A consistent approach to definitions and symbols in fisheries acoustics

David N. MacLennan Paul G. Fernandes John Dalen Long-standing problems with acoustical terminology in fisheries applications such as echo-integration indicate the need for a more consistent approach. Based where possible on existing terms, a scheme of explicitly named quantities is proposed, backed by clearly stated definitions and preferred symbols. The emphasis is on scattering phenomena because the terminology in this area presents the main source of difficulty. Starting with the scattering equations for a small target, the volume, area, and line coefficients relevant to multiple, distributed targets are defined, leading to practical formulas for the important application of remote biomass estimation from echointegration. The aim is to incorporate, as far as possible, common practice in fisheries-acoustics terminology and related fields. The developed scheme has been commended by the ICES Fisheries Acoustics Science and Technology Working Group as a constructive approach to better communication standards in fisheries-acoustics publications. 1054-3139/02/040365+05 $35.00/0 - In any scientific field it is essential to be clear about the definition of physical quantities and naming conventions. In the case of fisheries acoustics there has been a long-standing problem mainly due to confusing descriptions of the various scattering measures that are central to biological observations using sonars and echointegrators. With the growing importance of acoustic methods in remote biomass estimation, many practitioners agree that a more consistent approach to acoustical terminology must be adopted in fisheries applications. Existing guidance on these matters is limited and somewhat contradictory. General texts on acoustical terminology (ANSI, 1994; Urick, 1983) do not define adequately processes like area scattering which are seldom mentioned outside fisheries applications. At the more specialised level, Hall (1995) considers that solid angle measures should be included in the definition of target strength and related parameters. However, this idea is not supported by Medwin and Clay (1998) in their more complete treatment of the ground rules that apply to acoustical oceanography. For historical and other reasons different practices appear in the fisheries literature (Craig, 1981; MacLennan and Simmonds, 1992; Foote and Knudsen, 1994). Our primary concern is to address the lack of consistency arising in the latter field. A common pitfall, for example, is the distinction between the quantities sa and sA. Although these terms have been described (e.g. Foote and Knudsen, 1994), there is no common name for the quantity sA, notwithstanding that this is the primary output from the most common scientific echosounder, the Simrad EK500. More disturbingly, although these terms differ by a factor of 4 (1852)2 (Foote and Knudsen, 1994), such that sa=sA/4 (1852)2, the Simrad EK500 instruction manual notes that . . . the Sa(mean) to be used for fish density calculations is Sa(mean)=SA/4 (note also the incorrect use of capitalisation: SA is used instead of sA). The definitions depend critically on the relationships between fish density, sa, sA, and fish target strength but no single document exists which encompasses and defines all these terms in a complete and consistent manner. Here, we propose a complete scheme of definitions and terminology which, hopefully, will encourage more uniform use of terms to describe measurements in fisheries-acoustics publications. The emphasis is on scattering phenomena because these are the main source of difficulty. Primary measurements Acoustical quantities such as the target strength are not measured directly. They are determined by numerical evaluation of a defining equation X=f(Qp) where Qp is a set of primary quantities which can be measured directly. The equations show inter alia the dimensions and the units of the derived quantity in terms of primary measurements. Different Qp might be selected for this purpose, however, to focus on scattering phenomena we start with the set listed below. r Distance of the measurement position from a small target. In this context, small means a target whose characteristic size is less than the radius of the first Fresnel zone, namely (r /2) where is the wavelength. , Spherical polar angle coordinates of the measurement position. The target is at the origin and the transmitted wave propagates in the direction (0,0). x,y,z Cartesian coordinates. The transmitted wave propagates towards the target in the +z direction. Iinc Intensity of the transmitted or incident wave at the target. Iscat(r, , ) Intensity of the scattered wave at the measurement position. Ibs(r) Intensity of the backscattered wave, equal to Iscat(r, 0). I(z) Intensity of a plane wave as a function of distance along the propagation path. V Volume occupied by a scattering medium or multiple discrete targets. A Area of a school echo-trace observed on an echogram. Naming conventions The first requirement is to adopt a set of names which are unique for each quantity having a specific physical definition. Furthermore, quantities which are scaled by factors other than powers of 10 should have different names, like degrees and radians in the case of angles. Given a non-confusing and widely accepted set of names, the symbols are less of a problem, or at least those which have dimensions. In that case, SI units are the norm, with 10n scaling factors as needed. On the other hand, it is not necessary to cover every quantity which might be expressed with non-decadal scaling. The need is to include those which are often used in fisheries acoustics in order to eliminate any risk of confusion. Table 1 shows a list of derived quantities relevant to scattering by one or more insonified targets. We start with the intensity scattered by a small target which is normally direction-dependent. This leads to various cross-sections that describe the acoustical size in terms of the ratio of the scattered and incident intensities. Medwin and Clay (1998) prefer to start with the complex scattering length, L( , ) which expresses phase as well as amplitude information. It is usual to consider cross-sections and scattering lengths as frequency dependent functions. Alternative models, based on time dependent functions, may be simpler and more robust. The latter could well become important as and when sonars have much wider bandwidths than current instruments. We concur with Medwin and Clay (1998) that the name differential scattering cross-section be used to describe the scattering over all directions, measured bistatically. However, we believe the related symbol should have a functional form such as ( , ) or (r), as opposed to ( , ). We prefer not to use the qualifier in this context because it normally indicates a small but finite increment, whereas ( , ) is a continuous function. It follows that other cross-sections relating to specific directions, or with no direc (...truncated)