What is source level?

Source level is a metric describing the power radiated by a sound source along a particular direction. It is a key component of the sonar equation and is used in conjunction with the concept of transmission loss to calculate received levels. (For more information on the sonar equation see SONAR Equation)

Unlike sound intensity (units of watts per square meter [W/m2]), source level does not depend on the distance from the source and does not depend on the propagation environment surrounding the source. A simplified interpretation of source level is that it represents the mean-squared sound pressure level that would be measured at a 1-m distance from the acoustic source along a specific direction, if all the power generated by the source were radiating from a single infinitesimal point. Source level is expressed in terms of underwater decibels (dB), and thus requires a reference level, which traditionally is 1 µPa2, resulting in reported units of dB re 1 uPa @ 1 m. The reader is referred to Introduction to Decibels for more details.

Source levels are generally not measured by placing a hydrophone 1 m away from a source, as this is both impractical in many situations and causes problems for sources that are not a single point in space. Instead, a hydrophone is placed some distance away from the source and the measured square-pressure is adjusted for propagation loss to estimate the square-pressure at 1 m distance.

There are various subtleties to consider when defining source level that have led to different formal definitions being adopted by different scientific standards organizations. These subtleties arise because real physical acoustic sources are often directional and are not infinitesimal in volume.

Many acoustic sources, particularly high-frequency sources, are directional in the sense that they radiate more acoustic power in certain directions than others. For example, echolocation clicks generated by most odontocetes have a beam pattern that results in more acoustic power being radiated from the front of the animal than from the back. Because of this fact, when reporting source levels, it is important to specify a source’s direction or orientation relative to a receiver. Sources that radiate energy equally in all directions are called omnidirectional; under those circumstances the source level does not need to indicate source orientation.

Real physical sources also have finite dimensions and may even be comprised of multiple individual sources spread over space. A seismic airgun array is an example of the latter situation. Because an airgun is a distributed source, the source level calculated from acoustic measurements will vary depending on the distance of the measurement from the source, even when propagation conditions are taken into account. The reason for this variation is that at close ranges the different components of a distributed acoustic source will lie at different distances from the measurement point, and so the radiated power from these components will constructively and destructively interfere with each other. The distances over which a source interferes with itself is called the near field. At greater ranges from the source (far field), the distance between the measurement point and the source center becomes so large compared to the dimensions of the source, that the components of the source do not self-interfere; and it effectively acts like an infinitesimal point source. The distance of the transition from the near field to the far field depends on the frequency of the source as well as the dimensions of the source. (For further details please see Propagation from a sound source array in the near field and far field).

For this reason, formal definitions of source level require that any measurements used to compute source level must be made in the source’s far field. The advantage of this restriction is that it ensures that the source level of a radiating object can still be described by a single number. The disadvantage is that the numerical value of source level does not realistically represent the true square pressure measured at 1 m distance from a non-point source. This can cause calculations based on source level to overestimate received levels at ranges within the near field of the source. This discrepancy between the hypothetical and actual levels received at 1 m range for many physical sources has led to different approaches to defining source level, as well as different reference units for reporting decibels.

The American National Standards Institute (ANSI/ASA S1.1-2013, ANSI 2013), which defines acoustic standards for the United States, defines source level as a “sound pressure level on the axis of the sound projector measured in the far field and scaled back to a standard reference distance of 1 meter from the effective acoustic center of the projector. Unit, decibel (dB).” In this definition, the far field measurement of acoustic intensity is adjusted for propagation effects incorporating propagation loss such that source level is equal to the measured far field sound pressure level plus propagation loss. This standard makes it clear that the far field acoustic field is of interest and that the source level does not relate to the near field acoustic pressure. The reference to 1 m is to provide a standard distance for comparing acoustic fields; it is not intended to imply that the sound pressure level is measured 1 m from the sound source. An example of a source level reported according to the ANSI standard is “160 dB re 1 µPa @ 1 m,” and can be considered the traditional approach for reporting sound level.

By contrast, the International Organization for Standardization (ISO) has created ISO 18405:2017, an international standard for underwater acoustics terminology. In ISO 18405:2017, the term source level is defined as “ten times the logarithm to the base 10 of the ratio of the source factor, FS, to the specified reference value, FS,0, (units decibels, dB)” (https://www.iso.org/obp/ui/#iso:std:iso:18405:ed-1:v1:en:term:3.3.1.5). The source factor is the product of the square of the distance from the acoustic center of a source in a specified direction and the mean-squared sound pressure in the acoustic far field at that distance, in a hypothetical uniform lossless medium. The value of the source factor is independent of distance.

The ISO entry for source level notes that the “source level in a specified direction is equal to the mean-square sound pressure level at a distance of 1 m from a hypothetical point source, placed in a hypothetical lossless medium” (i.e., there is no propagation loss). This acknowledges the widespread practice of citing source level with a reference value of “1 µPa @ 1 m.” However, ISO 18405 requires that the reference value should be cited as “1 µPa2m2,” which ties back to the definition of source level in terms of a source factor ratio, and not a squared sound pressure ratio. Thus, using the ISO standard, the source level of the same source in the previous example is “160 dB re 1 µPa2m2.” The motivation behind this approach is to emphasize that the source level metric is derived from a far-field measurement, raising awareness that the source level and actual measured levels at 1 m from a source are generally not equivalent.

As a practical matter, both formal definitions provide the same numerical values, and only change the reference unit. Both standards can be used interchangeably when combined with transmission loss models to estimate received levels.

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Additional Resources

References

  • American National Standard Institute. 2013. Acoustic terminology. ANSI/ASA S1.1-2013.
  • International Organization for Standardization. 2017. Underwater acoustics – Terminology. ISO 18405:2017.
  • Ainslie, M. A., Halvorsen, M. B., & Robinson, S. P. (2022). A Terminology Standard for Underwater Acoustics and the Benefits of International Standardization. IEEE Journal of Oceanic Engineering, 47(1), 179–200. https://doi.org/10.1109/JOE.2021.3085947