Proceedings of the Institute of Acoustics

 

The influence on correlation loss of reflection from rough sea surfaces

 

M.K. Prior, TNO, The Hague, Netherlands

M.A. Ainslie, TNO, The Hague, Netherlands

M.E.G.D. Colin, TNO, The Hague, Netherlands

P.H. Dahl, Applied Physics Laboratory, University of Washington, USA

D. Dall’Osto, Applied Physics Laboratory, University of Washington, USA

D.D. Ellis, Mount Allison University, Sackville, New Brunswick, Canada

P. Hines, Hines Ocean S&T Consulting Inc., Dartmouth, Canada

S. Pecknold, DRDC Atlantic, Dartmouth, Nova Scotia, Canada

R. van Vossen, TNO, The Hague, Netherlands

 

 

1 INTRODUCTION

 

Acoustic propagation in shallow-water environments is strongly influenced by sea-surface interactions. Surface waves cause incident sound to be scattered over a range of angles, while air-bubbles beneath breaking waves increase acoustic attenuation and change local sound speeds via their influence on the average density and compressibility of seawater^{1, 2}.

 

The acoustic consequences of these surface effects cannot be considered in isolation and there is an interaction with the acoustic influence of the seabed. Sound incident on the seabed at low grazing angles suffers reflection loss as some proportion of the incident intensity is transmitted into the sediment, reflection loss being proportional to the grazing angle. This behaviour continues until a sharp rise in reflection loss around a seabed “critical angle” determined by the ratio of seawater and sediment sound-speeds. The changes of propagation angle undergone by sound incident on the sea surface will therefore have an effect on the reflection loss encountered during subsequent bottom interactions. Furthermore, the cycle distance of a ray (the distance between successive seabed reflections) is generally smaller for larger propagation angles. Consequently, an increase in propagation angle due to surface scattering will increase acoustic losses via a double effect of increasing the reflection loss per bounce and increasing the rate of surface interactions with range.

 

This paper considers a situation in shallow-water with a rough sea surface. Acoustic propagation is predicted using numerical solution of the wave equation and closed-form expressions based on depth-averaged formulas for ‘mode-stripping’ conditions where seabed reflection loss is proportional to grazing angle³. Acoustic propagation is quantified via the familiar ‘propagation loss’ and also a ‘correlation loss’ that measures the reduction (due to multipath) in gains expected from replica-correlation of active sonar transmissions. Measured data gathered in an ocean-acoustic experiment carried out in the Gulf of Mexico are used to illustrate correlation loss. The following section discusses the experimental configuration and introduces the concept of correlation loss.

 

The following section discusses the experimental configuration and introduces the concept of correlation loss. Section 3 presents numerical predictions of correlation loss and compares them with values derived from measured data. It then derives closed-form expressions for correlation loss and propagation loss for mode-stripping conditions in the presence of a rough sea surface. Limitations of the closed-form expressions are discussed.

 

 

2 THE TREX EXPERIMENT

 

2.1 General

 

In 2013, the large scale Target and Reverberation Experiment (TREX2013) was organised⁴ near Panama City, Florida, supported by the U.S. Office of Naval Research (ONR). A specific run organised by Defence Research and Development Canada (DRDC) provided an opportunity to measure matched-filter gain in a characterised environment. During this experiment the DRDC SMART-ER echo-repeater⁵ was towed by CFAV Quest at increasing ranges from the Five Octave Research Array (FORA) 6 deployed by the Applied Physics Laboratory of the University of Washington (APL-UW) and Pennsylvania State University. In addition to the FORA data, acoustic recordings of the one-way-propagated field were made on a hydrophone co-located with the echo-repeater. Measurements of the surface roughness spectrum carried out by APL-UW 7 provided input for modelling the effect of the surface.

 

2.2 Correlation Loss Measurements

 

Matched filter gain is equal to ten times the logarithm of the ratio of the signal to noise ratio after matched filtering (s_mf ) and before (s) :

                                                                   

 

We define correlation loss (CL) as the difference between 10 log₁₀ [BT] dB and MFG where B and T are the bandwidth and duration of the transmitted pulse:

                                                                

 

Correlation loss can be evaluated with the following expression⁸:

                                                             

 

where p(t) is the received waveform and p_mf (t) is the matched filtered received waveform. If_p(t) is a delayed and attenuated version of the transmitted waveform CL=0. This quantity can either be evaluated from measurements or from simulations. In the case of the TREX experiment, CL was estimated by considering the signal recorded at the DRDC echo-repeater⁵ deployed at depth of 6.5 m along the “reverberation track” of the TREX experiment. The echo-repeater was pinged at by an ITC 2010 ring deployed at 18.35 m with linear frequency modulated waveforms of 200 Hz bandwidth and 0.5 s duration. The results considered here are for a 3.5 kHz centre frequency signal. These time series were used to compute one-way correlation loss. Active-sonar echoes will be distorted by two-way propagation and by multipath imposed by target characteristics. The correlation losses here are therefore lower than would be observed with active-sonar echoes.

 

2.3 Sea-Surface Measurements

 

In parallel to acoustic measurements, parameters of the sea surface were measured by a directional wave-buoy deployed by APL-UW⁷ on the acoustic path. This system recorded the directional sea surface spectrum over the duration of the experiment every 30 minutes. Based on these measured spectra, realisations of the sea surface were generated⁹. The spatial spectrum of such a realisation, used later in the analysis, is shown in Figure 1.

 

 

Figure 1: Spatial spectrum of a sea surface realisation based on TREX2013 measurements overlaid on a Pierson-Moskowitz spectrum for a fully developed sea with 4 m/s wind speed.

 

 

3 PROPAGATION LOSS AND CORRELATION LOSS IN SHALLOW WATER

 

3.1 Numerical Simulation Of Acoustic Field In A Shallow-Water Waveguide With A Rough Sea Surface

 

The RAM parabolic equation propagation code¹⁰ was used to generate time-series after one-way propagation, using Fourier integration, with and without rough surface realisations. The geo-acoustic parameters and configurations were based on the TREX setup (around 20 m water depth). The results of this modelling are shown in Figure 2:

- In the top left quadrant, a typical example of low CL (0.3 dB) is shown, computed for a flat surface environment. Only a few multipaths contribute to the echo, resulting in a pulse similar to the transmitted waveform.

- In the top right quadrant, a pulse generated in the same environment, but simulating a receiver at a longer range (3.4 km) is shown. The greater multipath spreading results in a higher CL (5.5 dB).

- In the bottom left quadrant, measurements of the same quantities at a range of 3.4 km collected during TREX 2013 are presented. The correlation loss is 1.7 dB - less than that obtained with the flat surface simulations.

- In the bottom right quadrant, simulations made in the same environment as the previous results are shown, with the addition of a rough surface realisation computed as described in Section 2.3. The correlation loss (3.7 dB) is less than that of the flat surface simulations.

 

This illustrates that rough surfaces contribute to the attenuation of later multipath arrivals, resulting in a lower correlation loss. Rough-surface scattering therefore has two effects with opposite impacts on post-replica-correlation signal-to-noise ratio: increasing propagation loss while decreasing correlation loss. The relative sizes of these two effects are now studied via the derivation of closed-form expressions to estimate them.

                                                   

 

Figure 2: Top left: Simulated raw and matched filtered time series envelopes at short range (100 m) with a smooth surface. Top right, same at 3.4 km range. Bottom right: same including rough surface. Bottom left: measured raw and matched-filtered time series envelopes at 3.4 km.

 

3.2 Propagation Loss In Mode-Stripping Conditions With Roughness

 

The propagation factor, F, is a linear version of depth-averaged propagation loss and for ‘mode-stripping’ conditions in isovelocity water with bottom loss proportional to grazing angle is given by³.

                                                                          

 

Where r is range, D is the water depth, β is the coefficient quantifying absorption in nepers per metre, η is the reflection loss gradient at near-grazing incidence in nepers per radian and θ_u is an upper limit on the integration angle θ. The rough surface alters the angle of propagation of sound after every surface bounce, imposing a random part. If this random part is modelled as being zero-mean with mean-square value σ² then the mean-square angle of propagation can be expressed as

                                                                         

 

Where θ o is the angle at which a ray is launched from the source, θ is now the propagation angle at range r and σ² is multiplied by a factor giving the number of surface bounces undergone between ranges 0 and r. The number of surface bounces is modelled as a smooth function of r proportional to the launch angle, consistent with the consideration of a depth-averaged propagation factor. The randomization is shown to lead to an increase with range in the mean-square value of propagation angle.

 

A second effect of the randomization is associated with the upper limit of the angular integral. In flat-surface conditions this is the critical angle of the seabed, θ_c, given by the inverse cosine of the ratio of seawater and sediment sound-speeds. Reflection loss increases rapidly in the region of θ_c and, to a first approximation, any sound hitting the seabed at a greater angle can be considered lost. In the presence of a rough sea surface, a ray launched from the source at less than the critical angle may go beyond it at some range, due to repeated surface interactions. Thus, the effective upper limit of the angle integral decreases with range because only sound leaving the source close to the horizontal experiences a level of surface interaction small enough to guarantee that it remains below θ_c. If the r.m.s. angle deviation is used as an estimate of the average angular deviation per surface bounce, the expression for θ_u becomes

                                                                                          

 

Substitution of (5), (6) this int o th e e xp re s sion (4) for F yields an integral of standard form.

                                                                                         

 

This form appears problematic because the b-parameter is proportional to range, suggesting an exponential rise with range. However, the difference between the bracketed term evaluated at the upper and lower limits falls off with range faster than the exponential rises and the integral remains bounded. To avoid underflow and overflow errors when implementing the expression for F, the error function is more conveniently expressed via the scaled, complementary error function erfcx(x)¹¹,

                                                                                      

 

Where ρ is a ‘scaled range’ given by the range divided by the water depth. Figure 3 shows propagation loss (10 log₁₀ [F/m ^-2 ]) plotted for a shallow-water environment with a smooth sea-surface case and for a rough surface imposing a r.m.s. angle deviation of 2^o per bounce. The crosses show results of the closed-form expression (8) while the line joining them shows the result of a numerical evaluation of (4) with the upper angle limit given by (6). The circles show propagation loss in the absence of surface roughness. Figure 3 shows how the rough surface causes an increase in propagation loss even though there is no extra attenuation introduced into the environment. This is because of the increase with range of the mean-square propagation angle and the reduction with range of the upper limit on the angular integration.

 

Figure 3:Propagation loss as a function of range for a smooth-surface case and for a rough-surface case, evaluated numerically and with the closed-form expression for propagation factor F.	Table 1: Environmental and acoustic parameters

 

 

3.3 Correlation Loss In Mode-Stripping Conditions With Roughness

 

In mode-stripping conditions, one-way pulse shape is predicted to become independent of propagation range¹² having a form

                                                                                     

 

where τ is the “reduced time”, i.e. the time after the first arrival and

                                                                                       

 

While the derivation of this form assumes isovelocity water, the phenomenon of range-independent pulse shape has been observed in practice¹³ and used to estimate seabed geoacoustic properties^14,15. This expression for the pulse shape leads to an expression for CL in mode-stripping conditions:

                                                                                         

 

Where the pulse has bandwidth B and the numerator is integrated from time zero because peak intensity occurs at the earliest times. This expression for CL in mode-stripping conditions does not depend on propagation range, as would be expected for a pulse with range-independent shape. This situation is not observed at the shortest ranges where pulse-length increases with range until all sound travelling outside the critical angle is attenuated¹². The range at which this occurs, r_ms, is given by

                                                                                     

 

Thus, CL shows a rise at short ranges, followed by a levelling out as mode-stripping conditions are achieved. A dimensionless parameter, g_ms may be introduced such that

                                                                                    

 

and mode-stripping conditions are observed for g_ms >>1. If the critical angle is replaced with the upper angular limit θ_u as set out in ( 6 ) then the expression for mode-stripping conditions becomes

                                                                                  

 

This function reaches a peak value of ( ηθc² )/(4σ) at ρ=2/σ. Thus, the full level of correlation loss observed for mode-stripping conditions in the absence of surface roughness will be observed only if g_ms rises above 1.0 and consequently if (ηθ _c2 )>(4σ).

 

The left-hand panel in Figure 4 shows CL calculated for a shallow-water environment with acoustic and environmental data given in Table 2. The results for the smooth-surface case (upper curve) show the behaviour predicted for mode-stripping conditions¹², whereby CL rises initially then levels out as the pulse duration ‘saturates’ in mode-stripping conditions. The predicted saturation value CL_ms =3.2 dB is in good agreement with the results shown in the figure, although the CL predictions made by RAM show fluctuations with range about this value. The saturated condition is reached at around 50 water depths whereas Table 2 suggests that this should have occurred at about one-third of the distance. This illustrates that the value of r ms is an order-of-magnitude indication of the transition to mode-stripping conditions and should not be considered as a sharp boundary.

 

Figure 4: Correlation loss predicted by RAM as a function of scaled range for smooth and rough cases (left). Functional form of the expression for gms shown in right panel	Table 2: Environmental and acoustic parameters

 

 

The lower curve in the left-hand panel shows how CL is predicted by RAM to vary with range for the rough-surface case resulting from a wind-speed of 10 m/s. CL is shown to rise but at a lower rate with range than in the smooth-surface case. This indicates that the pulse length is reduced by the presence of the rough surface. This is because the extra losses imposed by scattering on the higher-angle paths reduce the time-spread. CL rises to a peak at between 50-100 water depths from the source but then decreases with range as the rough surface continues to attenuate high-angle paths and reduces the time-spreading. The right-hand panel in the figure shows the form of the function relating g ms to the scaled range, calculated for an r.m.s. angular deviation of 2 o and scaled to unit maximum value. The function is shown to have a shape similar to the variation of CL with scaled range. The qualitative agreement between the curves in Figure 4 suggests that the decrease in correlation loss with range is explicable in terms of the reduction of the ‘effective critical angle’ with range due to surface scattering.

 

3.4 Combined Correlation Loss and Propagation Loss

 

The results in the previous sub-sections illustrate that the presence of a rough sea surface has two oppositely directed effects. On one hand, propagation loss increases with surface roughness as a result of extra attenuation imposed on high-angle paths. On the other hand, the extra attenuation of high-angle paths reduces correlation loss as it decreases the time-spread of the signal. In these circumstances, the question arises as to whether the two effects cancel out, leading to a situation where there is no effect of wind-speed on the combined propagation- and correlation-loss. However, Figure 3 and Figure 4 show that propagation loss and correlation loss in the presence of a rough sea surface have different range dependences. Thus, although it is possible that the total loss may be the same for some combinations of range, wind-speed and environmental properties, this will not generally be the case and the losses must be considered separately.

 

 

4 SUMMARY AND DISCUSSION

 

The results of numerical propagation modelling and the measured data from the TREX experiment show that rough sea surfaces decrease correlation loss, i.e. the difference between obtainable replica-correlation gains and the commonly used value of 10log10(BT). The physical cause of this reduction in loss is extra attenuation of high-angle propagation multipaths and the same process increases propagation loss. Closed-form expressions relating correlation loss and propagation loss to mean-square angular deviations due to surface scattering have different functional forms, meaning that the reduction in correlation loss does not compensate for the increase in propagation loss. While these expressions are useful in providing insight to important acoustic processes, they do not consider near-surface bubble layers which have important effects on refraction² and attenuation¹⁶ close to the sea surface. A full assessment of rough surfaces should include these processes.

 

 

5 ACKNOWLEDGEMENTS

 

This work was sponsored by the Defence Material Organisation of the Netherlands Ministry of Defence and by the US Office of Naval Research, Ocean Acoustics.

 

 

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