The mighty SONAR equation#
The Sonar Equation provides a framework for understanding the different components involved in either pure listening or active pinging (echolocation) using sound. The term SONAR stands for SOund Navigation And Ranging.
In pure listening scenarios, the sonar equation is written as:
and in the active sensing scenario, it is written as:
where:
\(RL\) denotes receive level, or the strength of the received sound
\(SL\) denotes source level, or the intensity of the emitted sound
\(TL\) denotes transmission loss, or the attenuation of sound as it travels
\(TS\) denotes target strength, or the acoustic reflectivity of the target
You may find variations of the sonar equation that include additional terms, such as noise level (\(NL\)), array gain (\(AG\)), or directivity index (\(DI\)), as seen on the DOSITS website. These variations arise from the specific problem setup and the instrumentation used.
Note
The SONAR equation effectively breaks down the complex ocean acoustics “system” into multiple individual pieces that are each much more manageable, making it a lot easier to analyze and model first each component and ultimately the whole system.
In the following tutorials, we will use the SONAR equation as a guide to explore key components of an ocean acoustics problem (the “system”), including acoustic sources and receiver (both biological or human-made), sound propagation and scattering (due to biotic or abiotic factors), and applications of signal processing and statistical methods to real-world ocean acoustic data through both conceptual introductions and hands-on exercises.
But first, let’s see how we can use the SONAR equation to help us break down the complex problem of studying the lives of orcas using sound.
Tip
Through the tutorials, you will find that each term in the SONAR equation is much more than just a level (intensity) that you see here, but that the SONAR equation remains a useful tool to think about the big picture when you work on an ocean acoustics problem.