PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Shipping noise propagation at the shallow sea
Eugeniusz KOZACZKA; Grazyna GRELOWSKA
Gdansk University of Technology, Poland

ABSTRACTThe paper proposes a method to determine the noise map on the shallow sea basin based on the classicalsolution of the wave equation for specific boundary conditions. As a result, we get a solution consisting of asuperposition of analytical solutions for the issue of own waves related to the depth in relation to changes in
the function responsible for changes from distance to source. For a stationary problem, the expression
describing the noise of the selected vessel in spectral form will be used as a function of excitation. This
formulated issue allows us to estimate the underwater noise level at any distance and depth from the source.
The analysis of the superposition of underwater acoustic disturbances makes it possible to determine thevalue of the sound pressure level from the sources of these disturbances.
Keywords: Shipping noise, Shallow sea, Modal propagation

1. INTRODUCTION
The issue of rapid noise growth in the oceans and seas is currently a challenge for research teams
dealing with underwater pollution. At present, for the EU water areas, a direct ive has been developed,
which is intended to cause a reduction of acoustic background, the main component of which isunderwater noise caused by human activities, mainly related to maritime transport (shipping noise).
It’s common knowledge that the underwater environment contamination by noise has been growing
year by year especially close to fairways along which transport ships, touristic motor boats and otherwater surface communication means operate [1], but also close to active objects of marine
infrastructure [2]. The situation becomes relatively serious as excessive noise and other energy sources
significantly affect not only living conditions inside ship [3] but also underwater biological life [4,5]which becomes more and more endangered not only by noise, light, uncontrolled impact of chemical
products, but also unbalanced management of fish resources.
For that reason the EU has issued an appropriate directive obligating EU countries to obey definite
acoustic standards concerning water environment. The directive of EU Parliament and Council
2008/56/WE of 17 June 2008 enacts framework for EU activities in the domain of sea environmental
policy, within which EU countries have to undertake necessary actions aimed at reaching ormaintaining a good environmental status of sea waters (Good Environmental Status – GES) not later
than before 2020 [6,7]. According to the directive, in order to protect sea water environment, EU
countries have to prepare and implement a maritime strategy and sea water monitoring pr ogram.
In the directive 2008/56/WE there are defined 11 descriptive indices for which an assessment as tothe defined criteria of good environmental status should be performed. One of them is the index W11– Underwater noise and other energy sources.
Relating the considerations to the Baltic Sea, especially to its southern region, one can state that
propagation of acoustic waves is of a specific character associated with small depth of the water areas
in question [8,9]. In view of occurrence of the geometrical limitations of the medium in which acoustic
wave propagates, namely, close presence of free water surface and seabed, a form of propagation of
disturbances definitely differs from that typical for deep waters [10,11,12] where water depth is muchgreater than length of wave of the lowest frequency produced by a ship sailing nearby.
Therefore in a distance from the ship there is produced an acoustic field which has a character ofmoving waves, called wave modes. This results from a complex structure of i nterferring waves which
multifold reflect from both seabed surface and free sea water surface [ 13,14]. Apart from thephenomenon of reflection from free sea water surface we have to do with the change in wave phase by
the angle π, which means that the wave reflected from the surface is in counter-phase in regard to theprojecting wave. Therefore the interferential acoustic field has a property of moving the wave modes,

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for which a group velocity is characteristic. It means that we have to do with the phenom enon ofgeometrical dispersion of velocity, known from physics.
Apart from the modal propagation of acoustic waves, additional phenomena associated withpresence of seabed take place. The seabed has physical features called the material constants such as
density and elastic wave propagation velocity [15,16], of values close to respective properties of sea
water. It means that seabed impedance is usually greater or a little greater than that of sea water.
For this reason some part of acoustic wave energy penetrates the seabed. In case of a rocky seabed,i.e. that having shape elasticity additional transverse acoustic waves in the range associated witha spectrum of acoustic waves produced by underwater acoustic disturbance sources (i.e. ships), may
occur. In this paper there are presented results of numerical investigations based on the real data frommeasurements of noise produced by a selected floating unit (ship) [17], concerning selectedcharacteristic spectral components. The simulations were performed by applying a shallow sea modelof definite physical parameters such as acoustic wave propagation velocity, geometrical dimensions(water depth) as well as acoustic parameters of seabed, that was discussed more thoroughly in the
publications [18,13]. The data in question were presented in the form of distribution of particular wave
modes in function of water depth for selected horizontal distances from source of disturbances. Resultsof the investigations will be used for the determining of acoustic climate of a water area, that is the key
procedure for taking into account a single object emitting underwater noise.

2. UNDERWATER NOISE EMITTED BY SHIPS
Ship traffic is a main source of underwater noise, especially in regions of fairways. Ship is abroad-band source of spectral characteristics which is tightly associated with applied design solutions
as well as current working parameters of shipboard devices.
On ships, their propellers are the most efficient source of underwater noise. One of its parts is thepropeller rotation frequency and its harmonics. Noise components coming from the propeller
constitute usually a dominating part of underwater disturbances in the low -frequency band at large
speeds of ship, especially when the propeller is in developed cavitati on state [11]. Ship propulsion
engine is the main source of underwater noise at a moderate speed of ship. Generally, a level ofunderwater noise spectrum components of a ship is not stable due to changes in propeller load in
different sea states. The acoustic power radiated at the fundamental ignition frequency is associatedwith engine output and may be estimated equal to about 0,1% of the total engine power.
Information on spectrum characteristics, called also ship’s signatures, we obtain on the basis ofunderwater noise measurements carried out in mobile or stationary testing grounds [17,11]. The
mobile testing ground may be consisted of a few hydrophones fastened on a frame in some distancefrom each other. The measurements can be conducted with hydrophones arranged either in horizontal
or vertical plane. A merit of such measuring system is its possible location in an arbitrary point ofwater area. More precise measurements of underwater noise are conducted in stationary testing
grounds. In this case sensors are located in strictly determined points and strictly determined depth
whereas a tested ship moves over them at a given course. A drawback of the solution is that there is notpossible to obtain results for one depth and one kind of seabed. On the ba sis of measurement resultsa series of ship underwater noise characteristics can be obtained, that allows to assess pressure levelchanges in function of distance and depth for different ship speed values and different settings ofshipboard devices. One of the characteristics is spectrum characteristics, called often ship’s signature.
An example of ship’s signature is shown in Fig. 1.

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Figure 1 – An example of ship’s signature
Worth stressing, that, independent of ship’s type, the main part of acoustic energy radiated to water
is located within low frequency band, up to a few hundred Hz.

3. PROPAGATION OF ACOUSTIC WAVES IN THE WATER LAYER OVER A
BOTTOM WITH FINITE ACOUSTIC IMPEDANCE
The case of propagation of acoustic waves generated by a source of zero ord er in flat-parallel
waveguide corresponded to idealized conditions. The simplifications concerned, in particular, thelower half space. In reality, the sea bottom with properties close to these of the perfectly rigid medium
is rather an exception [19,20,21]. The assumption allowing us to simplify the effects occurring on thewater-air boundary is in principle always valid, as the acoustic impedance of water is about 3500 times
higher than the acoustic impedance of air [6,22].
On the lower boundary of the system, the situation is entirely different. Acoustic impedance of thesea bottom is typically close to this of water. In the case of sandy seabed, acoustic impedance of water
is only four times lower than impedance of the sea bottom. For silty and clayey bo ttom the ratio is evenlower. Therefore, some portion of acoustic energy will be transferred from the water layer to thebottom, resulting in a decrease of the acoustic pressure level with increasing distance. After manytransformations which were presented at work [23] we obtained, finally,p  r, z  

2 Q i /4 
  1
  1  i 4
2 ikrn r  2 n r
,
e
cos
n

z
cos
e e


 0
 n   ze
h
h
2
h
2
 krn r
n 0

(1)

where

1

n  2
 2n h ln bˆ1  n0

 
1 
2
2 hk     n  
2 
 

2

,

(2)

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2
2
ˆb    m cos   n1  sin  ,1
m cos   n12  sin 2  n0  arc sin 

1
2

(3)

n  kh.

(4)

Symbol r denotes the distance from the source in a horizontal plane, z is the depth of the receiver, Q
stands for source volumetric velocity, ρ – density of medium in which wave propagates, h – depth of waterlayer, z0 – depth of the source, krn – horizontal wave number.
(5)c  
1 
krn  1  
 n  2 
 h 

2𝑏(𝛼𝑛0 ) is the reflection coefficient at incident angle α for a zero-order point source, m – relative density ofbottom material, m=ρ1/ρ, n – relative sound speed in bottom material, n=c1/c, ρ1, c1 – density and speed ofsound in bottom, ρ, c - density and speed of sound in water.
The impact of sea bottom properties on acoustic wave propagation is included in the expression exp(-δ2nr). When deriving expression (1), modulus of the reflection coefficient constituting a multiplier at
hyperbolic functions was assumed to be unity. This allowed us to obtain a simple representation of wave
modes propagating along depth of the layer. However, the actual value of the reflection coefficient
responsible for attenuation of individual wave modes was retained in the exponent.
Relationship (1) describes the acoustic field generated by a zero-order point source. Comparing it withperfectly reflecting the bottom it can be seen that they include additional terms. The terms represent a
decrease of the acoustic potential with the distance.
The relationships (1) will be further used in numerical investigations of the impact of properties of sea
bottom on acoustic fields and confronted with results measured in the experiment. Reflection coefficients,
for different sea bottom materials, have been determined by the authors by means of the impulse method.

4. WAVEGUIDE SOUND PROPAGATION IN SHALLOW
Characteristic features of waveguide propagation in shallow sea will be presented on the example
of results of experimental and numerical investigations of a tug. In the spectrum there is possible todistinguish a series of characteristic components within a rather broad frequency band, namely almost
up to 1000 Hz. In Table 1 are shown the components determined on the basis of measurements
conducted under the ship in a 20 m deep water area with the use of a hydrophone placed 1 m over theseabed, whose pressure level exceeded 155 dB.
Table 1 – Components of underwater noise spectrum of a tug whose pressure level exceeded 155 dB,i.e. about 56 PA
Frequency
48
60
107
169
213
322
426
449
459 484 851 966[Hz]
Pressure
91.9 123.2 121.8 60.1 113.6 95.5 137.9 96.5 75.6 79.1 59.3 90.1
p0[Pa]
The calculations were made for all distinguished frequencies under the following assumptions:• Water depth h=20 m• Salinity S=7.1 PSU• Water temperature T=14°C• Sound speed in water, c=1470.8 m/s• Water density, ρ = 1004.7 kg/m3• Source immersion depth z = 1m under water surface.
There were considered situations of sound propagation over a sand, gravel and silt seabed,
respectively, of the following geo-acoustic parameters [15,16,24,21]:• Medium silt: m = ρ1/ρ = 1.147; n = c1/c = 0.9801

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• Fine sand: m = ρ1/ρ = 1.2236; n = c1/c = 1.0364• Fine gravel: m = ρ1/ρ = 2.4923; n = c1/c = 1.338
Distributions of the total underwater noise of the tug within the frequency band up to 1000 Hz in
the distance from the ship equals 1000 m, in the case of disturbance propagation over different types ofseabed: fine sand, fine gravel and medium silt, is presented in Fig. 2. It should be observed that the
spatial pressure distribution depends on a type of seabed. The non-uniform pressure distribution infunction of water depth results from the forming and propagating of wave modes.

Figure 2 – Broadband pressure at distance of 1000 m from the source for different types of bottom
Based on the results of calculation, there is possible to examine an impact of formation of wave
modes on distribution of resultant acoustic pressure for particular components of frequency spectrumof the tug in question. On the diagram, Fig.3, are shown the vertical wave modes pressure distributions
for the tug’s spectrum component of 213 Hz frequency and the resultant pressure at the distance of 100
m from the ship.

Figure 3 – Modes of the spectrum component of 213 Hz frequency at the distance of 100 m from the ship
The wave modes start to form in a rather small distance from source, namely that at which sphericalpropagation resulting from reflections from the surfaces limiting the layer becomes conversed intocylindrical one. In the case in question the wave modes are formed for all components of the tug’s
spectrum, and their number depends on frequency. The higher the frequency the bigger the number ofwave modes.

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In the case of modes propagation we have to do with dispersion of sound propagation velocity.
Every wave mode propagates with a different velocity. The modes gradually fade out along withgrowing distance and finally we have propagation of a single mode.
The assessment of impact of a kind of seabed on acoustic energy absorption we conduct on the basisof changes in the resultant pressure which is a sum of modes for a selected component of the tug’s
frequency spectrum. In Fig. 4 and 5 there is demonstrated in which way the vertical resultant pressure
distribution for the 213 Hz frequency component changes at different distances from the ship andunder the assumption that we have to do with the seabed formed of fine gravel and fine sand,respectively.

Figure 4 –Vertical resultant-pressure distribution for the 213 Hz frequency spectrum component indifferent distances from the ship, in case of fine gravel seabed

Figure 5 –Vertical resultant-pressure distribution for the 213 Hz frequency spectrum component indifferent distances from the ship, in case of fine sand seabed
The 213 Hz frequency component reaches 1000 m distance over the fine sand seabed and up to 2000
m – over the fine gravel seabed. 12 significant frequency components were distinguished within the
tug’s spectrum. The acoustic energy emitted to water is composed mainly of them.
Examining the diagrams we are able to assess the changes in vertical distributions of total tug–
generated pressure, which occur along with growing distance. We may also assess impact of a kind ofseabed on disturbance propagation range, as it is shown in Fig. 6.

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Figure 6 – Vertical distribution of total tug-generated pressure in the distance up to 10000 m fromthe ship in the case of propagation over the seabed composed of fine sand
The total ship-generated pressure distributions confirm that effects of disturbance propagat ion in
the form of wave modes are visible only up to some distance. The wave propagates further in the formof one mode. The distance depends on a kind of seabed. In the considered case higher modes fade out
fastest over fine sand seabed and latest over medium silt seabed.

5. FINAL REMARKS
While assessing the range of acoustic disturbances in the Baltic Sea one should take into accountthat the acoustic wave propagation in this water area completely differs from the propagation in a deepsea. Application of the spherical propagation model is a too -far -going simplification which may leadto an erroneous estimation of energy transmission losses. The Baltic Sea exemplifies a shallow sea
which can be represented as an acoustic system of a flat-parallel waveguide structure filled with liquid
layer and separate boundary conditions for each of the boundaries of the layer. In this paper the use wasmade of the method, presented already in the preceding publications, for estimation of energy
transmission losses in shallow sea for case modal propagation of broad-band signal in water areas ofdifferent kinds of seabed. The investigations were performed on the basis of these author’s own
measurements of underwater noise emitted by ships, for definite bottom sediments. At tention was paid
to the forming of modes for all frequencies contained in underwater noise spectrum of the considered
ship. For the higher spectral frequency components, a greater number of modes is formed andmulti-mode propagation phenomenon reaches a greater range than in the case of the low frequency
components. A kind of seabed, i.e. its geo-acoustic parameters, affects the range of the total noise
generated by the ship, similarly – the range of the propagation in the form of wave modes, that resultsfrom that a part of acoustic energy penetrates into seabed. Attention was drawn to the fact that thewater layer has discriminative features which make propagation of the waves having length fourfold
greater than water depth, impossible in the conditions assumed in the considered case.

ACKNOWLEDGEMENTS
The investigations have been performed partly due to funds granted by Polish Ministry of Scienceand Higher Education for statutory activity of the Faculty of Offshore Engineering and Ship
Technology, Gdansk University of Technology.

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