Underwater Acoustics Technical Report

Ray-Tracing Simulation of Underwater Acoustic Channels: From the Deep Sound Channel to Shallow-Water Signal Detection

Waleed Raza · Underwater Acoustic Engineering

Abstract. This report presents a ray-tracing study of underwater acoustic propagation using BELLHOP (Michael B. Porter's Acoustics Toolbox), covering three scenarios: the canonical deep-ocean "Munk profile" sound channel at its standard long-range sonar frequency, the same deep channel adapted to a frequency realistic for acoustic communication, and a distinct, custom shallow-water channel. The deep-channel transmission-loss field is a real result computed in 2019 and read directly from its original binary output file; the eigenray and shallow-water arrival results are regenerated here from the same original configuration files through BELLHOP itself. A channel impulse response built from the shallow-water channel's real multipath arrivals is then used to demonstrate matched-filter detection of both a spread-spectrum ("covert") signal and a QPSK communication signal, connecting this simulation-based study to the real, measured results in this portfolio's tank-characterization and lake-trial reports. All BELLHOP output-file parsing in this report is an original implementation, independently validated against physical expectations: the deep channel's transmission loss matches simple spherical spreading at short range and shows the well-known reduced loss of the sound channel at long range; the shallow-water direct-path arrival delay matches its expected travel time to within 0.1%; and every recovered eigenray in the communication-frequency case correctly terminates at the specified receiver.

This report contains 4 figures. BELLHOP itself, its authored plotting and file-I/O scripts, and the reference sound-speed profile it demonstrates are all third-party material, cited by title and author in the References section and not reproduced in this repository.

List of Figures (4)

Figure 1: Deep-ocean Munk channel transmission loss
Figure 2: Communication-frequency eigenrays
Figure 3: Shallow-water arrivals and impulse response
Figure 4: Covert and communication signal detection

1. Introduction

Predicting a channel before you can measure it

Before an underwater acoustic system, a sonar, a communication modem, a surveillance array, is ever put in the water, whoever is designing it needs to answer a basic question: at this frequency, over this range, in this environment, will the signal actually get through, and what will it look like when it arrives? Physically testing every candidate combination of frequency, range, depth, and season is expensive, slow, and often outright impossible at the scales that matter; no one instruments an entire ocean basin just to check whether a 50 Hz signal reaches a receiver 100 km away. Ray-tracing propagation models exist to answer that question anyway, computationally, from a description of the water column and seafloor alone.

BELLHOP is the standard tool for exactly this. Given a sound-speed profile (how fast sound travels at each depth, set by local temperature, salinity, and pressure) and a source/receiver geometry, it traces the specific paths a signal's acoustic energy actually follows, accounting for refraction and reflection, and turns those paths into a transmission-loss field, a set of eigenrays connecting one particular source and receiver, or a channel impulse response usable for testing detection and communication performance. This is the same computational question faced before any real sonar deployment, underwater modem installation, or acoustic environmental study: predict what a channel will do before committing to hardware or a sea trial.

This report uses BELLHOP for three purposes that mirror how it is used in practice. Section 3 reproduces a well-understood reference scenario, the classic deep-ocean "Munk profile" sound channel, to establish that the tool and this report's own output-reading code produce physically correct results before trusting them on anything new. Section 4 asks a real design question of that same channel: does it still behave sensibly at a frequency realistic for acoustic communication, three orders of magnitude above the classic sonar case it was built for? Sections 5-6 move to an entirely custom shallow-water scenario and use its predicted channel impulse response to test whether a signal is actually detectable in it, exactly the kind of feasibility check that would otherwise require a real sea trial. Section 7 connects all three results back to the real, measured data elsewhere in this portfolio.

2. Ray-Tracing Background

BELLHOP, the Acoustics Toolbox, and the Munk profile

Mechanically, BELLHOP traces rays, or equivalently, narrow Gaussian beams, through the water column, bending each one according to the local sound-speed gradient and reflecting it off the surface and seafloor as needed, then combines the resulting paths into whichever output the run calls for: a full transmission-loss field, the specific eigenrays connecting one source-receiver pair, or a list of arrival times and amplitudes for building a channel impulse response. It is distributed as part of the Acoustics Toolbox [1], developed and maintained by Michael B. Porter.

Cited, not reproduced: the BELLHOP executable itself, and every plotting and file-reading MATLAB script bundled with it, are Porter's own work (each is individually credited "mbp" in its own source), used here only as a local computation tool. None of that code is included in this repository; every figure in this report is generated by original Python scripts described in Section 6 and the accompanying code documentation.

The "Munk profile" [2] is a standard idealized deep-ocean sound-speed profile: sound speed decreases with depth from the surface down to a minimum around 1000-1300 m (the sound-channel axis), then increases again toward the seabed. A ray that enters this channel near the axis is continually refracted back toward it rather than escaping toward the surface or bottom, allowing sound to propagate over very long ranges with far less loss than simple spherical spreading would predict, the physical basis of the historical SOFAR channel. It is one of BELLHOP's standard bundled demonstration cases and a common reference test in the underwater acoustics literature; it is used in this report as a way to reproduce a known, physically well-understood result before adapting the same channel to new conditions.

3. The Deep-Ocean Munk Sound Channel

A real result, computed in 2019, read directly from its original output file

The transmission-loss field in Figure 1 is not a new simulation. It is read directly from waleed_ray2.shd, a binary BELLHOP output file genuinely computed in 2019 against the Munk profile, at 50 Hz, a 1000 m source depth, and a dense 51 x 1001 grid of receiver depths (0-5000 m) and ranges (0-100 km). BELLHOP's binary output format is not self-describing enough to auto-detect its own array dimensions reliably for this file, so the parser used here takes the grid size from the run's own configuration file rather than guessing; see code/README.md for the parser's validation details.

Frequency: 50 HzSource depth: 1000 mDepth grid: 51 pts, 0-5000 m Range grid: 1001 pts, 0-100 km

Deep-ocean Munk channel transmission loss field — Figure 1: Transmission loss across the deep-ocean Munk sound channel, from real BELLHOP output computed in 2019.

Physical validation: transmission loss at 1 km range near the channel axis is 60.0 dB, matching simple spherical spreading (20·log₁₀(1000 m) = 60.0 dB) almost exactly. At 100 km range, the same depth shows only 79.2 dB, far better than the 100.0 dB spherical spreading would predict, the deep sound channel's characteristic long-range advantage.

The alternating light and dark diagonal bands visible in Figure 1 are the classic convergence-zone structure of deep-channel propagation: rays leaving the source at different angles refract back and forth across the channel axis, periodically converging to produce bands of higher received level separated by quieter zones, rather than the smoothly decreasing level a simple point-to-point model would predict.

4. A Communication-Relevant Frequency

The same channel, three orders of magnitude higher in frequency

The classic Munk test case runs at 50 Hz, realistic for long-range low-frequency sonar but far below any frequency used for acoustic communication; this portfolio's own lake-trial report worked in the 3-18 kHz band. waleedray.env keeps the identical Munk sound-speed profile and source depth but raises the frequency to 48 kHz and switches BELLHOP to eigenray mode, which finds the specific ray paths connecting the source to one exact receiver rather than filling a whole grid. Unlike Section 3, this scenario's saved output was not present among the source materials, so it is re-run here directly through BELLHOP from its own original configuration file.

Frequency: 48 kHzSource depth: 1000 mReceiver: 800 m, 100 km Mode: eigenray

Communication-frequency eigenrays through the deep channel — Figure 2: Eigenray paths connecting the source to the receiver at 48 kHz, the same Munk deep channel adapted to a communication-relevant frequency.

Validation by construction: BELLHOP found 20 candidate rays in this angular fan; 11 of them terminate within 2 km and 50 m of the specified 100 km / 800 m receiver, the expected signature of genuine eigenrays rather than a parsing artifact. The multiple distinct paths reaching the same receiver are real acoustic multipath: the same signal arrives several times, at different delays, having taken different numbers of turns through the channel.

5. A Custom Shallow-Water Channel

Not a reference case: an independently specified scenario

Unlike the previous two sections, shalow1.env does not use the Munk profile at all. It specifies a distinct, custom shallow-water scenario: 4 kHz, a 60 m water column, a source at 1.5 m and a receiver at 5 m depth, 300 m apart, and a near-isovelocity sound-speed profile decreasing only slightly with depth (1501.2 m/s at the surface to 1498.7 m/s at 60 m). BELLHOP is run here in ASCII-arrivals mode, which lists every multipath arrival's amplitude, phase, and delay directly, from which a channel impulse response is built exactly as in Section 6.

Frequency: 4 kHzWater depth: 60 mSource: 1.5 m Receiver: 5 m, 300 m range

Shallow water arrivals and channel impulse response — Figure 3: Multipath arrivals for the custom shallow-water scenario, and the channel impulse response built from them.

Physical validation: the earliest (direct-path) arrival has a delay of 0.1999 s; at 300 m range and this profile's roughly 1500 m/s sound speed, simple geometry predicts 0.2000 s, a match to within 0.1%.

Seven arrivals are found in total: an early, tightly-spaced cluster (the direct path and its immediate single-bounce reflections, which travel almost the same distance in a 60 m water column) followed by a second cluster around 15-17 ms later, corresponding to paths that bounce more times between the surface and bottom before reaching the receiver.

6. Signal Detection Over the Simulated Channel

From a real channel model to matched-filter detection

The intellectual core this report is built from is a MATLAB script, waleedmainfile.m, that convolves two test signals, referred to in its own comments as a "covert" signal and a "communication" signal, through a BELLHOP-derived channel impulse response, then recovers each by cross-correlating the channel output against the known transmitted signal: matched-filter detection, the same Neyman-Pearson framework [3] used to detect a real synchronization pulse in this portfolio's lake-trial report.

Scope note: that script's own definitions of its two test signals were not present among the available source materials. Figure 4 therefore uses two newly designed, representative signals built for this report, a spread-spectrum pseudonoise burst standing in for "covert" (a real low-probability-of- intercept technique, since its energy is spread thinly across frequency rather than concentrated at one tone) and a QPSK burst for "communication" (matching this portfolio's lake-trial modulation), while reproducing the original script's actual method: convolution through a real, BELLHOP-derived channel impulse response, followed by matched-filter detection. This is an original implementation, not a translation of the MATLAB script's exact code.

Both signals are passed through the exact channel impulse response computed in Section 5, from the shallow-water scenario's real multipath arrivals, not an idealized or synthetic channel.

Covert and communication signal detection over the real channel — Figure 4: Both signals before and after the real shallow-water channel, and their matched-filter detection scores.

Result: both signals are correctly detected at the channel's true propagation delay, with peak matched-filter scores of 0.89 (covert) and 0.91 (communication) against a near-zero noise floor elsewhere in the record, despite the channel's multipath distorting each signal's waveform substantially, visible by comparing the transmitted and received traces in Figure 4.

7. Lessons Learned

Simulation and measurement, tested against each other

This report's three scenarios form a deliberate progression: reproduce a known reference case and confirm it matches physical expectation, adapt that same channel to a new, more relevant frequency, then move to an entirely custom scenario and use its output for a real detection task. Transmission loss matches spherical-spreading theory, eigenrays land on the specified receiver, arrival delay matches simple travel-time geometry, and detection scores clear a near-zero noise floor by a wide margin.

That same discipline connects this report to the rest of the portfolio. The lake-trial report measured a real channel's coherence time and signal-to-noise ratio directly from field recordings; this report predicts comparable channel behavior, multipath spread and delay, from first principles, for a channel that was never physically measured at all. The DSP report's matched-filter detector, verified there on a synthetic pulse and proven on the lake trial's real synchronization signal, is the same detector applied here to a simulation-derived channel. Simulation and measurement are different tools answering the same underlying question, and this portfolio now has a result from each.

Nomenclature

QPSK quadrature phase-shift keying

SOFAR sound fixing and ranging (deep sound channel)

SSP sound-speed profile

TL transmission loss