8393863717E-01 -0.1285683019E-10 1497.090141 1464.761578`

`15 0.8380272668E-01 -0.2261354744E-09 1499.518108 1465.064585`

`16 0.8366989890E-01 -0.2750609980E-08 1501.898625 1465.355728`

``

If the program aborts in some way, examine the print file which is produced. Frequently an expected line has been omitted and the environmental file is therefore misinterpreted.

The message "FAILURE TO CONVERGE IN SECANT" occurs when KRAKEN requires more than 500 iterations to converge to a mode. Usually less than 20 iterations are needed but convergence to interfacial modes (Scholte or Stoneley waves) can be exceptionally slow,especially at higher frequencies. The simplest solution is to exclude interfacial modes by setting the lower phase-speed limit to the minimum p-wave speed in the problem. Alternately, you can increase the value of MAXNIT which controls the MAXimum Number of ITerations in the root finder.

***** Group speed *****

KRAKEN and KRAKENC compute group speed using the formula in Ch. 5 of Jensen, Kuperman, Porter, and Schmidt, Computational Ocean Acoustics. Note that this formula is only valid for acoustic problems (with no elasticity). It also does not address the role of interfacial or boundary scatter. In these cases, the value displayed is not reliable.