# BELLHOP

## Overview

## Sample Input

## Description of Inputs

### Source/Receiver Depths and Ranges

### Run Type

### Beam Fan

### Numerical Integrator Info

## Running BELLHOP

## Overview

BELLHOP computes acoustic fields in oceanic environments via beam tracing. The environment treated consists of an acoustic medium with a sound speed that may depend on range and depth.

A theoretical description may be found in:

Michael B. Porter and Homer P. Bucker, ``Gaussian beam tracing for computing ocean acoustic fields,'' J. Acoust. Soc. Amer. 82, 1349--1359 (1987).

Michael B. Porter and Yong-Chun Liu, “Finite-Element Ray Tracing'', Proceedings of the International Conference on Theoretical and Computational Acoustics, Eds. D. Lee and M. H. Schultz, pp. 947-956, World Scientific (1994).

The following programs are used with BELLHOP :

BELLHOP Main program for doing Gaussian beam tracing

PLOTRAY Produces plots of central rays of beams

PLOTARR Produces plots of arrivals (the echo pattern)

PLOTATI Produces plots of the altimetry

PLOTBTY Produces plots of the bathymetry

ANGLES Given the source and receiver sound speeds, computes the angle of the limiting ray.

PLOTSSP Plots the sound speed profile

PLOTSSP2D Plots the range-dependent sound speed profile

BELLHOP produces pressure fields in the NRL standard format and can therefore be plotted using the MATLAB script, plotshd.m.

The steps in running the program are as follows:

1. Set up your environmental file and run PLOTSSP to make sure the SSP looks reasonable.

2. Do a ray trace. That is,

A. Run BELLHOP with the ray trace option to calculate about 50 rays.

B. Run PLOTRAY to make sure you have the angular coverage you expect. Do the rays behave irregularly? If so reduce the step-size and try again.

3. Re-run BELLHOP using the coherent, incoherent or semicoherent option for transmission loss. (Use the default number of beams.)

4. Run plotshd.m to plot a full range-depth field plot.

5. Double the number of beams and check convergence.

Files:

Name Unit Description

Input
*.ENV 1 ENVironmental data

Output
*.PRT 6 PRinT file
*.RAY 21 RAY file
*.SHD 25 SHaDe file

## Sample Input (Environmental) File:

'Munk profile' ! TITLE
50.0 ! FREQ (Hz)
1 ! NMEDIA
'SVN' ! SSPOPT (Analytic or C-linear interpolation)
51 0.0 5000.0 ! DEPTH of bottom (m)
0.0 1548.52 /
200.0 1530.29 /
250.0 1526.69 /
400.0 1517.78 /
600.0 1509.49 /
800.0 1504.30 /
1000.0 1501.38 /
1200.0 1500.14 /
1400.0 1500.12 /
1600.0 1501.02 /
1800.0 1502.57 /
2000.0 1504.62 /
2200.0 1507.02 /
2400.0 1509.69 /
2600.0 1512.55 /
2800.0 1515.56 /
3000.0 1518.67 /
3200.0 1521.85 /
3400.0 1525.10 /
3600.0 1528.38 /
3800.0 1531.70 /
4000.0 1535.04 /
4200.0 1538.39 /
4400.0 1541.76 /
4600.0 1545.14 /
4800.0 1548.52 /
5000.0 1551.91 /
'V' 0.0
1 ! NSD
1000.0 / ! SD(1:NSD) (m)
2 ! NRD
0.0 5000.0 / ! RD(1:NRD) (m)
501 ! NRR
0.0 100.0 / ! RR(1:NR ) (km)
'R' ! Run-type: 'R/C/I/S'
51 ! NBEAMS
-11.0 11.0 / ! ALPHA(1:NBEAMS) (degrees)
200.0 5500.0 101.0 ! STEP (m) ZBOX (m) RBOX (km)

## Description of Inputs

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

### (7) - SOURCE/RECEIVER DEPTHS AND RANGES

Syntax:

NSD
SD(1:NSD)
NRD
RD(1:NRD)
NR
R(1:NR )

Description:

NSD: The number of source depths
SD(): The source depths (m)
NRD: The number of receiver depths
RD(): The receiver depths (m)
NR: The number of receiver ranges
R(): The receiver ranges (km)

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

You can specify a receiver at zero range; however, the BELLHOP field is singular there--- the pressure is returned as zero.

Some of the subroutines that calculate the beam influence allow an arbitrary vector of receiver ranges; others require it to be equally spaced in range. In particular, only the following allow an arbitrary range vector:

'G' GeoHatCart
'B' GeoGaussianCart
CerveyRayCen

### (8) - RUN TYPE

Syntax:

OPTION

Description:

OPTION(1:1): 'R' generates a ray file
'E' generates an eigenray file
'A' generates an amplitude-delay file (ascii)
'a' generate an amplitude-delay file (binary)
'C' Coherent TL calculation
'I Incoherent TL calculation
'S' Semicoherent TL calculation
(Lloyd mirror source pattern)

OPTION(2:2): 'G' Geometric hat beams in Cartesian coordinates (default)
'^' Geometric hat beams in Cartesian coordinates (same as 'G' but easier to remember)
'g' Geometric hat beams in ray-centered coordinates
'B' Geometric Gaussian beams in Cartesian coordinates
'b' Geometric Gaussian beams in ray-centered coordinates

OPTION(3:3): '*' read in a source beam pattern file
'O' don't (omni-directional) (default)

OPTION(4:4): 'R' point source (cylindrical coordinates) (default)
'X' line source (Cartesian coordinates)

OPTION(5:5): 'R' rectilinear grid (default)
'I' irregular grid

The ray file and eigenray files have the same simple ascii format and can be plotted using the Matlab script plotray.m.

The eigenray option seems to generate a lot of questions. The way this works is that BELLHOP simply writes the trajectories for all the beams that contribute at a given receiver location. To get a useful picture you normally want to use a very fine fan, only one receiver location, and the geometric beam option. See the examples in at/tests.

The amplitude-delay file can be used with the Matlab script stackarr.m to 'stack the arrivals', i.e. to convolve them with the source spectrum and plot the channel response. stackarr.m can also be used to simple plot the impulse response. We loosely refer to the amplitudes of the arrivals or echoes here; however, these values are really complex numbers that provide the amplitude and phase of each echo.

For TL calculations, the output is in the shdfil format used by all the codes in the Acoustics Toolbox and can be plotted using the Matlab script, plotshd.m. (Use toasc.f to convert the binary shade files to ascii format for use by plotshd.m or whatever plot package you're using.)

The pressure field is normally calculated on a rectilinear grid formed by the receiver ranges and depths. If an irregular grid is selected, then the receiver ranges and depths are interpreted as a coordinate pair for the receivers. This option is useful for reverberation calculations where the receivers need to follow the bottom terrain. This option has not been used much. The plot routines (plotarr) have not been modified to accomodate it. There may be some other limitations.

There are actually several different types of Gaussian beam options (OPTION(2:2)) implemented in the code. Only the two described above are fully maintained.

The source beam pattern file has the format

NSBPPts
angle1 power1
angle2 power2
...

with angle following the BELLHOP convention, i.e. declination angle in degrees (so that 90 degrees points to the bottom). The power is in dB. To match a standard point source calculation one would used anisotropic source with 0 dB for all angles. (See at/tests/BeamPattern for an example.)

### (9) - BEAM FAN

Syntax:

NBEAMS ISINGLE
ALPHA(1:NBEAMS)

Description:

NBEAMS: Number of beams
(use 0 to have the program calculate a value automatically, but conservatively).

ISINGLE: If the option to compute a single beam in the fan is selected (top option)
then this selects the index of the beam that is traced.

ALPHA(): Beam angles (negative angles toward surface)

For a ray trace you can type in a sequence of angles or you can type the first and last angles followed by a '/'. For a TL calculation, the rays must be equally spaced otherwise the results will be incorrect.

### (10) - NUMERICAL INTEGRATOR INFO

Syntax:

STEP ZBOX RBOX

Description:

STEP: The step size used for tracing the rays (m). (Use 0 to let BELLHOP choose the step size.)
ZBOX: The maximum depth to trace a ray (m).
RBOX: The maximum range to trace a ray (km).

The required step size depends on many factors. This includes frequency, size of features in the SSP (such as surface ducts), range of receivers, and whether a coherent or incoherent TL calculation is performed. If you use STEP=0.0 BELLHOP will use a default step-size and tell you what it picked. You should then halve the step size until the results are convergent to your required accuracy. To obtain a smooth ray trace you should use the spline SSP interpolation and a step-size less than the smallest distance between SSP data points. Rays are traced until they exit the box ( ZBOX, RBOX ). By setting ZBOX less than the water depth you can eliminate bottom reflections. Make ZBOX, RBOX a bit (say 1%) roomy too make sure rays are not killed the moment they hit the bottom or are just reaching your furthest receiver.

The default step size has generally been OK; however, with the paraxial (Cerven) beams it was too aggressive on one simple test. The paraxial beams are generally much wider than the geometric beams so a given receiver gets contributions from beams with much more distance to the central ray. It is assumed that that increases the sensitivity to the accuracy of the ray trace (and its normals) which determine the phase of these distant beams as observed at the receive.

## Running BELLHOP

The main issue to be aware of is that ray tracing is very sensitive to environmental interpolation (both boundary and volume). The Gaussian beam options reduce that sensitivity significantly; however, one should still be attentive to this issue. The spline interpolation option to the SSP should be used with particular caution. In some cases, the spline fit is very smooth as desired; in other cases, the spline introduces large wiggles between ssp points, in its effort to produce a smooth curve. Use PLOTSSP to see how your fit looks.

BELLHOP numerically integrates the ray equations to trace a ray through the ocean. To avoid artifacts at discontinuties in the SSP, the step size is dynamically adjusted to make sure a step always lands on an SSP point, rather than stepping over it. (The beam curvature needs to be adjusted at each such point.) It's better to not use more points to describe the SSP than necessary to capture the physics because BELLHOP will end up using lots of small steps to have each ray land on the SSP points. Similarly, BELLHOP uses the altimetry and bathymetry points to define segments in range, and adjusts the step size so that the rays land on each segment boundary.

BELLHOP has no direct capability for modeling elastic wave propagation; however, elastic boundaries can be treated using BOUNCE to generate an equivalent reflection coefficient.

You can have BELLHOP use a range-dependent SSP by creating a separate SSPFIL containing that SSP data in a matrix form. (See Range-Dependent SSP File). The range-dependent SSPFIL is read if you select 'Q' (quadrilateral) for the SSP interpolation. The depths for the SSP points are read from the ENVFIL; the ranges are specified in the SSPFIL. See the example in at/tests/Gulf.

BELLHOP will produce some artifacts for receivers very close the the surface or bottom, because a beam is essentially folded onto itself upon reflection. The zone of overlap (which depends on the fatness of the beam) is not treated with a lot of care. You can minimize such artifacts by making the beams narrow, which in turn can often be done by using lots of rays. If you want to explore some behavior of the field for a receiver on the bottom, you generally should offset it a little bit. Alternatively, you can use reciprocity and interchange the role of the source and the receiver; sources near the bottom are not a problem.

## Frequently Asked Questions

Why is it that when I do an eigenray run, the rays do not seem to go through the receiver location?

An eigenray is a ray that connects the source and receiver. To find it precisely requires a root-finding process to identify the launch angle that generates a ray passing though the receiver location. The receiver position is a nonlinear and often discontinuous function of the launch angle, which complicates the root finding. Bellhop adopts a quick and lazy implementation and simply modifies the ray trace option to write only the rays that contribute to the receiver. Strictly speaking, these are not eigenrays. The number of such contributing rays depends on the type of beam that has been selected in Bellhop. If you use Geometric Hat-Shaped beams then typically you will get two contributing rays that bracket the receiver. This is usually the type of beam you would want to use to get the best picture of the eigenrays. If you use Gaussian beams then beams further away from the receiver may contribute.

Regardless of the type of beam, the beam width typically increases with arclength. To get contributing rays resembling eigenrays you will want them to have narrow beamwidths. The beam width (for a geometric beam) is defined by the spacing between adjacent rays. So here finally is the answer to the question: use a *LOT* of rays/beams to get narrow beams. An eigenray trace is typically very quick because you're looking at a single (or few) receivers. Use at least 1000 rays. Don't be afraid to use 10,000 or even a million rays. Each ray is traced independently so using a lot of rays does not increase the memory requirements. The run time will go up, but that is not usually a problem for a single receiver. Keep in mind that a real channel can produce a lot of micro-multipath and the idealized view of a high-frequency field being derived some a simple sum of a few paths is, well, idealized. You will tend to get less complicated eigenray pictures with smoother profiles, since each kink in the SSP or bathymetry contributes to the Pachinko (パチンコ) effect on the rays.

Why is the launch angle in the arrival file not one of the launch angles selected in the Bellhop input file?

Bellhop aggregates arrivals that have similar delay times. This reduces the storage requirements in both memory and in the output file. It also reduces the computation required in convolving a source waveform with the channel impulse response as defined by the arrivals. Finally, it presents a less confusing plot of the channel impulse response.

The aggregation is based on a wavelength tolerance. The angles written in the arrivals file are also an average of contributing rays and therefore do not necessarily correspond to the launch angles.

`The reason you get multiple arrivals that are all really part of a single arrival is because of:`

`` `1) with the geometric beam, it creates an arrival for each of a pair of rays that bracket the receiver.`

`` `2) with Gaussian beams you further get contributions from rays that are within a few beam widths of the receiver`

`` `3) with more complicated SSPs the ray fan can become unsmooth, producing a sort of micro-multipath.`

Why am I getting a message about there being insufficient storage for the ray trajectory?

Storage is pre-allocated for each ray based on the MaxN parameter in BellhopMod. (Dynamic allocation is a bit complicated because one doesn't know the number of ray steps needed in advance.) You can easily change MaxN. Bellhop doesn't use a lot of memory so you can make MaxN a large number. However, in unusual circumstances a ray can outrun the MaxN limit, using up a lot of CPU time in the process. When that happens, it usually indicates some kind of problem. So MaxN is a kind of governor that prevents infinite loops. It rarely happens, but when it does, it is often when a curvilinaer boundary is used. The curvilinear option is a bit odd in that it uses a piecewise linear approximation to adjust ray steps to land on the boundaries. However, it adjusts the angle of the reflected ray using a higher-order fit to the boundary. Sometimes that inconsistency causes confusion in the logic that detects a ray crossing the interface and then Bellhop may make a large number of infinitesimal steps trying to get the ray back into the water column. If you get this error, it is a good idea to do a ray trace plot to see if there is a ray getting stuck at a boundary. You can also look in the ray file itself and see if there is a ray with a lot of steps that has gotten stuck.

Why does plotray.m not show the rays at the point where they actually hit the bottom?

When the number of steps in a ray is very large, Bellhop may (depending on the version) sub-sample the rays so that the file is not too large. The sub-sampled rays may not include the steps where the ray hits the bottom. It is trivial to change the routine that writes the rays to turn that feature on or off. In recent versions, I've tended to disable that feature to avoid confusion.

What is causing the error message about a ray exiting the box where the bathymetry, altimetry, or SSP is defined?

The ray box (rBox, zBox) is a mask that traps rays that exit that box. The environment (SSP, bathymetry, altimetry) needs to be defined for any place where the rays get to. Usually the bathymetry and altimetry are the key limits in the vertical direction. If, for example, your bathymetry dips below the lowest tabulated depth for the SSP, you could have problems. Similarly, if rBox is larger than the greatest range of the bathymetry, altimetry, or SSP then the ray enters a domain where the environment is not defined, causing an error.

The ray box is defined in terms of an absolute value, so the limits of the ray are z in [ -zBox, +zBox ] and r in [ -rBox, +rBox ].
BELLHOP and BELLHOP3D can trace rays that turn around and go back to the source. They may then travel to negative ranges. If you did not define the bathymetry for negative ranges, then you will also get this error message. These rays, including the negative ranges, are indeed physical--- you should think of the range slice as a slice through a 3D environment with negative ranges just being along the 180 degree radial. In this case, make sure your bathymetry covers the domain [ -rBox, rBox ].

Of course, this message can also happen when the rBox limit fails to trap an outgoing ray before it gets past the last bathymetry point. You would then need to reduce rBox or increase the coverage of your bathymetry to include larger ranges.