Reverberation clutter induced by nonlinear internal waves in shallow water

One major factor hindering the performance of active systems is false alarms due to clutter. Clutter refers to target-like signals appearing in reverberation. Clutter has been attributed to strong backscattering strength from, for example, seafloor features¹ and fish schools.² Another possible mechanism for clutter, discussed in this paper, is a propagation effect, with ordinary backscattering strength. A sound speed feature, such as a nonlinear internal wave (NLIW) with large amplitude, deflects sound into the bottom as a beam, causing a higher insonification at a higher grazing angle, both aspects resulting in increased backscatter. We demonstrate that observed NLIWs in measured stratification can give a greater than 10 dB target-like return above the general reverberation level. For purposes of realism, our oceanographic and acoustic modeling is based on measured stratification and observed wave amplitudes on the New Jersey shelf during the SWARM experiment.³ Ray tracing is performed that shows, qualitatively, the physical effect of deflection by the internal wave of sound into the bottom at higher grazing angle. A full wave model then gives quantitative results for the clutter.

Nonlinear internal waves are very common on the continental shelf where a thermocline exists. Several experiments, including SWARM, combining oceanography and acoustics have been carried out on the New Jersey shelf. Furthermore, this region is of continuing interest for additional experimental study in the near future, therefore, the predictions presented here could be investigated in future field programs.

The sound speed profile used for modeling is derived from a typical conductivity, temperature, and depth (CTD) cast from the SWARM experiment³ and is shown in the left panel of Fig. 1, where a mixed layer extends down to 10 m. A warm salty layer near the bottom due to the shelf-break front resulted in a minimum in the sound speed at 35 m depth. This is a typical feature on the New Jersey coast and occurs in all SWARM and Shallow Water 2006 profiles⁴ on the outer part of the shelf. In this paper, we investigate the situation where a train of nonlinear internal waves approaches the acoustic source and receiver. In this case, the leading wave usually has the largest amplitude, and the sound speed profile is relatively range independent before reaching that wave. The effect of a leading wave of sufficient amplitude is to deflect the ducted sound near the sound speed minimum into a beam that strikes the bottom, leading to a target-like clutter signal. The subsequent behavior of that deflected beam depends on the details of the following waves in the train. Dispersion of the beam leads to lower and more time spread reverberation, unlikely to look like a target. Therefore, we model only the leading wave as a solitary wave, and ignore the following waves. The leading wave is almost a solitary wave, which we model as a solution of the fully nonlinear Dubriel-Jacotin-Long (DJL) equation (formerly referred to as Long's equation).⁵ For a given stratification, the DJL equation has a set of one-parameter solutions. The amplitude of the wave used for modeling is chosen as typical of waves observed in SWARM and is shown as a sound speed field in color in Fig. 1 in the online version. The DJL equation models the two-dimensional structure of a NLIW of that amplitude much more accurately than does weakly nonlinear equations, such as the Korteweg-deVries equation. The wave is assumed to be at a 5 km range from the source and receiver in order to give quantitative clutter to reverberation.

To picture the mechanism, a set of rays was launched from a source at range zero and depth 38 m, close to the sound speed minimum. Figure 1 shows rays between ±6°, which stay in the sound channel and contribute to the clutter mechanism of this paper, although the detailed calculations to follow use an omnidirectional source, including propagation at the larger angles responsible for the reverberation at earlier times. When the rays encounter the solitary wave they are deflected to a higher angle of about 11 deg, and leave the channel as a beam, impinging onto the bottom. This beam, of higher grazing angle sound, is then backscattered around the reciprocal path to the receiver near the source, arriving as a strong target-like clutter signal. In order for this deflection of sound to occur, the amplitude of the internal wave needs to be large. Smaller wave would not change the direction of the propagating sound out of the channel. Ray tracing is unlikely to quantitatively predict this phenomenon for frequencies of a few kilohertz. Therefore, we resort to a full wave method in Sec. III for the quantitative study; however, ray tracing still offers an intuitive picture.

For quantitative results on reverberation, we resort to a full wave method to handle the two-way propagation, and perturbation theory for reverberation.⁶ The bottom is assumed to be a fluid half-space with sound speed of 1650 m/s, density of 2000 kg/m³, and an attenuation of 0.5 dB/wavelength, so seabed absorption is included in the calculation. The acoustic field of an omnidirectional point source is expanded in unperturbed modes, and the equation for their evolution including mode coupling by the wave is solved following Eq. (29) of Ref. 7, where we make their forward-scattering approximation by dropping the second line and we refrain from expanding K² in the sound speed perturbation. Higher order modes were included in the calculation so the high angle waves from the point source are properly included. Alternatively, one could use another full wave approach, such as a parabolic equation method, to obtain the same results. We choose a point source of 3 kHz at the common choice of being near the sound axis; specifically, our source depth is 38 m. The solitary wave is at a range of 5 km, and extends the calculation to 10 km. Figure 2 shows the calculated horizontal flux. Before encountering the solitary wave, most of the sound energy propagating to long distances is trapped in the sound channel in the middle of the water column. At 5 km range, the internal wave converts most of the sound at low modes (small angle) to higher modes (larger angle), in a beam which interacts strongly with the seafloor. This result is qualitatively consistent with the ray analysis shown in Fig. 1. The deflected beam is refracted by the sound speed profile, periodically hitting the bottom. At these subsequent bottom interactions, the beam has significantly broadened.

Target-like clutter occurs when the narrow beam backscatters from the bottom. To calculate the reverberation and clutter, the rough seafloor backscatter model,⁶ based on perturbation theory, is used. The water/sediment interface is assumed to have small-scale roughness with a typical roughness power spectrum as defined in the Office of Naval Research Reverberation Workshop.⁸ The reverberation vs time is given in Fig. 3, with a 100 Hz bandwidth centered on 3 kHz. At slightly before 7 s, corresponding to the range where the deflected rays of Fig. 1 hit the bottom, a large arrival appears more than 10 dB above the background reverberation level with a time spread consistent with the inverse bandwidth of the transmitted pulse. Additional calculations with twice the bandwidth around the same center frequency show a 2-dB increase of the clutter arrival while the width remains to be consistent with the inverse bandwidth. The large return is the result of both larger insonification at the place the deflected beam strikes the bottom and the stronger backscatter at higher grazing angles. Because the deflected sound behaves like a narrow beam impinging onto the bottom, the arrival shows up like a target. Following the large arrival, the reverberation is generally higher than the level extrapolated from before the arrival of the internal wave. There are additional individual arrivals due to the repeated interaction of the deflected beam with the bottom. However, even in the absence of the rest of the wave train, they are more spread out in time and smaller in amplitude than the first peak because of the spreading of the deflected beam.

Nonlinear internal waves are a common phenomenon on the continental shelf when strong stratification exists. Under the right conditions, such a wave induces a false target in an active system due to strong insonification at high angle of the bottom just behind the deflecting wave. Considering typical internal waves on the shelf move at a speed of order 1 m/s, the induced false target could be tracked as a slowly moving target. When the source is near the channel minimum, as was shown in the previous calculation, the effect is most pronounced; a source outside the duct does not have as dramatic an effect. To experimentally verify the effect presented, a monostatic reverberation system properly placed in the duct aimed toward the oncoming nonlinear internal waves, and a means of monitoring the location of such waves, such as radar or visual, would suffice.

This work was supported by the Office of Naval Research.