The input file

The general structure of the input file (hereafter called INFIL) can be better understood if one thinks of it as composed of blocks; each block describes a particular element of the waveguide, from top to bottom. In order to provide a friendly view of the INFIL the blocks are separated with a long line, which is ignored by the model. The structure of the INFIL is as follows:

Title
Source	Block
Altimetry	Block
Sound Speed	Block
Objects	Block
Bathymetry	Block
Array	Block
Output	Block

The Title is a character string, which is written in the LOGFIL (the file with the *.log extension).

The structure of each block is as follows:

Source Block:

ds	ray step
rx,zx	source coordinates
rbox(1),rbox(2)	range box
freqx	source frequency
nthtas	number of launching angles
theta(1), theta(nthtas)	first and last launching angles

Optionally, the user can set $ds$ to zero; in such case TRACEO uses the ranges of the rbox to calculate a preliminary step.

Altimetry Block:

atype	surface type
aptype	surface properties
aitype	interpolation type
atiu	attenuation units
nati	number of surface coordinates

atype can be one of the following characters:

'A'	absorbent surface
'E'	elastic surface
'R'	rigid surface
'V'	vacuum over surface

aptype can be one of the following characters:

'H'	homogeneous surface
'N'	non-homogeneous surface

aitype can be one of the following strings:

'FL'	flat surface
'SL'	surface with a slope
'2P'	piecewise linear interpolation
'3P'	piecewise parabolic interpolation
'4P'	piecewise cubic interpolation

atiu can be one of the following characters:

'F'	dB/kHz
'M'	dB/meter
'N'	dB/neper
'Q'	Q factor
'W'	dB/$\lambda$

(same units used by Bellhop; for specific details regarding the definitions of these units see [2]).

nati is the number of surafce coordinates.

For aptype = 'H' the properties and coordinates of the surface are specified as follows:

cpati(1),csati(1),rhoati(1),apati(1),asati(1)

rati(1),zati(1)

rati(2),zati(2)

rati(3),zati(3)

...

rati(nati),zati(nati)

Alternatively, for aptype = 'N' the properties and coordinates of the surface are specified as:

rati(1),zati(1),cpati(1),csati(1),rhoati(1),apati(1),asati(1)

rati(2),zati(2),cpati(2),csati(2),rhoati(2),apati(2),asati(2)

rati(3),zati(3),cpati(3),csati(3),rhoati(3),apati(3),asati(3)

...

rati(nati),zati(nati),cpati(nati),...

Sound Speed Block:

cdist	type of sound speed distribution
cclass	class of sound speed
nr0,nz0	number or points in range, number of points in depth

cdist can be one of the following strings:

'c(z,z)'	sound speed profile	$c = c(z)$
'c(r,z)'	sound speed field	$c = c(r,z)$

For a sound speed field both range and depth derivatives are calculated using a bi-dimensional barycentric parabolic interpolator, on the grid of nr0$\times$nz0 points. For a sound speed profile all range derivatives are zero; depth derivatives are calculated depending on the value of cclass, which can be one of the following strings:

'ISOV'	isovelocity	profile
'LINP'	linear	profile
'PARP'	parabolic	profile
'EXPP'	exponential	profile
'N2LP'	$n^2$-linear	profile
'ISQP'	inverse-square gradient	profile
'MUNK'	Munk	profile
'TABL'	tabulated	profile

All but the last cclass describe analytical profiles, whose derivatives can be calculated explicitely. The parameters of those profiles can be specified through a simple list of the form

z0(1),c0(1)

z0(2),c0(2)

Here it follows a description of each analytical profile:

• Isovelocity profile:
  
  $$c(z) = c_0 = \makebox{ constant } , \frac{dc}{dz} = 0 , \frac{d^2c}{dz^2} = 0 ;$$
  
  
  therefore, only the value c0(1) is used during the calculations.
• Linear profile:
  
  $$c(z) = c_0 + k\left( z - z_0 \right) , \frac{dc}{dz} = k , \frac{d^2c}{dz^2} = 0 ;$$
  
  
  the parameters are calculated as $z_0$ = z(1), $c_0$ = c(1) and
  
  $$k = \frac {\makebox{\texttt{c(2)-c(1)}}}{\makebox{\texttt{z(2)-z(1)}}} .$$
  
  

• Parabolic profile:
  
  $$c(z) = c_0 + k\left( z - z_0 \right) ^2 , \frac{dc}{dz} = 2k\left( z - z_0 \right) , \frac{d^2c}{dz^2} = 2k ;$$
  
  
  the parameters are calculated as $z_0$ = z(1), $c_0$ = c(1) and
  
  $$k = \frac {\makebox{\texttt{c(2)-c(1)}}}{ \left( \makebox{\texttt{z(2)-z(1)}} \right) ^2 } .$$
  
  

• Exponential profile:
  
  $$c(z) = c_0 e^{ -k\left( z - z_0 \right) } ,$$
  
  
  
  
  $$\frac{dc}{dz} = -kc_0 e^{ -k\left( z - z_0 \right) } , \frac{d^2c}{dz^2} = k^2c_0 e^{ -k\left( z - z_0 \right) } ;$$
  
  
  the parameters are calculated as $z_0$ = z(1), $c_0$ = c(1) and
  
  $$k = \frac {1}{ \makebox{\texttt{z(2)-z(1)}} }\ln\left[ \frac ... ...ebox{\texttt{c(1)}} }{ \makebox{ \texttt{c(2)} } } \right] .$$
  
  

• $n^2$-linear profile:
  
  $$c(z) = \frac {c_0}{ \left[ 1 + k\left( z - z_0 \right) \right] ^{1/2} } ,$$
  
  
  
  
  $$\frac{dc}{dz} = \frac {-kc_0}{2\left[ 1+k\left( z-z_0 \right)... ... {3k^2c_0}{4\left[ 1+k\left( z-z_0 \right) \right] ^{5/2}} ;$$
  
  
  the parameters are calculated as $z_0$ = z(1), $c_0$ = c(1) and
  
  $$k = \frac {1}{ \makebox{\texttt{z(2)-z(1)}} }\left[ \left( \f... ...tt{c(1)}}}{\makebox{\texttt{c(2)}}} \right) ^2 - 1 \right] .$$
  
  

• Inverse-square gradient profile:
  
  $$c(z) = c_0 \left\{ 1 + \frac {k\left( z - z_0 \right) }{ \left[ 1 + k^2\left( z - z_0 \right) ^2 \right] ^{1/2} } \right\} ,$$
  
  
  
  
  $$\frac{dc}{dz} = \frac {kc_0}{2\left[ 1+k^2\left( z-z_0 \righ... ...ht) }{\left[ 1+k^2\left( z-z_0 \right) ^2 \right] ^{5/2}} ;$$
  
  
  the parameters are calculated as $z_0$ = z(1), $c_0$ = c(1) and
  
  $$k = \frac {1}{ \makebox{\texttt{z(2)-z(1)}} }\sqrt{ \frac {a}{1-a} } ,$$
  
  
  with
  
  $$a = \left[ \frac {\makebox{\texttt{c(1)}}}{\makebox{\texttt{c(2)}}} - 1 \right] ^2 .$$
  
  

• Munk profile:
  
  $$c(z) = c_0 \left[ 1 + \varepsilon( \eta + e^{-\eta} - 1 ) \right] ,$$
  
  
  
  
  $$\frac{dc}{dz} = \frac {2\varepsilon c_1}{B}(1-e^{-\eta}) ,... ...frac{d^2c}{dz^2} = \frac {4\varepsilon c_1}{B^2}e^{-\eta} ,$$
  
  
  with the parameters $\varepsilon = 7,4\times10^{-3}$, $\eta = 2\left( z - z_0 \right) /B$, $B$ = 1,3 km, ($z_0$ represents the depth of the channel axis and $c_0$ the corresponding value of sound speed); the parameters are calculated as $z_0$ = z(1) and $c_0$ = c(1). The remaining values are ignored.

The combination cdist = 'c(z,z)' and cclass = 'TABL' requires the sound profile to be specified as follows:

z0(1),c0(1)

z0(2),c0(2)

...

z0(nz0),c0(nz0)

The specification cdist = 'c(r,z)' (a sound speed field) should be followed by cclass = 'TABL', otherwise the program stops execution; the sound speed field should be specified as follows:

r0(1),r0(2),r0(3),...,r0(nr0)

z0(1),z0(2),z0(3),...,z0(nz0)

c(1,1) c(1,2) ... c(1,nr0)

c(2,1) c(2,2) ... c(2,nr0)

c(3,1) c(3,2) ... c(3,nr0)

...

c(nz0,1) c(nz0,2) ... c(nz0,nr0)

When specifying the sound speed profile or field it is highly recommended to use an evenly spaced grid, avoiding vertical segments where a smooth variation is followed by an isovelocity layer. Including such segments introduce unrealistic artifacts, which result from the calculation of inaccurate sound speed gradients.

After the Sound Speed Block it should follow the single line

nobj

which indicates the number of objects defined inside the waveguide. If nobj = 0 the Objects Block is empty; otherwise (with nobj $>$ 0) the INFIL should contain the following line

oitype

which describes the method of interpolation ('2P', '3P' or '4P', no other types are allowed), to be applied to the boundaries of all objects. For each object it should be defined an Object Block with the following structure:

otype	object type
obju	attenuation units
no	number of coordinates
ocp(i), ocs(i), orho(i) ...	Object $c_p$, $c_s$, etc.
ro(1),zdn(1),zup(1)
ro(2),zdn(2),zup(2)
...
ro(no),zdn(no),zup(no)

otype and obju are the same as those indicated for the Altimetry Block. The list above shows that the upper and lower boundaries of the object are sampled along a common range interval.

Bathymetry Block: the structure of this block is identical to the structure of the Altimetry Block.

Array Block:

artype	array type
nra nza	number of hydrophones along range and depth
r(1) r(2) .... r(nra)	hydrophones ranges
z(1) z(2) .... z(nza)	hydrophones depths

The option artype can correspond to one of the following strings:

'RRY'	Rectangular	aRray
'HRY'	Horizontal	arRay
'VRY'	Vertical	arRay
'LRY'	Linear	arRay

The option artype = 'LRY' requires that nra = nza.

Output Block:

outype	output type
miss	eigenray parameter

The option outype defines the type of output and can correspond to one of the following strings:

'RCO'	output Ray COordinates;
'ARI'	output All Ray information;
'ERF'	output Eigenrays (use Regula Falsi);
'EPR'	output Eigenrays (use PRoximity method);
'ADR'	output Amplitudes and Delays (use Regula falsi);
'ADP'	output Amplitudes and Delays (use Proximity method);
'CPR'	output Coherent acoustic PRessure;
'CTL'	output Coherent Transmission Loss;
'PVL'	output coherent Particle VeLocity;
'PAV'	output Coherent acoustic Pressure And Particle velocity.

The miss parameter is used as a threshold to find eigenrays and to calculate arrivals.