Source and propagation modelling scenarios for environmental impact assessment: Model verification^a)

Acoustical terminology follows ISO (2017), supplemented by definitions from other sources as indicated (Table I). Reference values (Table II) are needed when expressing levels in decibels. The reference value for the source level is $pref2 rref2$⁠. The reference value for the source spectral density level is $pref2 rref2/fref$⁠. Selected units outside the International System of Units (SI) are listed in Table III.

A marine sound source and propagation modelling workshop took place in June 2022. The workshop, which was sponsored by the E&P Sound and Marine Life Joint Industry Programme (JIP), is referred to henceforth as the JIP Acoustic Modelling (JAM) Workshop; Ainslie (2023)]. The scope of the JAM Workshop included:

• Model verification (model-model comparison) for airguns, an airgun array, a low-frequency multi-beam echo sounder (LF MBES), and a surface vessel (eight verification scenarios); and

• Model validation (model-measurement comparison) for airguns and an airgun array, and a surface vessel (four validation scenarios).

The objectives of the workshop were to:

• Facilitate evaluation of source models (especially airgun array models);

• Facilitate evaluation of propagation models;

• Identify relevant metrics for environmental impact assessment; and

• Promulgate results and conclusions.

The purpose of this paper is to specify the eight verification scenarios, thus avoiding the need for individual authors to duplicate this information. Four verification scenarios involve airguns, which create sound by releasing a bubble of compressed air into the water (Ewing and Zaunere, 1964). The four validation scenarios are specified separately (Ainslie , 2024).

Although the details of each scenario were, to an extent, arbitrary, it was valuable to have a set of well-defined verification scenarios not only to ensure that the workshop participants worked on the same specification but also so that later researchers, if they wish, can use them to perform a direct comparison of their work with that of others.

In principle, for the source waveform (by definition, a far-field quantity) only the spatial direction (not the origin) needs to be specified. Whereas the source waveform of a monopole is independent of direction, the surface-affected source waveform of a monopole (which includes the contribution from the monopole's surface-reflected image), or the source waveform of more complex sources, varies with direction. The source waveform of a single airgun or airgun cluster is typically represented in modelling codes as a monopole, in which case the source waveform does not depend on direction. This approximation is acceptable at low frequencies because the sound wavelength is large compared with the dimensions of the bubble, but it might not be a good approximation at high frequencies. In the airgun verification scenarios, the individual airguns are specified to behave as monopoles at all frequencies.

The case for model verification in underwater acoustics was made eloquently by Professor Leo Felsen more than 30 years ago (Felsen, 1990): “After spending many frustrating hours trying to account for unexplained wiggles in certain data, and finally contacting the originator of the data for clues, it often turned out that what I had regarded as a real observable was actually computational artifact.” Felsen's article was one of a series of publications in the April 1990 issue of JASA (pp. 1497–1545), all addressing one or more test cases that had been specified for an ASA special session in 1986 (Felsen, 1990). One of the test scenarios specified in the April 1990 issue involved a penetrable wedge environment referred to as “Benchmark case III” (penetrable lossy bottom), for which solutions were presented by multiple authors in March and April 1990 using different techniques (Collins, 1990a,b; Jensen and Ferla, 1990; Thomson, 1990; Westwood, 1990). Differences of 1–2 dB were observed between solution methods for an identical carefully specified problem (Jensen and Ferla, 1990), which meant that at least some of the 1990 solutions for case III were in error. The discrepancy was fully resolved by Collins and Evans (1992), who showed close agreement for case III between the energy-conserving parabolic equation and two-way parabolic equation solutions, which are now accepted as correct. The point is that many one-way propagation codes of the time were missing part of the physics, introducing an artefact that was only removed by concerted effort by multiple modellers on an identical problem, thus motivating the present work.

This paper describes eight model verification scenarios for the JAM Workshop. There are four main source types (monopole, airgun(s), LF MBES (sonar), and surface vessel), denoted by the upper case letters A-D, respectively, followed by an integer to distinguish between scenarios for the same type (Table IV).

Each scenario specifies the characteristics of an underwater sound source and of the medium in which the sound propagates to a receiver. From this information, workshop participants were invited to make predictions of quantities associated with the sound field produced by the source (e.g., sound pressure, sound particle acceleration, propagation loss), and of the source itself (e.g., source waveform and source spectrum). The purpose is to verify the suitability of source and propagation models for environmental impact assessment by quantifying differences between model predictions prior to model validation. The four validation scenarios, known as b2, b3, b4, and d1 (Ainslie , 2024), are closely related to the verification scenarios (B2, B3, B4, and D1). The intention is that models verified on one or more of these verification scenarios would then be validated using the corresponding validation scenario.

All verification scenarios involve a smooth horizontal pressure release sea surface, implying perfect specular reflection, with a π phase change and no scattering, and a fluid seabed with constant water depth. Scenarios A1, B1, B2, and B3 assume isovelocity and lossless seawater, while A2, B4, and C1 are for a deep water Munk profile with Horton-Thorp attenuation. Finally, D1 uses an isothermal profile, also with Horton-Thorp attenuation. The water current is zero for all verification scenarios.

The purpose of making these simplifications in the verification scenarios is to avoid unnecessary differences when comparing model output and to focus instead on differences between modelling methods. The validation scenarios remove these simplifications and apply them to real-world measurements.

For all verification scenarios, the intended result is the solution to the linear wave equation for the specified source and propagation medium. All scenarios specified in this paper are verification scenarios.

Of the manuscripts submitted to this special issue, about one third described contributions to the JAM Workshop, of which two (Dahl , 2024; Petrov , 2024) have been published at the time of writing. The complete set of model verification scenarios described in this paper provides information for others who wish to test new approaches to any of the test cases.

No time origin is specified. For each scenario, once a time origin is selected, it should be kept fixed for that scenario.

Three spatial coordinate systems are used:

• Cartesian coordinates are used to specify the three-dimensional (3-D) geometry. A right-handed Cartesian coordinate system is adopted with x increasing ahead, y increasing to starboard, and z increasing downward. The spatial origin is at the sea surface. Cartesian coordinates are used for scenarios B2, B3, B4, C1 and D1. For B4 a distinction is made between “world coordinates,” which are stationary in a reference frame on the Earth's surface, and “array coordinates,” which are stationary in the source array frame of reference, and otherwise aligned with the world coordinates.

• Spherical polar coordinates are used to characterize the dependence of the source waveform on emission direction: bearing and elevation. The elevation angle (θ) is relative to the vertical downward direction, always non-negative and increasing upward from the downgoing vertical direction. The bearing angle (φ) is measured clockwise seen from the previous from the Cartesian x-axis.

• Cylindrical polar coordinates (r,z) are used for acceleration [e.g., B1 (Table X), B2 (Table XII), B3 (Table XIII)]. The horizontal and vertical coordinates of acceleration are denoted $art$ and $azt$⁠, respectively, as described in the following.

Scenario A1 (scenario id: A1R) involves a point source in shallow water (depth 50 m) and a sand seabed, with frequencies between 10 Hz and 10 kHz. It is based on Ainslie (2019) and Küsel and Siderius (2019). See Fig. 1.

The acoustic source is a monopole emitting a sine wave at a specified frequency. The source depth is 5 m. Requested frequencies are 10, 100, 1000, and 10 000 Hz. Optional additional frequencies are 50 and 500 Hz.

The propagation medium is a Pekeris waveguide (Pekeris, 1948) specified in Table V (see also Fig. 1). The water depth is 50 m. The sea surface and seabed are flat (not rough), and the sea surface has a reflection coefficient of minus one.

The sediment attenuation coefficient is $α=0.5 f/csed dB$⁠, where $csed$ = 1700 m/s is the sediment sound speed (Table V). This can be written $α=Kf$⁠, with $K≈0.2941$ dB/(m kHz).

Requested outputs for each source frequency are listed in Table VI. The output quantities are to be provided vs horizontal range (0–30 km).

Scenario A2 (scenario id: A2R) involves a point source in deep water (depth 1500 m) and a clayey silt seabed, with frequencies between 10 Hz and 10 kHz. It is a deep water propagation problem with a Munk sound speed profile.

The acoustic source is a monopole emitting a sine wave at a specified frequency. The source depth is 7 m. Requested frequencies are 10 Hz, 100 Hz, 1000 Hz and 10 000 Hz.

The channel axis depth (⁠ $z1$⁠) and the sound speed at that depth (⁠ $c1$⁠) are parameters selected to match the Gulf of Mexico profile. The axis depth is estimated from Sidorovskaia and Li (2022) as $z1$ = 800 m.

Sediment sound speed and density were chosen to represent clayey silt (say 8 f, corresponding to a grain diameter of 2⁻⁸mm) (Table VII) (Ainslie, 2010). The sediment density ratio (1.5) and the attenuation per wavelength (0.1 dB) are rounded up from 1.407 and 0.09 dB.

The sediment thickness is chosen to coincide with the maximum of the quadratic, which occurs when $z−H$ = 1200 m (i.e., $h$ = 1200 m).

The substrate is a uniform half space, with density, sound speed, sound speed gradient, and attenuation coefficient all continuous across sediment-half space boundary to minimize reflection (Table VII).

Requested outputs for each source frequency are listed in Table VIII.

Scenario B1 (scenario id: B1R) involves a single airgun in the same shallow water environment as A1 (depth 50 m, sand seabed). It is based on the S1 airgun source from the International Airgun Modelling Workshop held in Dublin, Ireland on 16 July 2016 (Ainslie , 2019). However, instead of specifying the airgun parameters, the source waveform for B1 is specified. The purpose is to investigate differences in propagation modelling for a fixed (and known) source waveform.

The acoustic source is a monopole based on a 2.5 litre airgun (pressure 13.79 MPa) from Ainslie (2019) and defined by the digitised source waveform shown in Fig. 4 (provided as SuppPub1.txt). The source depth is 5 m. Some of the outputs require propagation loss at selected frequencies. These frequencies are 500 and 7000 Hz.

The propagation medium is specified in Table V (see also Fig. 1). The water depth is 50 m.

The requested outputs are listed in Table IX (for the sine waves the output quantities are to be provided vs horizontal range (0–50 km) and Table X [for the specified source waveform, s(t)]. See also Fig. 5.

Scenario B2 involves a single airgun (2.0 L, 14 MPa) in infinitely deep water. It is closely related to validation scenario b2, for a single airgun and is based on sequence 047 of the 2010 Svein Vaage measurements (Prior , 2021). The measurement geometry is shown in Fig. 6. The purpose of B2 is to provide a stepping stone to b2 in the form of a reference solution for a carefully controlled problem.

The source is a single “Bolt 1900LLXT 120” or “Bolt 1900LLX 120” airgun² at a depth of 6 m (Table XI). For B2, individual modellers are requested to choose between scenarios B2R and B2T and clarify which one was selected by specifying the scenario id as “B2T” for the 1900LLXT airgun model and “B2R” for 1900LLX. When making this choice, they should consider that the LLXT airgun was used in validation scenario b2L, while the LLX was used in b4L.

The chamber pressure is approximately 2000 lbf/in². The total airgun pressure (sum of atmospheric and airgun chamber pressures) is 13 890.840 kPa (approximately 2015 lbf/in²).

The water temperature is specified, but the temperature of the air inside the airgun just before firing is not specified and it is likely to be different. Typically, airgun models include an estimate of the internal air temperature immediately before firing. Some models also include the firing time interval in this estimate of the internal air temperature, which is 10 s, corresponding to the 0.1 Hz repetition rate.

The medium is a uniform isovelocity water with sound speed 1500 m/s and infinite water depth. No seabed parameters are specified or needed.

Requested outputs are listed in Table XII. Scenario B2 uses a 3-D Cartesian coordinate system.

Scenario B3 (scenario id: B3R or B3T) involves an airgun cluster (4.1 L, 14 MPa) in infinitely deep water. It is closely related to validation scenario b3, for a cluster of two airguns, with a horizontal separation of 1 m. It is based on sequence 236 of the 2010 Svein Vaage measurements (Prior , 2021). The measurement geometry is shown in Fig. 6. The purpose of B3 is to provide a stepping stone to b3 in the form of a reference solution for a carefully controlled problem. Modellers planning to make predictions for b3 are requested to also provide solutions for B3.

The source is a pair of “Bolt 1900LLXT 125” or “Bolt 1900LLX 125” airguns³ at a depth of 6 m (Table XIII). The two airguns are triggered simultaneously. The scenario id is B3T for the 1900LLXT airgun model and B3R for 1900LLX. The corresponding validation scenario (id b3L) is for 1900LLXT.

The medium is a uniform isovelocity water with sound speed 1500 m/s and infinite water depth. No seabed parameters are specified or needed.

Requested outputs are listed in Table XIV. Scenario B3 uses a 3-D Cartesian coordinate system.

Scenario B4 (scenario id: B4R) involves an airgun array (68 L, 14 MPa) in the same deep water environment as A2 (depth 1500 m, clayey silt seabed). It is closely related to validation scenario b4, which is based on the SCS07 measurements in the Gulf of Mexico (Sidorovskaia and Li, 2022). The purpose of B4 is to provide a stepping stone to b4 in the form of a reference solution for a carefully controlled problem.

The source is a horizontal array of 30 Bolt 1900LLX and 1500LL airguns at a depth of 7 m (Tables XV and XVI). All airguns in the array are triggered simultaneously.

The SCS07 source array geometry (Fig. 7) is described in Table XVI. The array's origin is at the sea surface, directly above the 1900LLX 120 airgun in the centre sub-array, numbered 17. For this single-pulse scenario, the source array origin coincides with the spatial origin in world coordinates (Cartesian coordinates that are stationary in the Earth's reference frame). This array origin is 1000 m ahead of the receiver.