Anechoic Effect of Coating Covered on Target Submerged in Typical Shallow-water Waveguides

CHEN Yan,TANG Wei-lin,FAN Wei,FAN Jun

(School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

1 Introduction

Anechoic coating is one of the most important stealth measures of modern submarines.The reduction of the Target Strength(TS)in free space was usually used to indicate the anechoic effect of coating in previous estimation and prediction research.This can lead two problems as follows.First,what is the relation between the reduction of the TS in free space and the real echo reduction in various shallow water waveguide?Second,what the difference in the echo reduction of target with varied anechoic coatings in shallow-water channel is?The problems mentioned above are caused by different formation mechanisms of echo from objects in free space and in shallow-water environment.The ray acoustic method shows the echo formation mechanism clearly.In free space,the echo is the combination of the direct in-

cident wave and the direct reflection wave,as shown in Fig.1(a).But in shallow water environment,the multi-path effect has a great impact on the propagation.The first incident wave is reflected by boundaries and turns into infinite incident waves,and each incident wave is then reflected by the target and the boundaries and turns into infinite reflection waves.That means the scattering in shallow-water waveguide involves the double multi-path effects.Fig.1(b)and(c)give the picture of rays reflected by surface and bottom for only one time.In fact,there are infinite incident and reflection rays.The ray angles relative to reflection areas of target are different from each other.

Fig.1 Rays in free space and in shallow-water waveguide

In 1987,Ingenito[1]derived the scattered field expression in terms of the normal modes and plane-wave scattering functions in free space,which was a groundwork for wave acoustic method in shallow-water waveguide.Makris promoted Ingenito’s method and put forward the spectral approach in the article about the detection of a submerged object insonified by surface noise in an ocean waveguide in 1994.The advantage of this method is that the waveguide Green’s function is decomposed into plane wave spectrum,including both discrete spectrum(normal mode)and continuous spectrums,so as to enable to calculate the scattered field much closer to the object.After that,the team of Makris did further studies of spectral approach.They developed a unified model for reverberation and submerged target scattering in a stratified medium,and discussed the validity of the sonar equation for object scattering in a shallow water waveguide[3-6].In recent years,we developed a simple and practical ray acoustic method for sonar engineering application[7-8].Since the sound propagation is calculated by the ray-tracing technique and the scattering is expressed through Kirchhoff approximation,the method can be used to deal with the scattering of complex targets in shallow-water waveguide with arbitrary velocity profile in principle.

The main characteristic of coating covered on the target surface is the reflection coefficient,which changes with frequency and incident angle.In free space,the echo is the direct incident-reflected wave,so the coating only works on a reflection area illuminated by the direct incident wave.But in shallow water waveguide,the echo is the summation of reflection waves from various combinations of rays and each combination has the varied incident and reflection angles,which causes the different anechoic effect of coating.Especially in the situation of the negative gradient velocity profile as shown in Fig.1(c),when the horizontal range is larger than a skip distance,there is no direct echo from target.That will lead to larger difference of the action mechanism of coating between in free space and in shallow-water environment.

A numerical procedure for calculating echoes from objects with anechoic coating submerged in shallow-water waveguide based on ray-tracing technique and physical acoustic method is developed.The coating has no effect on propagation of the waveguide but changes the target scattering function,the Kirchhoff approximation is extended to treat the scattering of objects with anechoic coating.Taking the Benchmark submarine model and two supposed coatings with different reflection coefficient,we discussed the echo characteristics of target with rigid and coated surface in two typical shallow water environment:weak positive gradient profile(W.P.G-profile)and negative gradient profile（N.G-profile).The analysis of the influence of velocity profile on the anechoic effect of coating is given and the difference of the anechoic effect in free space and shallow-water waveguide is obtained.

2 Numerical approach

The references[7-8]gave the numerical approach of the scattering of target submerged in shallow-water waveguide.The scattered field is the summation of all the monostatic and bistatic scattered fields.

where（φs）l=mis the monostatic scattered field with the same incident ray and reflection ray,（φs）l≠mis the bistatic scattered field with different incident ray and reflection ray.It is only under the condition of waveguide environment,the bistatic scattering can come back to the source and contribute to the echo.Using the ray-tracing technique,the monostatic echo is expressed as

where ΔΦz(mì)lis the path difference from arrival pointr,（）z of incident ray on target surface to reference pointαzlis the included angle between incident ray and the normalat the arrival point of surface.Bl,lis the bright region for lth incident-reflection rays.The bistatic scattered field is:

where Sl,mis the bistatic scattering function.If the target is rigid,then we get

where Bl,mis the common bright region for both lth incident ray and mth reflection ray,and Bl,m=Bm,l,Sl,m=Sm,land （φs）l,m= （φs）m,lcan be easily obtained.

The ray-tracing technique is used to calculate the transmission factors of incident and reflection rays and the Kirchhoff approximation is applied to obtain the monostatic or bistatic scattering function from each combination of rays.The echo in shallow water waveguide is the summation of all the monostatic and bistatic scattering.The summation process is convergent because that only limited rays work on the echo in the far field.

In this paper,we promoted the numerical procedure in reference[8]so as to use it for target with coating.The real effect of coating in two typical ocean environments is discussed.When calculating the object with coating in shallow water environment,the transmission characteristic of waveguide is changeless but the target scattering function changes relatively.The reflection coefficient V（）α is used to present the anechoic behavior of coating,where α is the incident angle relative to the surface normal.According to the physical acoustic method for nonrigid surface[9],the scattering function is related to the reflection coefficient at the incident angle.The monostatic scattering function is modified as

The bistatic scattering function is modified as

It is necessary to indicate that

When the incident ray and reflection ray swap,the bistatic scattering function changes,that means （φs）l,m≠ （φs）m,l.Even then the bistatic scattering can be composed as

When dealing with each component of the scattered field,the transmission and scattering can be decoupled.However,this does not mean that the total scattered field can be decoupled,since the summation of each scattered component can not define the total transmission factor and total scattering function.In traditional sonar equation,the waveguide transmission loss and target scattering are decoupled artificially and the echo level is defined as follows:

where SL is the source level;TL is the transmission loss in the shallow-water waveguide,which usually indicates the transmission loss form the source to the center of the target;TS is the Target Strength in free space.But the echo level can not be represented as in formula(10)in the shallow water environment because the total transmission factor and total scattering function can not be decoupled.According to formula(2),the Target Strength in free space is expressed as

There has no bistatic scattering in the Eq.(11).In order to evaluate the error due to traditional sonar equation in shallow-water waveguide,a physical quantity-Equivalent Target Strength ETS is defined as[7]:

In this paper,the TS in free space,the ETS in waveguide and the TS reduction and ETS reduction after covering various anechoic coatings are analyzed.The ETS reduction can be used to evaluate the anechoic effect of coating in shallow-water waveguide because in the same shallow-water environment the echo reduction equals the ETS reduction.We discussed the influence of velocity profile on the anechoic effect of coating and the difference of the anechoic effect in free space and in shallow-water waveguide.

3 Results and analysis

The reflection coefficient of two supposed coatings as a function of incident angle at the frequency of 5 kHz is shown in Fig.2.It can be seen that reflection coefficients of the two coatings are equal with each other at the zero incident angle when the ray is vertical incidence.But the increasing rate of the reflection coefficient of the coating E1 is larger than the coating E2 when incident angle getting larger.The anechoic behavior of the coating E1 is worse than the coating E2.

The shallow-water waveguide is range-independent with 80 m deep as illustrated in Fig.3.The transducer is in the depth of 10 m.The target is in the depth of 40 m.The frequency is 5 kHz and the absorption loss of sea water is 0.3862 dB/km.The sediment layer is clay with constant density of 1420 kg/m3and sound speed of 1510 m/s.The attenuation of the sediment is 7.5×10-5dB/m·Hz.Considering the sea surface is release.

Fig.2 Reflection coefficient of coatings E1 and E2

Fig.3 Positions of transducer and target in shallow-water waveguide

In the winter and summer shallow-water waveguide,the typical velocity profile and the corresponding eigen rays from transducer to the target with the range of 1 km are shown in Fig.4.

Fig.4 Typical velocity profile and eigen rays in winter and summer shallow-water waveguide

The isothermal layer in winter leads to W.P.G-profile,which makes the rays slowly bending upward.There exists thermocline in summer waveguide,which leads to N.G-profile and makes the eigen rays so bending downward that there is no direct ray when the distance over the skip distance of limiting ray.

3.1 The echo reduction of cylinder with coating in shallow water waveguide

The references[7-8]pointed out that when a rigid cylinder is placed at cross direction with its axis of symmetry perpendicular to the range and depth coordinates,the ETS is less influenced by shallow water waveguide;when the cylinder is set at longitudinal direction with its axis of symmetry parallel to the depth coordinates,the shallow water environment has great effect on the ETS.The cylinder set at longitudinal direction is a typical target which cannot use the traditional sonar equation to calculate its echo level in shallow water waveguide.Therefore,we analyze the echo characteristics from the cylinder with coating firstly.The cylinder is 5 m long with radius of 1m.Its position used in the following example is shown in Fig.3.The range varies from 500 m to 2000 m.At the frequency of 5 kHz,the ratio of the cylinder length to wave length is about 16.7.

Fig.5gives the anechoic effects of the two coatings when the cylinder is set at cross direction.Both the TS reduction(△TS)in free space and the ETS reduction(△ETS)in shallow water waveguide caused by the two coatings are close with each other.The anechoic effects caused by coating E2 is larger than that by coating E1 only 0.5 dB in free space and 1 dB in shallow water waveguide.It means that for a cylinder with anechoic coating set at cross direction the shallow-water environments has little effect on the anechoic effects and the advantage of the coating E2 is enlarged slightly in waveguide.

Fig.5 The anechoic effects of the two coatings when cylinder setting at cross direction

Fig.6gives the anechoic effects of the two coatings when the cylinder is set at longitudinal direction.The TS reductions caused by coatings E1 and E2 are almost the same in free space compared with Fig.5.But in shallow-water environment,the waveguide make the ETS reduction of the coating E1 worse,especially in N.G-profile,there is a difference of 1.5 dB between the coating E1 and the coating E2.

The main reason that brings out the difference between coatings E1 and E2 are:①The echo of a cylinder set at longitudinal direction is sensitive to the incident angle,it just so happened that the multi-path effect leads to larger incident and reflection angle,as shown in Fig.1(b)and(c);②The reflection coefficient of the coating E1 increases rapidly in small angle range(0°to 30°approximately),which makes the anechoic effect of the coating E1 behave worse at larger incident angle;③In the situation of N.G-profile in shallow water waveguide,there is no direct eigen ray.All the incident-reflection angles of eigen rays are larger than zero,so that the advantage of coating E2 is more obvious.

Fig.6 The anechoic effects of the two coatings when cylinder setting at longitudinal direction

In this paper,we focus on the difference of the anechoic effect of coatings between in free space and in shallow-water waveguide.After covering a coating,the absolute value of ETS of cylinder still differs greatly between set at cross direction and longitudinal direction,just like the result in reference[8],not repeat any more.

3.2 The echo characteristics of the Benchmark submarine in shallow-water waveguide

The Benchmark submarine model is the standard model for checking echo calculation in some countries of NATO,as shown in Fig.7.The size of the model is listed in reference[12].Fig.3 gives the position of the transducer and model and their range is 1000 m.

The echo levels EL of the Benchmark submarine with various coating as a function of azimuth angle are shown in Fig.8.No matter whether the surface is rigid or covered with anechoic coating,the EL in shallow-water waveguide with N.G-profile is always smaller than that in W.P.G-profile.This is because that N.G-profile makes the rays downward and enlarge the transmission loss.The EL in waveguide with N.G-profile is 9～10 dB lower than the EL in W.P.G-profile for rigid submarine,but for submarine with coating,the difference of EL is only about 4～5 dB,especially near the abeam direction.

Fig.7 Benchmark submarine model

Fig.8 The EL of Benchmark submarine with various surface in shallow-water waveguide with N.G-profile or W.P.G-profile(5 kHz)

Next,we analyze the ETS of the Benchmark submarine with various coatings in shallowwater environment with N.G-profile or W.P.G-profile.When the target is rigid,the ETS changes a little in shallow-water waveguide,which is consistent with the result in reference[8].However when the target is covered with anechoic coating,the ETS in waveguide with N.G-profile is larger than that in waveguide with W.P.G-profile.According to the definition EL=ETS-2TL when the source level is 0 dB.The ETS is about 5 dB higher in waveguide with N.G-profile than with W.P.G-profile,as illustrated in Fig.9.At the same time the 2TL is 9 dB larger because the 2TL is 112.8 dB in waveguide with N.G-profile and 103.8 dB in waveguide with W.P.G-profile if the frequency is 5 kHz and the range is 1000 m.As a result the EL in waveguide with N.G-profile is 4dB lower than the EL in waveguide with W.P.G-profile.

Fig.9 The ETS of Benchmark submarine with various surfaces in shallow-water waveguide with N.G-profile or W.P.G-profile(5 kHz)

3.3 The echo reduction of the Benchmark submarine caused by coatings in shallow-water waveguide

In this section,we will analyze the difference of echo reduction caused by coatings in various environments.The TS of the Benchmark submarine model with rigid and coated surface as a function of azimuth angle in free space is shown in Fig.10.The ETS of the Benchmark submarine with rigid and coated surface as function of azimuth angle in shallow-water waveguide with the two velocity profiles is illustrated in Fig.11 and Fig.12,respectively.

Fig.10 The TS of Benchmark submarine with rigid and coated surface in free space

It can be seen from Fig.10 to Fig.12 that the coatings E1 and E2 cause the echo reduction obviously both in free space and shallow-water waveguide.Since the echo of the subma-rine as a function of azimuth angle is complex,to analyze the anechoic effect directly is hard.To make a further quantitative analysis,we calculate the TS reduction in free space and the ETS reduction in waveguide with W.P.G-profile or N.G-profile,as shown in Fig.13.

Fig.11 The ETS of Benchmark submarine with rigid and coated surface in shallow-water waveguide with W.P.G-profile

Fig.12 The ETS of Benchmark submarine with rigid and coated surface in shallow-water waveguide with N.G-profile

Fig.13 The TS reduction and the ETS reduction of Benchmark submarine with anechoic coating E1 or E2

Fig.13(a)illustrates the TS reduction of the submarine with anechoic coatings E1 and E2 in free space and Figs.13(b)and 13(c)show the ETS reduction of submarine with anechoic coatings E1 and E2 in waveguide with W.P.G-profile and N.G-profile,respectively.We find out that:①The anechoic effect of the coating E2 is a little better than that of the coating E1 in free space,but the difference is small.② The anechoic effect of the coating E1 is about 2～3 dB worse than that of the coating E2 in shallow-water waveguide.The results are due to the difference of echo formation mechanisms in free space and in waveguide:

(1)In free space,the echo is caused by the highlight on the target surface,because there is only the direct incident-reflection ray.In the examples of this paper,the incident angle of the direct ray is about 1.7°.At this angle the reflection coefficient of the coatings E1 and E2 is nearly equal,this makes the difference of the anechoic effect of coatings E1 and E2 very small.

(2)In shallow-water waveguide,the echo comes from not only the direct incident-reflection ray but also the combination of various incident and reflection rays with larger angles caused by multi-path effect.For the later the reflection coefficient of large incident angle played a greater role.The reflection coefficient of the coating E1 increases rapidly in small angle,but the reflection coefficient of coating E2 changes very little in the angle range of 0°～30°approximately.That is why the anechoic effect of the coating E1 is not as good as the one of the coating E2 in shallow-water waveguide.

4 Conclusions

The Benchmark submarine model and two anechoic coatings with different reflection coefficients are used in this paper.We calculate the echo characteristics of rigid and coated target in various shallow water environments,especially for two typical velocity profiles in winter and summer.The influence of velocity profiles on the anechoic effect of coatings and also the difference of the anechoic effect in free space and in shallow-water waveguide are analyzed.The following results can be obtained:

(1)The difference of reflection coefficient between the coatings E1 and E2 affects little on the TS reduction in free space.It is because that there is only direct mirror reflection ray in free space but no incident-reflection rays with larger angle.At small angles the difference of the reflection coefficient between the coatings E1 and E2 is very little.

(2)The difference of reflection coefficient between the coatings E1 and E2 makes larger effect on the ETS reduction in shallow-water waveguide.The anechoic effect of the coating E2 is 2～3dB larger than the coating E1.It is because that the echo in waveguide contains contributions from various ray combinations with larger incident-reflection angles and the reflection coefficient of the coating E2 is smaller at these larger incident angles.In order to obtain a larger anechoic effect in shallow-water environment,the reflection coefficient of the coating should be maintained in small value not only at zero incident angle but also in a range of angle from 0 degree to 30 degrees approximately.

(3)The anechoic effect of a coating in free space can not entirely reflect the real effect in shallow-water waveguide.We should pay a special attention to this result in both experimental study and theoretical evaluation.

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