THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

Active and Passive Equations15.12 The Sonar Equations 429The sonar parameters are determined by the equipment, the medium, and the target.We denote the following parameters, which are stated in terms of dB relative tothe standard reference intensity of a 1-μPa plane wave:Equipment parametersSL: projector source levelNL: self-noise level (also called electronic noise)DI: directivity indexDT: detection thresholdMedium parametersTL: transmission lossRL: reverberation levelNL: ambient noise levelTarget parametersTS: target strengthSL: target source level.Note that two pairs of parameters are given the same symbol because they areidentical. This set of parameters are not necessarily all inclusive, nor is this setunique, for other parameters such as sound velocity or backscattering cross sectioncould be considered. The parameters chosen above are conventional ones appliedin underwater technology.In order to understand the significance of the above listed quantities, considerFigure 15.9, which illustrates a schematic of an echo-ranging process. A transduceroperating as both sound source and receiver produces a source level of SL decibelsat a unit distance (generally 1mworldwide and 1 yard in the English system)on its axis. Let the axis of the sound source be properly aimed toward the target;the radiated sound will reach the target with a transmission loss, and the levelof the signal reaching the target will be SL − TL. On reflection or scatteringfrom the target with target strength TS, the reflected or the backscattered levelwill be SL − TL + TS (at a distance of 1 m from the acoustic center of thetarget in the direction returning to the source). This reflected signal also undergoesattenuation by the transmission loss TL as a result of its travel to the source. Thelevel of the echo reaching the source thus becomes SL − 2TL + TS. Now ifwe consider the background noise and assume it to be isotropic noise rather thanreverberation, the background level will simply be noise level. But this level willbe lessened by the directivity index (DI) of the transducer serving as a receiver,so the relative noise power at the transducer interface is NL − DI. Because theaxis of the transducer points in the direction from which the echo is traveling, therelative echo power is unaffected by the transducer directivity. At the transducerterminals, the echo-to-noise ratio becomesSL − 2TL+ TS − (NL − DL)