In This Issue
Fall Bridge on Ocean Exploration and its Engineering Challenges
September 18, 2018 Volume 48 Issue 3
This issue is dedicated to the engineering methods used to enhance understanding of the world’s oceans.

Using Noise to Image the Ocean

Tuesday, September 18, 2018

Author: William A. Kuperman

This article is about opportunities for using noise to image the ocean, its bottom, and objects in the water.[1] I review aspects of ocean sound propagation, sources of ocean ambient noise, and some relevant signal processing to deal with the fluctuating, incoherent nature of noise. Then, the processing methods are applied to noise. Finally, potential opportunities and applications are discussed in the context of developing technology.


In the atmosphere there are electromagnetic (EM) and sound waves for sensing, whereas the physics of seawater more or less limits the ocean environment to sound propagation. In the atmosphere, imaging in the optical regime is typically based on incoherent processing that takes advantage of refraction using lens-like devices. At lower frequencies used in communications, radar, TV, and the like, antennae take advantage of the coherence of the signals, providing both gain and directivity. In the ocean, the highest acoustic frequencies are attenuated and randomized by the irregular medium such that propagation is limited to very short ranges, whereas frequencies below, say, a few kilohertz can propagate to respectable distances. Even for signals not extinguished by attenuation, medium complexity diminishes their coherence.

At the lower frequencies, antennae, typically referred to as acoustic arrays, can coherently process signals at a level analogous to that of EM signals. For example, at the height of the Cold War, acoustic arrays (the sound surveillance system, known as SOSUS) were detecting very low frequency sounds (say, less than 100 Hz) emitted from submarines at distances of thousands of kilometers. The detections were possible because the signals after array processing exceeded the ocean noise background.

Because the extraction of signals of interest is limited by competing ambient noise, noise has, until recently, exclusively played the role of spoiler. An alternative to this nuisance role is to make noise the signal of interest.

Ocean Acoustics


The ocean is an acoustic waveguide bounded above by air and below by the ocean bottom (figure 1a[2]) (Jensen et al. 2011). The acoustic index of refraction, typically represented by the ocean sound speed, is mostly dependent on temperature and then depth and salinity. Aside from geometric loss (spherical spreading for short- and cylindrical spreading for long-range propagation), seawater attenuation is roughly proportional to frequency squared, thereby restricting long-range propagation to lower frequencies.

Figure 1 

Acoustic propagation paths obey Snell’s law, which can be thought of as bending sound paths toward low-speed or away from high-speed regions. There are many types of paths, some interacting with the ocean boundaries and others totally contained in the ocean water column.

In the deep ocean, the upper water column is warmest at the surface and then cools with depth, producing a sound speed that decreases with depth; then, with increasing depth, pressure takes over and increases the sound speed. The result is a sound speed minimum at some intermediate depth referred to as the deep sound channel axis (figure 1b). This axis identifies the sound fixing and ranging (SOFAR) channel, which is near the surface in polar regions but gradually goes down to ~1,000 m at midlatitudes.

For example, the SOSUS arrays were placed at midlatitudes on the bottom topography intersecting the SOFAR channel. Since Snell’s law dictates that sound emitted near the minimum sound speed axis will oscillate about that axis without undergoing any boundary scattering loss as it propagates, submarines hiding under the ice could be detected thousands of kilometers away. The effectiveness of these arrays decreased as submarines became quieter relative to ocean noise. In this case, the dominant source of low-frequency noise was shipping.


Just as incoherent optical “noise”—light—is used for seeing, the analogy in the ocean is referred to as acoustic daylight (Buckingham et al. 1992), and the acoustical analogue of a lens is used for short-range imaging.

Noise in the ocean is either man-made (e.g., from ships or other activities) or natural (e.g., from the ocean surface, seismicity, or biologics).

  • Ship noise is dominant in regions where most long-range passive sonars operate (below 1,000 Hz). Not surprisingly, it is loudest in the frequency regimes where detections are mostly sought.
  • Surface-generated noise, dependent on wind speed, occupies the higher frequency region. Noise from ocean surface activity, for example, emulates a diffuse sky.
  • Seismic noise, extending considerably below 1 Hz, originates in the earth except for the micro-seismic region (~.1–.3 Hz), whose source is nonlinear, -coupling ocean wave activity with the ocean bottom.
  • Ice noise originates from cracking, analogous to the acoustic emissions studied in structural health -acoustics and the collision of ice floes. It is of particular interest in the context of global change.

All of these types of noise cover large frequency bands so that the relative absence of shipping (at one frequency) might be filled in by ice or surface noise. Figure 2 illustrates the distribution of shipping noise and of ocean surface wind speed that can be translated into noise levels using Wenz (1962) curves (Porter and -Henderson 2013).

Figure 2 

Signal Processing Using Acoustic Arrays

Common to all noise types is that their aggregate, either in total or by category, creates a mostly nonstationary, temporally incoherent input to an acoustic array. There are therefore various measures of  noise complexity.

A Fourier decomposition of broadband noise would reveal that each frequency component has a random phase relation with respect to the other frequencies, resulting in a rather short temporal coherence. Further, the analogous spatial decomposition would reveal limited spatial coherence. These properties enable the extraction of coherent signal from noise fields by using a correlation time dictated by the space-time coherence.

The random nature of noise and scattered fields tends to suggest their limited utility. Nevertheless, it is possible to coherently extract information from noise. First a review of the simplest array processing is in order.

Array Processing for Signal Gain over Noise

Localizing a source or scatterer is the most basic form of imaging. An acoustic array (for simplicity, discussion is restricted to line arrays but the physics easily generalizes to three-dimensional arrays) of N elements sums the data from each element. The idea is that the signal is coherent and the noise is less coherent, so the signal adds up linearly whereas noise ideally adds up as a random walk. In terms of intensity, which is proportional to amplitude squared, the signal adds up as N2 and the noise as N, with the signal-to-noise ratio (SNR) then being N, which in decibels is an array gain of 10logN.

The fast Fourier transform (FFT) has made frequency domain processing extremely advantageous, so received data are segmented into time snapshots and transformed with the associated time-frequency resolution: longer snapshots have narrower frequency bins. In the fre-quency domain, arrays actually sum the received fields with an additional element-to-element phase factor that is equivalent to a delay in the time domain, both phase and delay corresponding to an arrival angle. For future reference, time delay beamforming can be accomplished by correlating signals between elements. The strongest coherent fields will show peaks at the angles of arrival on the array (with some sidelobe ambiguity associated with the array aperture and ocean physics).

The size of the array aperture determines its angular resolution, which is related to the aperture size measured in wavelengths. Further, the beamwidth is narrow-est broadside to the array and widest at “endfire,” which is along the array axis or in the direction between the two receiver elements being cross-correlated (e.g., top of figure 3a). For a narrowband source that remains in a resolution cell (i.e., a single beam), long-time FFT processing results in a very narrow frequency bin, reducing noise while retaining the signal. The signal received from a moving source will appear to come from the same angle if it stays within the beam and otherwise will “spill” out to other beams. Hence, a long integration time for a source crossing beams lowers the SNR in a particular beam since the signal leaves while the noise remains. For studies of background noise, this long-time integration presents opportunities of building up noise and averaging down signal.

Coherence is another processing limitation. The frequency components of broadband radiation that originate from a random process have a correlation time related to inverse bandwidth. Therefore, while a narrowband signal can be integrated over long times, a 1,000 Hz bandwidth random radiator has only a milli-second coherence time, thereby limiting the accumulation of coherent gain. This also impacts methods to use noise.

Simple Examples

A very simple example of array processing involves using one’s own ship noise reflected off the ocean bottom and received on the ship’s acoustic array to determine properties of the ocean bottom (Battle et al. 2004). Another is using information from the Automatic Identification System (AIS) that provides the location of all ships greater than 300 tons to 10-meter or better accuracy (Verlinden et al. 2018).

Localizing ships in complex coastal environments is often difficult because their acoustic signature is distorted through sound propagation. The combination of noise from ships and AIS information provides the learning data to track ships not included in the pre-collected data. Ships have different source signatures, and correlation processing produces data that are independent of individual ship radiation characteristics. Further, with continuous shipping, the learning data can be updated to include space-time changes in the ocean environment that affect the received noise fields.


Inversion for medium properties is the most general form of imaging in the sense that a radiating object or scatterer can also be considered part of the medium. In ocean acoustic tomography, active controlled sources ensonify the medium for inversion (Munk et al. 1995; Sabra et al. 2016; Sagen et al. 2016; Worcester 2001; Worcester et al. 2013). The process is analogous to, say, a medical CAT scan in which a multiple source-receiver configuration provides information over different paths undergoing different attenuation representative of the medium along the paths. Inversion then provides an attenuation map that can be related to specific medium properties.

In the ocean, though, time delays instead of attenuation associated with the different paths are used and the inversion yields a sound speed map that can be converted into ocean medium properties (figure 1). The ocean method requires precisely known signals emitted by accurately synchronized (~.001 s) and accurately positioned (<1 m) sources relative to the receivers. The total processing stream for this type of imaging involves fusing acoustic data with ocean models, referred to as data assimilation, to obtain an image of the ocean. Though using noise to accomplish the latter processing sequence with precision is problematic, this is precisely the new frontier that is being crossed.

Noise Processing: Correlation and Deconvolution

Because of the random nature of the sources of noise, processing must rely on either correlation or deconvolution. The correlation of data from two receivers in which the same signal (random or not) passes through both (endfire) yields a peak at the delay time of the propagation between the two receivers. Otherwise the time delay is associated with direction and sound speed, which are ambiguous. The endfire time delay peaks are related to the transfer function between the two -receivers and hence invertible for the sound speed.

In the deconvolution process, the signal is a convolution of source and transfer function. If the source function can be eliminated, the transfer function remains (Anderson et al. 2015). A method used in communications does the opposite, eliminating the transfer function to obtain the source function that is the message.

Examples of correlation and deconvolution methods applied to the noise problem are presented below.

Correlation Processing

Correlation processing between two receivers yields peaks at the time delays of components of the traveling noise, whose path traverses both receivers in either direction and is independent of the specific spectral structure of the emitter. Noise can arrive from all directions but the endfire beam is the broadest and long-term correlation processing results in peaks only for the endfire direction.

Peaks rigorously derived from the endfire beam (-Lobkis and Weaver 2001; Snieder 2007) represent the two-way transfer function (also referred to as the time-domain Green’s function, TDGF), in which one receiver acts as a source and the other a receiver and vice versa. Peaks associated with the time delays emerge at a rate proportional to the square root of the time-bandwidth product. That is, both receivers gather in all the noise but the correlation that builds up of the coherent part is only from the paths that travel through both receivers; so the noise on the individual receivers can be thought of as the self-noise while the noise passing through both receivers is the “signal.” The broader the bandwidth and the longer the time the better the result. However, if the ocean medium changes over the time scale of the correlation, the time delays will vary and not build up. Thus there is a limitation of the signal processing time versus the ocean time scale. Methods are emerging for circumventing this limitation with array processing (Fried et al. 2008) and optimization that reduces the required correlation time (Woolfe et al. 2015b).

Figure 3 

Results of ocean noise correlation processing applied to ocean acoustic data are illustrated in figure 3 (Roux et al. 2004). Random ship noise was cross-correlated between acoustic arrays converting, for example, a receiver on one of the arrays to a virtual source to produce a coherent traveling wavefront that passes through all the elements of the other array.

In another example, collective noise from croaking fish (Sciaenidae), which emit signals very much analogous to those of fireflies, was received and cross--correlated between elements of an array to determine some bottom layer properties (Fried et al. 2008). There were many subsequent experimental validations of this type of processing but the most practical was with the passive fathometer (Siderius et al. 2010; figure 4). -Rather than receive a well-timed bottom echo from an active source, surface-generated noise was decomposed by a vertical acoustic array into up-and-down-going beams, which were cross-correlated to yield time delays equivalent to those from an echo produced by an active source.

Figure 4 

Another application of noise correlation processing took advantage of the fact that an asymmetric two-way TDGF senses flow to detect and measure currents (Godin et al. 2014).

Figure 5 

Correlation-based thermometry (figure 5) with polar ice noise uses only the last arrival (Woolfe et al. 2015a), so only the temperature in the region of the sound channel axis is obtained rather than throughout the whole water column. Results compared favorably with the oceanographic point measurements obtained from Argo (Roemmich et al. 2015; also see Fu and Roemmich 2018 in this issue), indicating a temperature trend.

Deconvolution Processing

As mentioned above, the efficacy of noise correlation processing is dependent on the time interval of the processing relative to the ocean time scale of the medium fluctuations that affect propagation. Hence, at first glance, it is difficult to precisely determine peak arrival times necessary for multipath tomography. But as shown in figure 1c,d, the final arrival in the SOFAR channel is quite robust.

The next step would be to obtain multiple peaks corresponding to a more complete representation of the TDGF with multiple arrival times (figure 1c,d). The goal is to convert the noise from random sources such as moving ships to tomographically useful, synchronized, precisely located individual sources (as opposed to the results shown in figures 3–5, in which noise is collectively processed).

Because it is not likely that individual absolute position or time measurements will reach the required accuracy of active tomography, the deconvolution processing involves differences in space/time corresponding to the order of centimeter/microsecond required precision. AIS provides the location of ships to an accuracy of order meters. Though not enough for the near surgical requirements of tomography, AIS can be extremely valuable by limiting the search space when combined with differencing and deconvolution to precisely determine the transfer functions from source to receiver. The deconvolution requires the simultaneous multiple-path receptions that an acoustic array can provide and then takes advantage of the fact that the source function for that instant has to be the same for all received paths, thereby providing enough information to eliminate the instantaneous source function (Gemba et al. 2018).

Figure 6 

Figure 6 shows the processing sequence of deconvolution noise tomography. Not only do ships have different spectra (example shown in figure 6a) at different speeds but these received spectra differ with range. The deconvolution process must produce TDGFs from different ships, ranges, and speeds that can be assimilated into a single dynamic ocean model. The input for the deconvolution is shown in figure 6b. Each array (orange dot) receives the noise field from a moving ship and after beamforming the acoustic paths are identified using basic AIS information. For a given “snapshot,” the beam output corresponding to the identified paths has to have the same random source function. That information is enough to deconvolve the source function from the TDGF.

An example of TDGFs is shown in figure 6c, indicating four ray paths from the source to the array. The wavefronts are analogous to those in figure 3d, but the deconvolution here yields the one-way TDGF as opposed to the two-way TDGF that emerges from correlations. A sequence of snapshots together with a model (in the sense of the lower plot of figure 1d) would correspond to the paths illustrated in figure 6d. At this point, the noise data have been converted to tomographic source receiver data and the subsequent tomographic inversion would follow the already developed methodology of tomography.

The use for tomographic deconvolutions is in its infancy, but already there is experimental evidence of localizing acoustic elements of arrays to order centimeters using noise from passing ships, an important step in the required position accuracy for tomography. An experiment for actually doing the tomography from ships of opportunity has been recently completed and the data are under analysis in an Office of Naval Research–-directed Defense Department Multiple University Research Initiative program entitled the Information Content of Ocean Noise.

The Future

Both natural and man-made sources of noise will remain or increase in abundance. As an important example, with changing climate, ice noise is expected to increase because of more cracking and collisions among ice floes—and will make it easier to monitor global change.

The physics of the imaging processes, including tomography and ocean model data assimilation, is quite advanced. Probably the greatest technology enablers (still to be developed) will enhance the distribution of acoustic sensors, fixed and/or mobile, that have available energy sources and communication capability to deliver the data. Opportunities for using global noise as illustrated in figure 2 will increase with the growing sophistication of computers, data analytics, and -acoustic, oceanographic, and satellite sensing technology.

In a future inversion scenario, ship location from AIS and noise would be the input data together with acoustic data and other information. The final step of global internal ocean imaging would be based on rapidly developing methods of artificial intelligence and machine learning  pioneered with intelligent imaging as the main goal.


The author’s research is supported by the Office of Naval Research.


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William Kuperman (NAE) is a professor at the Scripps Institution of Oceanography, University of California, San Diego, and director of its Marine Physical Laboratory.


[1]  The noise methods discussed have also been applied to a range of mechanical wave propagation, from earth (Sabra et al. 2005; Shapiro et al. 2005) and helioseismology (Duvall et al. 1993) to structural health monitoring (Tippmann et al. 2015) and even some medical imaging (Gallot et al. 2011; Sabra et al. 2007).

[2]  Unless otherwise indicated, figures are the result of federally -funded research and hence not bound by private, assignable -copyright.

About the Author:William Kuperman (NAE) is a professor at the Scripps Institution of Oceanography, University of California, San Diego, and director of its Marine Physical Laboratory.