Effective measures for protecting and preserving the marine environment require an understanding of the potential impact of anthropogenic sound on marine life. A crucial component is a proper assessment of the anthropogenic soundscape: which sounds are present where, when and how strong? We provide an extensive case study modelling the spatial, temporal and spectral distribution of sound radiated by several anthropogenic sources (ships, seismic airguns, explosives) and a naturally occurring one (wind) in the Dutch North Sea. We present the results as a series of sound maps covering the whole of the Dutch North Sea, showing the spatial and temporal distribution of the energy from these sources. Averaged over a two year period, shipping is responsible for the largest amount of acoustic energy (∼1800 J), followed by seismic surveys (∼300 J), explosions (∼20 J) and wind (∼20 J) in the frequency band between 100 Hz and 100 kHz. Our study shows that anthropogenic sources are responsible for 100 times more acoustic energy (averaged over 2 years) in the Dutch North Sea than naturally occurring sound from wind. The potential impact of these sounds on aquatic animals depends not only on these temporally averaged and spatially integrated broadband energies, but also on the source-specific spatial, spectral and temporal variation. Shipping is dominant in the southern part and along the coast in the north, throughout the years and across the spectrum. Seismic surveys are relatively local and spatially and temporally dependent on exploration activities in any particular year, and spectrally shifted to low frequencies relative to the other sources. Explosions in the southern part contribute wide-extent high energy bursts across the spectrum. Relating modelled sound fields to the temporal and spatial distribution of animal species may provide a powerful tool for understanding the potential impact of anthropogenic sound on marine life. Detailed sound maps of the Dutch North Sea, which can serve as a basis for further impact assessment studies and legislation, are calculated and analyzed.

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The sea surface acts as a very strong reflector because of the large impedance contrast between water and air. The reflection coefficient is -1 in a very good approximation. Apart from the surface multiples, the sea surface is also responsible for generating the source and receiver ghost wavefields. These cause the well-known ghost notches in the spectrum: areas where the signal-to-noise ratio is very low. To model the ghost wavefields, ghost operators can be computed and applied to ghost-free data. Modeling experiments indicate that in the case of a flat sea surface, the character of the notches in various gather types, e.g., receiver gather, common-offset gather, shot record, is largely determined by the complexity of the earth. In a simple earth, e.g., horizontally layered, the notches are always well-defined and deep, but in a complex earth, they become blurry in some of the gather types. Therefore, in the case of a complex subsurface, source deghosting is best carried out in the common-receiver domain and receiver deghosting is best carried out in the common-shot domain. In the case of a simple subsurface, deghosting can be carried out in all domains. An additional factor is that the sea surface may be rough and dynamic. This causes blurry ghost notches in all gather types, even in the case of a simple earth. To model the source ghost for this situation, an effective static rough sea surface suffices. This keeps the computations simple. The condition is that the source has an impulsive character. However, to model the receiver ghost (and the source ghost for a nonimpulsive source), the dynamics of the sea surface must be included. This can be done by composing the final result from the results computed for several "frozen" snapshots of the dynamic sea surface.@en

Computer models can be used to predict the sound field near an airgun or airgun array. The accuracy of such predictions can be assessed either by a process of verification (comparison with alternative theoretical solution to the same computational problem) or by validation (comparison with measurement). A set of verification test problems is described, as used originally by participants in the International Airgun Modeling Workshop held in Dublin, Ireland on July 16, 2016, and now by other authors in this special issue. The main inputs specified are the characteristics of the source (array geometry, airgun type and volume, and chamber pressure) and of the propagation medium (mainly water depth and bottom type). Also specified are source waveforms for individual airguns for authors wishing to focus only on the propagation aspects of the problem. The outputs are specified in terms of metrics derived from the sound pressure and sound particle acceleration.@en

An analytical formulation for the calculation of the range and depth-dependence of propagation loss in isospeed water is introduced. The range-dependent bathymetry is handled with Weston's ray invariant approach, requiring a gradually varying water depth. The depth dependence of propagation loss is formulated using a transformation from an incoherent mode sum to an integral over angle, in the adiabatic approximation, and the results obtained in this way are tested by comparison with a full adiabatic normal mode sum. The validity of the adiabatic approximation itself is then investigated by means of a comparison with parabolic equation and coupled normal mode results for selected test cases from the Weston Memorial Workshop, held at the University of Cambridge in April 2010. Propagation loss calculations based on different methods are compared. The proposed analytical approach provides practical, fast and accurate results.@en

The calculation of air gun source signatures gives insight into applications such as air gun array design, deghosting and the impact of sound on marine life. Single air gun source signatures were calculated from the numerical solution of a set of differential equations based on different branches of physics. Some characteristic parameters of air guns were obtained from the Svein Vaage broadband air gun data set (SVBAD) measurements to calibrate the model. The comparison between measured and modeled air gun signals helps to investigate the accuracy of air gun source models. The modeled air gun signatures compared well with measurements from the SVBAD for the case of a calm sea surface of sea state 2 or less. The source ghost signal modeled for a rough sea surface showed amplitude and phase changes, affecting the ghost notches, which may explain discrepancies between the SVBAD measurements and modeled air gun signals at frequencies above 150 Hz.

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Comparisons are made of sound pressure and particle acceleration predicted by two methods in the vicinity of two arrays of marine-seismic airguns. Data describing the array properties and the environmental conditions are taken from test cases designed to facilitate intermodel comparison. The two propagation approaches, one based on method of images and the other on wave number integration, are shown to be capable of giving line-on-line agreement when the latter method implements the full form of the Hankel transform; when the more approximate Fourier transform is used, predictions are shown to differ at ranges of a few meters from the source.@en

The strong sea surface reflectivity causes source- and receiver-ghost notches: areas in the wavenumber-frequency domain where the signal is very weak and consequently the SNR (signel-to-noise ratio) is low. If the sea surface is flat, these notches are very deep, but if it is rough and dynamic, they become blurred. The same strong sea-surface reflectivity also causes the surface-related multiples and its effect increases with each next multiple order. When modeling the ghost wavefield of an impulsive source in the case of a dynamic sea surface, an effective static sea surface suffices. The latter is composed of the surface areas that are ‘touched’ by the source wavefield at successive snapshots in time. However, such an effective static sea surface is not sufficient for the case of the detector ghost: here the dynamic character of the sea surface needs to be taken into account. We introduce a method for doing this by computing ghost operators for a number of snapshots in time and compose the final result from applying these. Our modeling method can be used to test algorithms such as deghosting. It can also be used to quantify the error that is introduced when the effects of the rough and dynamic sea surface are ignored, e.g., by replacing it by a flat sea surface in combination with an effective reflectivity that aims at incorporating the effects of a rough and dynamic sea surface.@en

The strong sea surface reflectivity causes source- and receiver-ghost notches: areas in the wavenumber-frequency domain where the signal is very weak. If the subsurface is complex, the source-ghost notch is most apparent in common detector gathers. It may even be absent in common source gathers, i.e., in shot records. For the detector-ghost notches it is the other way around: they are most apparent in shot records and may be absent in detector gathers. Both notch types show up in the common-offset and CMP domains albeit less clearly. In the case of a complex subsurface, the deghosting process should be carried out in the right domain: source deghosting in the common receiver domain, detector deghosting in the common shot domain. In the case of a simple subsurface, deghosting can be carried out in any domain.@en

Sound mapping over large areas can be computationally expensive because of the large number of sources and large source-receiver separations involved. In order to facilitate computation, a simplifying assumption sometimes made is to neglect the sound speed gradient in shallow water. The accuracy of this assumption is investigated for ship generated sound in the Dutch North Sea, for realistic ship and wind distributions. Sound maps are generated for zero, negative and positive gradients for selected frequency bands (56 Hz to 3.6 kHz). The effect of sound speed profile for the decidecade centred at 125 Hz is less than 1.7 dB.@en

Anthropogenic sound in the marine environment can have negative consequences for marine fauna. Since most sound sources are intermittent or continuous, estimating how many individuals are exposed over time remains challenging, as this depends on the animals’ mobility. Here we explored how animal movement influences how many, and how often, animals are impacted by sound. In a dedicated study, we estimated how different movement strategies affect the number of individual harbour porpoises Phocoena phocoena receiving temporary or permanent hearing loss due to underwater detonations of recovered explosives (mostly WWII aerial bombs). Geo-statistical distribution models were fitted to data from 4 marine mammal aerial surveys and used to simulate the distribution and movement of porpoises. Based on derived dose–response thresholds for temporary (TTS) or permanent threshold shifts (PTS), we estimated the number of animals affected in a single year. When individuals were free-roaming, an estimated 1200 and 24000 unique individuals would suffer PTS and TTS, respectively. This equates to respectively 0.50 and 10% of the estimated North Sea population. In contrast, when porpoises remained in a local area, fewer animals would receive PTS and TTS (1100 [0.47%] and 15000 [6.5%], respectively), but more individuals would be subjected to repeated exposures. Because most anthropogenic sound-producing activities operate continuously or intermittently, snapshot distribution estimates alone tend to underestimate the number of individuals exposed, particularly for mobile species. Hence, an understanding of animal movement is needed to estimate the impact of underwater sound or other human disturbance.@en

The European Union requires member states to achieve or maintain good environmental status for their marine territorial waters and explicitly mentions potentially adverse effects of underwater sound. In this study, we focused on producing maps of underwater sound from various natural and anthropogenic origins in the Dutch North Sea. The source properties and sound propagation are simulated by mathematical methods. These maps could be used to assess and predict large-scale effects on behavior and distribution of underwater marine life and therefore become a valuable tool in assessing and managing the impact of underwater sound on marine life.@en

The production of underwater sound is more and more considered to be an environmental risk. This has already been the case for military sonar for more than a decade, as sonar was identified as a possible cause of marine mammal strandings. The approach we adapted for military sonar is the following. The risk is characterized by computing the exposure (sound produced by the sonar) in an area around the source and by coupling that information to the effects it causes on a certain animal species. The risk is then quantified by taking into account the probability of the presence of that species in the area. If too large, the risk can be mitigated. We observe a trend of shifting the focus from individual disturbance to more general population consequences. A similar approach is advised to characterize the risks involved in the use of airguns in seismic acquisition.

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Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.@en

Concern about possible impact of human activity on marine life has led to regulation in the USA and the EU. The EU's Marine Strategy Framework Directive requires member states to achieve Good Environmental Status (GES) by 2020. Descriptor 11 of GES is "Introduction of energy, including underwater noise, is at levels that do not adversely affect the marine environment", for which two indicators are specified. The effects of underwater sound on aquatic animals is a research topic in need of multidisciplinary effort between acousticians and biologists, in order to provide a quantitative description of the sound field and to understand the impact of the sound on aquatic life. Sound exposure level (SEL), sound pressure level (SPL) and peak pressure are widely used as metrics for assessing environmental impact . This paper described the calculation of SEL and SPL for impulsive sounds in shallow water (relevant to Indicator 11.2.1 of GES Descriptor 11), with particular attention to the difficulties associated with the effect of time dispersion, which can lead to large uncertainties and errors in SPL.@en