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Arctic Dispersion Interruption Phenomenon and Sound Source Depth Estimation

Weng Jinbao, Yang Yanming, Chen Benqing, Xu Dewei, Zhou Hongtao

arXiv:2608.30360v1physics.app-phcs.SD

TL;DR

The paper addresses source-depth estimation in the deep Arctic, where a distinctive surface normal-mode waveguide produces dispersion interruptions when source or receiver depths approach modal nodes. It analyzes this phenomenon and estimates source depth from interruption frequency, with validation through simulations and experiments.

  • Problem

    Deep-Arctic source-depth estimation is a challenging localization problem requiring methods suited to its distinctive acoustic environment.

  • Method

    The paper analyzes modal dispersion interruption and estimates source depth from interruption frequency using the relationship between modal nodes and frequency, with known receiver depth.

  • Results

    The dispersion structure exhibits modal dispersion interruption, and the source depth can be estimated from an interruption frequency under the stated depth conditions.

  • Takeaways & Limitations

    Interruption frequency provides a basis for source-depth estimation in the deep-Arctic surface normal-mode waveguide.

Abstract

from arXiv · show

The sound speed profile in the deep Arctic Ocean causes the surface layer to form a normal mode waveguide. When the depth of the sound source or receiver is near a node of the eigenfunction, the source cannot excite the mode, or the receiver cannot detect it, resulting in the modal amplitude at the receiver being approximately zero. This manifests as a dispersion interruption in the dispersion structure, which can be observed through time-frequency analysis of the received acoustic signal. Based on the interruption frequency identified from the received signal, combined with the relationship between node depth and modal frequency calculated from the ocean sound speed profile, the source depth can be estimated if the receiver depth is known. The phenomenon of dispersion interruption and the method of estimating source depth have been validated through simulations and experiments.

I. INTRODUCTION

Deep-Arctic source-depth estimation is complicated by distinctive sound-speed profiles, propagation conditions, and practical limitations of existing methods. This paper studies modal dispersion interruption and explores estimating source depth from its interruption frequency.

  • Motivation: Deep-Arctic source-depth estimation is more complicated than in conventional deep and shallow seas because acoustic-field characteristics vary with conditions.The surface water column contains multiple modes, while deeper columns are dominated by multipath rays.
  • Related methods: Existing Arctic approaches use synchronized vertical arrays, large-aperture arrays, deep-ray arrival angles, or direct–surface-reflection arrival differences.These methods support matched-field localization, mode separation, range estimation, or depth estimation under specified propagation conditions.
  • Practical limitations: Large-aperture synchronized vertical arrays pose significant challenges for at-sea experiments.Single-hydrophone methods can also require complex mode separation, modal-dispersion matching, and modal-amplitude matching.
  • Practical limitations: A single-hydrophone upper-frequency-limit approach is affected by ice attenuation and requires the receiver to be shallower than the source.That deployment constraint is difficult to implement practically.
  • Paper contribution: The paper studies modal dispersion interruption in the deep-Arctic surface normal-mode waveguide and its relationship with source and receiver depths.It presents theoretical analysis, a source-depth estimation method, simulations, and experimental validation.

II. THEORETICAL ANALYSIS OF THE MODAL DISPERSION INTERRUPTION PHENOMENON

The deep Arctic surface layer supports normal-mode propagation, with modal amplitudes determined by source and receiver depths through mode eigenfunctions. When a source lies at an eigenfunction node, the corresponding modal amplitude approaches zero and creates a dispersion interruption.

  • Sound-field characteristics: The surface layer of a typical deep Arctic environment contains normal-mode and ray arrivals, so source-depth estimation methods depend on depth range.At moderate and large depths, the field is mainly ray arrivals; in the surface range, both normal-mode and ray methods may apply.
  • Normal-mode model: The normal-mode sound field is a superposition of modes whose contributions depend on eigenfunctions evaluated at the source and receiver depths.The modal expression includes horizontal wavenumber, attenuation, eigenfunctions, source and receiver depths, range, effective-mode count, and source spectrum.
  • Eigenfunction structure: Different modes have different vertical eigenfunction distributions, enabling the same source depth to produce different modal excitation strengths.The vertical coverage of modal eigenfunctions increases with mode number, while lower-order modes concentrate energy near the surface layer.
  • Depth-estimation principle: Source depth can be inferred by identifying a modal interruption frequency and calculating that mode’s first eigenfunction node depth with a normal-mode propagation model.The first node is used because the mode amplitude below it is largest, making the node effect more visible in time-frequency analysis.

III. SOURCE DEPTH ESTIMATION BASED ON MODAL DISPERSION INTERRUPTION

The method estimates source depth from modal dispersion interruptions by relating observed interruption frequencies to eigenfunction node depths. Receiver position determines whether interruptions reflect the source alone or a combination of source and receiver nodes.

  • Applicability conditions: Because attenuation leaves only low-order modes with sufficient signal-to-noise ratio, the method is restricted to low-frequency, long-range, broadband sources.A clear dispersion structure is also required.
  • Applicability conditions: The interruption must lie within the mode’s frequency limits and be sufficiently clear in time-frequency analysis for the method to apply.The upper limit is set by the larger source or receiver depth, while the lower limit is affected by seabed topography.
  • Receiver-depth cases: When the receiver is shallower than the source within the surface 400 m, multiple interruption bands divide each modal dispersion curve into segments.The bands correspond to multiple node frequencies associated with the source and receiver depths.
  • Receiver-depth cases: When source and receiver depths are close within the surface 400 m, a wide interruption band depends on both depths; with the receiver at 500–600 m, a narrow band depends only on source depth.These cases provide different relationships between interruption structure and the unknown source depth.
  • Estimation principle: The modal interruption frequency corresponds theoretically to the first eigenfunction node, allowing source depth estimation when receiver depth is known.A modal interruption band can encode the first-node positions of both source and receiver depths.
  • Node-frequency relationship: The first-node depth decreases with frequency, so shallower source or receiver depths correspond to higher node frequencies.This relationship is represented by the first-node depth-versus-frequency curves.
  • Higher-node effects: Multiple receiver-related interruptions must be considered in shallow settings because higher node numbers produce lower frequencies at the same receiver depth.For a 250 m receiver depth and mode 7, the four node frequencies are 120, 90, 70, and an incompletely reported fourth value.

IV. SIMULATION OF MODAL DISPERSION INTERRUPTION AND SOURCE DEPTH ESTIMATION

The simulations evaluate modal dispersion interruptions and source-depth estimation across receiver-depth configurations in a representative deep Arctic environment. Broadband normal-mode modeling and time-frequency analysis are used to compare the resulting dispersion structures with the depth-based theory.

  • Simulation cases: The simulations examine two receiver configurations: both source and receiver within the surface 400 m, and receiver depth at 500–600 m with source within 400 m.These cases test the estimation method under different receiver-depth conditions.
  • Simulation cases: The source depth is set to 300 m, while receiver depths are grouped as less than, close to, or greater than the source depth.This grouping is used to analyze received-signal dispersion characteristics across receiver-depth ranges.
  • Simulation setup: The model uses a typical experimental deep Arctic sound-speed profile, 3800 m sea depth, a 10–160 Hz band, and the first experimental station distance.The station distance is 270.0128 km.
  • Simulation setup: Kraken calculates broadband complex sound pressure, which is inverse-Fourier-transformed into a time-domain signal for time-frequency analysis of modal dispersion interruptions.The analysis then relates interruption behavior to source and receiver depths.

1. Simulation of the modal dispersion interruption phenomenon

Simulations show that modal dispersion interruptions depend on the relative source and receiver depths and appear at node-related frequencies. Their pattern changes when the receiver is shallower, near, or deeper than the source.

  • Modal interruption structure: The simulated dispersion curves are divided into two or three segments, with interruption points linked mainly to source or receiver depths coinciding with first nodes.The high-frequency segment has larger energy and corresponds to the first wave packet of the modal eigenfunction.
  • Relative source and receiver depths: When the receiver is shallower than the source, interruptions occur first at the receiver-related frequency and then at the source-related frequency as modal frequency decreases.The receiver-related interruption frequency is higher because the receiver depth is smaller than the source depth.
  • Relative source and receiver depths: Higher-frequency interruptions can arise from second or third nodes associated with the source depth, in addition to first-node interruptions from source and receiver.Receiver-related node effects must be excluded to isolate the first-node frequency caused by the source depth.
  • Relative source and receiver depths: When receiver and source depths are close, modes 5 to 10 exhibit regular, wide-band interruptions because their modal amplitudes become small over a frequency band.The interruption regularity is reported as beneficial for quickly estimating source depth.
  • Relative source and receiver depths: When the receiver is much deeper than the source, high-frequency components of higher-order modes become unexcitable, concentrating observable interruptions mainly in lower-order or middle modes.The interruption phenomenon is mainly visible in mode 5 for the described large-depth case.

2. Modal dispersion structure with known source and receiver depths

For known source and receiver depths, modal amplitude products explain the simulated interruption structure, and group-velocity calculations reproduce the interruption frequencies observed in simulated time-frequency analyses.

  • Modal amplitude mechanism: When source and receiver depths are close, their modal amplitude variation patterns are similar, producing a high-amplitude high-frequency part followed by a first-node interruption band.The received modal amplitude is modeled through the combined effect of source and receiver depth.
  • Interruption identification: The combined source-and-receiver amplitude condition is used to identify interruption bands by thresholding frequencies on both sides of the band’s maximum.The threshold is the maximum amplitude within the interruption band.
  • Source-depth estimation: Modes 5 to 10 show similar frequency-dependent amplitude variation when source and receiver depths are close, supporting source-depth estimation under these conditions.The modal amplitudes are evaluated across frequencies for both depths.
  • Simulation validation: Modal group-velocity curves convert estimated interruption frequencies into arrival times for comparison with simulated acoustic signals.The resulting dispersion curves are compared with simulated signal time-frequency analyses.
  • Simulation validation: Predicted interruption frequencies are completely consistent with simulated dispersion results, explaining the modal interruption mechanism in the deep Arctic surface waveguide.The agreement is especially clear for interruption frequencies across different modes when source and receiver depths are close.

V. EXPERIMENT ON MODAL DISPERSION INTERRUPTION AND SOURCE DEPTH ESTIMATION

Arctic propagation experiments validate the predicted interruption frequencies across receiver depths for a calibrated 300 m source. The frequency agreement persists despite arrival-time errors caused by unavailable path sound-speed profiles.

  • Shallow and near-source receivers: For shallow receivers, source-related interruptions coexist with multiple receiver-related interruptions corresponding to the first through fourth nodes.Estimated interruption-frequency points agree well with experimental received signals, although some arrival times differ.
  • Experimental limitations: The method focuses on interruption frequency; modal arrival times contain errors because no sound-speed profile was available along the propagation path, especially for higher-node frequencies.Complex surface sound-speed variation particularly affects second-, third-, and fourth-node arrival times.
  • Shallow and near-source receivers: A larger source–receiver depth difference produces a wider modal interruption band, while the interruption becomes much smaller as receiver depth approaches the source depth.This comparison is reported for HTD06 and HTD07.
  • Deep receivers: At large receiver depths, interruptions concentrate mainly in mode 5 because higher-order modes have low high-frequency energy.The mode-5 interruption frequency estimated from source depth agrees well with the experimental interruption frequency.
  • Source-depth estimation: Deep reception can enable rapid source-depth estimation from interruption frequencies when the observable frequency segment is affected only by source depth.The receiver should not be so deep that reception becomes ray-like and loses dispersion effects.

VI. CONCLUSIONS

In the deep Arctic surface layer, modal dispersion interruptions arise from eigenfunction nodes and depend on both source and receiver depths. Their frequency characteristics support source-depth estimation across different depth configurations, with stated advantages over several conventional approaches.

  • A normal mode waveguide forms within approximately the upper 400 m of the deep Arctic Ocean.
  • Modal dispersion interruption occurs when a source lies at a modal eigenfunction node, preventing mode excitation.
  • When receiver and source depths are close, the interruption band spans a range whose upper and lower limits correspond to the smaller and larger depths, respectively.
  • When the receiver is much deeper than the source, the interruption range is small and determined only by source depth, enabling source-depth estimation.
  • When the receiver is shallower than the source, multiple interruptions can occur; receiver-related node frequencies can be excluded using simulations, leaving source-related frequencies.
  • The method requires no strict receiver-depth placement, remains applicable in the deep Arctic surface layer, and can use hydrophones deeper than 400 m.
  • The approach uses lower-frequency modal bands, avoiding double-duct crossing problems that make modal upper-frequency limits difficult to determine.
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