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.

 

A further slow down by a factor of 2 or more may

occur it the Twersky scatter option is used in KRAKENC. The

calculation of the Twersky scatter function can require

significant CPU time; enough to actually be a dominant part of

the cost of computing the modes. KRAKEN incorporates the scatter

perturbatively and is much less sensitive to the cost of Twersky

scatter.

 

KRAKEN does not at allow for losses in elastic media due

to material attenuation.  Thus, for attenuating elastic media,

KRAKENC should be used.

 

\begin{verbatim}

 

Files:

 

        Name           Unit         Description

Input

        *.ENV            1       ENVironmental data

        *.BRC           10       Bottom   Refl. Coef.  (optl)

        *.TRC           11       Top      Refl. Coef.  (optl)

        *.IRC           12       Internal Refl. Coef.  (optl)

Output

        *.PRT            6       PRinT file

        *.MOD           20       MODe  file

 

---------------------------------------------------------

 

EXAMPLE AND DESCRIPTION OF ENV FILE:

 

 'FRAMIV Twersky S/S ice scatter'         ! TITLE

 50.0                                     ! FREQ (Hz)

 4                              ! NMEDIA

 'NSF'                          ! OPTIONS

 0.0092  8.2  5.1               ! BUMDEN (1/m)  ETA (m)  XI (m)

 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                              ! NSD

 100.0 /                        ! SD(1:NSD) (m)

 1                              ! NRD

 200.0 /                        ! RD(1:NRD) (m)

 

 

---------------------------------------------------------------

 

DESCRIPTION OF INPUTS:

 

The following can be repeated as many times as wanted in a single ENVFIL.

KRAKEN and KRAKENC will generate a separate MODFIL for each case stopping when it

detects an end-of-file.

 

(1) - TITLE

 

      Syntax:

         TITLE

      Description:

         TITLE: Title of run enclosed in sinqle quotes.

 

 

(2) - FREQUENCY

 

      Syntax:

         FREQ

      Description:

         FREQ: Frequency in Hz.

 

 

(3) - NUMBER OF MEDIA

 

      Syntax:

         NMEDIA (<20)

      Description:

         NMEDIA: Number of media.

 

      The problem is divided into media within which it is

      assumed that the material properties vary smoothly. A new

      medium should be used at fluid/elastic interfaces or at

      interfaces where the density changes discontinuously. The

      number of media in the problem is defined excluding the

      upper and lower half-space.

 

 

(4) - OPTIONS

 

      Syntax:

         OPTION

      Description:

         OPT(1:1): Type of interpolation to be used for the SSP.

                   'C' for C-linear,

                   'N' for N2-linear (n the index of refraction),

                   'S' for cubic Spline,

                   'A' for Analytic.  The user must modify the

                       analytic formulas in PROFIL.FOR then

                       compile and link.

 

             If your not sure which option to take, I'd suggest

             you use 'C' or 'N'.  Practically, you can pick

             either one: the choice has been implemented to

             facilitate precise intermodel comparisons.

 

             Option 'S' is a little dangerous because splines

             yield a poor fit to certain kinds of curves,

             e.g. curves with sharp bends.  If you insist

             on splines, you can fix a bad fit by dividing the

             water column into two 'media' at the bend.

 

             Run PLOTSSP to check that the SSP looks the way you

             thought it should. Apart from potential typos,

             this will also show up fit-problems.

 

         OPT(2:2): Type of top boundary condition.

                   'V' VACUUM above top.

                   'A' ACOUSTO-ELASTIC half-space.

                       Requires another line as described in

                       block (4a).

                   'R' Perfectly RIGID.

                   'F' Reflection coefficient from a FILE

                       (available in KRAKENC only). Requires

                       additional lines as described in

                       block (4c).

                   'S' for Soft-boss Twersky scatter.

                   'H' for Hard-boss Twersky scatter.

                   'T' for Soft-boss Twersky scatter, amplitude

                       only.

                   'I' for Hard-boss Twersky scatter, amplitude

                       only. The Twersky scatter options require

                       another line as described in block

                       (4c). Mnemonically, T, I options are one

                       letter after S, H in the alphabet. Current

                       wisdom is that option T is most

                       appropriate for ice scatter.

 

                    For open ocean problems option 'V' should be

                    used for the top BC.  The Twersky options

                    are intended for under-ice modeling.

 

         OPT(3:3): Attenuation units.

                   'N' Nepers/m.

                   'F' dB/(kmHz)       (F as in Freq. dependent)

                   'M' dB/m            (M as in per Meter)

                   'W' dB/wavelength   (W as in per Wavelength)

                   'Q' quality factor

                   'L' Loss parameter (a.k.a. loss tangent)

                   'T' Thorp attenuation formula.  This overrides

                       any other attenuations specified.

 

                   KRAKEN ignores material attenuation

                   in elastic media. (KRAKENC treats

                   it properly).

 

         OPT(4:4): Added volume attenuation.

                   'T' Thorp attenuation formula.

 

         OPT(5:5): Slow/robust root-finder.

                   '.' As in: I want all the modes and I don't

                       care how long it takes. Period.

                       (Available in KRAKENC only.)

                       In certain problems with elastic layers

                       the old root-finder has been known to

                       skip modes.

                      

 

(4a) - TOP HALFSPACE PROPERTIES

 

      Syntax:

         ZT  CPT  CST  RHOT  APT  AST

      Description:

         ZT:   Depth (m).

         CPT:  Top P-wave speed (m/s).

         CST:  Top S-wave speed (m/s).

         RHOT: Top density (g/cm3).

         APT:  Top P-wave attenuation. (units as given in Block 2)

         AST:  Top S-wave attenuation. (  "   "    "    "   "   ")

 

         This line should only be included if OPT(2:2)='A', i.e.

         if the user has specified a homogeneous halfspace for

         the top BC.

 

 

(4b) - TOP REFLECTION COEFFICIENT

 

      Syntax:

         NTHETA

         THETA(1)       RMAG(1)       RPHASE(1)

         THETA(2)       RMAG(2)       RPHASE(2)

           .

           .

           .

         THETA(NTHETA)  RMAG(NTHETA)  RPHASE(NTHETA)

 

      Description:

         NTHETA:   Number of angles.

         THETA():  Angle.

         RMAG():   Magnitude of reflection coefficient.

         RPHASE(): Phase of reflection coefficient (degrees).

 

      Example:

         3

         0.0   1.00  180.0

         45.0  0.95  175.0

         90.0  0.90  170.0

 

      These lines should be contained in a separate '.TRC' file.

      This file is only required if OPT(2:2)='F', i.e. if the

      user has specified that the top BC is read from a '.TRC'

      (Top Reflection Coefficient) file.

 

      This option for tabulated reflection coefficients is

      somewhat experimental at this time. I haven't worried about

      the multivalued character of the phase function: choose

      your reference and make sure the phase varies continuously.

      A complicated reflection coefficient may well cause

      problems for the mode-finder. Finally, a reflection coefficient

      tabulated only for real angles does not provide a good result

      for complex angles of incidence. This happens when the sediment

      sound speed is less than the water sound speed. In that case,

      the modes are evanescent in the upper part of the water column

      and therefore have a complex angle of incidence.

 

 

(4c) - TWERSKY SCATTER PARAMETERS

 

      Syntax:

         BUMDEN  ETA  XI

      Description:

         BUMDEN: Bump density (ridges/km).

         ETA:    Principal radius 1 (m).

         XI:     Principal radius 2 (m).

 

      This line should only be included when one of the

      Twersky-scatter options is selected.

 

(5) - MEDIUM INFO

 

      Syntax:

         NMESH  SIGMA  Z(NSSP)

      Description:

         NMESH:   Number of mesh points to use initially.

                  The number of mesh points should be about 10

                  per vertical wavelength in acoustic media. In

                  elastic media, the number needed can vary quite

                  a bit; 20 per wavelength is a reasonable

                  starting point.

 

                  The maximum allowable number of mesh points is

                  given by 'MAXN' in the dimension statements.

                  At present 'MAXN' is 50000.  The number of mesh

                  points used depends on the initial mesh and the

                  number of times it is refined (doubled).  The

                  number of mesh doublings can vary from 1 to 5

                  depending on the parameter RMAX described

                  below.

 

                  If you type 0 for the number of mesh points,

                  the code will calculated NMESH automatically.

 

         SIGMA:   RMS roughness at the interface.

 

         Z(NSSP): Depth at bottom of medium (m).

                  This value is used to detect the last SSP point

                  when reading in the profile that follows.

 

(5a) - SOUND SPEED PROFILE

 

      Syntax:

         Z(1)     CP(1)     CS(1)     RHO(1)     AP(1)     AS(1)

         Z(2)     CP(2)     CS(2)     RHO(2)     AP(2)     AS(2)

          .

          .

          .

         Z(NSSP)  CP(NSSP)  CS(NSSP)  RHO(NSSP)  AP(NSSP)  AS(NSSP)

      Description:

         Z():     Depth (m).

                  The surface starts at the first depth point

                  specified. Thus if you have say, XBT data which

                  starts at 50 m below the surface, then you'll

                  need to put in some SSP point at 0 m, otherwise

                  the free-surface would be placed at 50 m giving

                  erroneous results. The points Z(1) and Z(NSSP)

                  MUST correspond to the depths of interfaces

                  between media.

 

         CP():    P-wave speed (m/s).

         CS():    S-wave speed (m/s).

         RHO():   Density (g/cm3).

                  Density variations within an acoustic medium

                  are at present ignored.

         AP():    P-wave attenuation (units as given in Block 2)

         AS():    S-wave attenuation (  "   "    "    "   "   ")

 

 

       These lines should be omitted when the 'A' option is used

       (indicating that an analytic profile is supplied by a user

       written subroutine).

 

       The '/' character signals that the remaining data on the

       line is the same as in the previous line of SSP data. For

       the very first line the default or 'previous' line is:

 

          0.0 1500.0 0.0 1.0 0.0 0.0

 

       This block should be repeated for each subsequent medium.

 

 

(6) - BOTTOM BOUNDARY CONDITION

 

      Syntax:

         BOTOPT  SIGMA

      Description:

         BOTOPT: Type of bottom boundary condition.

                 'V' VACUUM below bottom.

                 'A' ACOUSTO-ELASTIC half-space.

                     Requires another line with the half-space

                     parameters.  The format is the same as that

                     used for specifying the top halfspace BC.

                 'R' Perfectly RIGID.

                 'F' reflection coefficient from a FILE (available

                     in KRAKENC only). Requires a Bottom

                     Reflection Coefficient file with

                     extension '.BRC'.  The format is the same as

                     that used for a Top Reflection coefficient.

                 'P' Precaculated internal reflection coefficient

                     from a FILE (available in KRAKENC and SCOOTER, not KRAKEN).

                     These files are generated using BOUNCE.

                 Option 'A' is generally used for ocean bottom

                 modeling.

         SIGMA:  Interfacial roughness (m).

 

 

(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 as

                 possible to minimize execution time.

 

                 On the other hand, CHIGH controls the maximum

                 ray 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. In

                 the 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 DEPTH INFO

 

      Syntax:

         NSD

         SD(1:NSD)

         NRD

         RD(1:NRD)

 

      Description:

         NSD:  The number of source   depths.

         SD(): The source   depths (m).

         NRD:  The number of receiver depths.

         RD(): The 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 up

         to 4095 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/wavelenght) is needed

         to calculate the coupling integrals accurately.

  

--------------------------------------------------------------

 SAMPLE PRINT OUT

 

 The print-out for this deck is shown below. The version we run, has the complicated

Twersky ice scatter model disabled since that part of the code has not been upgraded

to Fortran95. Therefore the results do not actually include that effect of ice scatter loss.

 

KRAKEN- FRAMIV Twersky S/S ice scatter                                         

Frequency =   20.00     NMedia =   4

 

 

    N2-LINEAR approximation to SSP

    Attenuation units: dB/mkHz

    Twersky SOFT BOSS scatter model

 

Twersky ice model parameters:

Bumden =    0.920000E-02  Eta =    8.20      Xi =    5.10   

 

 

 

     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   

 

--------------------------------------------------------------

\end{verbatim}

 

 

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 *****

 

By popular demand, the new versions of 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.