Definition of signal-to-noise ratio and its critical role in split-beam measurements

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1 ICES Journal of Marine Science, 62: 123e130 (2005) doi: /j.icesjms Definition of signal-to-noise ratio and its critical role in split-beam measurements Robert Kieser, Pall Reynisson, and Timothy J. Mulligan Kieser, R., Reynisson, P., and Mulligan, T. J Definition of signal-to-noise ratio and its critical role in split-beam measurements. e ICES Journal of Marine Science, 62: 123e130. The signal-to-noise ratio (SNR) plays a critical role in any measurement but is particularly important in fisheries acoustics where both signal and noise can change by orders of magnitude and may have large variations. Textbook situations exist where the SNR is clearly defined, but fisheries-acoustic measurements are generally not in this category as signal and noise come from a wide range of sources that change with location, depth, and ocean conditions. This paper defines the SNR and outlines its measurement using splitbeam data. Its effect on target-strength (TS) measurements is explored. Recommendations are given for the routine use of the SNR in fisheries-acoustic measurements. This work also suggests a new equation for TS estimation that is important at low SNR. Crown Copyright Ó 2004 Published by Elsevier Ltd on behalf of International Council for the Exploration of the Sea. All rights reserved. Keywords: digital data, echosounding, noise, reverberation, signal-to-noise ratio, split beam, target-strength bias. Received 4 March 2004; accepted 8 September R. Kieser and T. J. Mulligan: Pacific Biological Station, 3190 Hammond Bay Road, Nanaimo, BC V9T 6N7, Canada. P. Reynisson: Marine Research Institute, PO Box 1390, Skulagata 4, 121 Reykjavik, Iceland. Correspondence to R. Kieser; tel: C ; fax: C ; kieserr@pac.dfo-mpo.gc.ca. Introduction The signal-to-noise ratio (SNR) is well defined and understood in electrical engineering and communications (Tucker and Gazey, 1966; Carlson, 1968; Haykin, 1994; Ziemer and Tranter, 1995). It is frequently used in fisheriesacoustic work that is concerned with the measurement process and instrument design (Ehrenberg and Weimer, 1974; Weimer and Ehrenberg, 1975; Ehrenberg, 1978; Ehrenberg, 1979; Ehrenberg, 1981; Mitson, 1983, 1995; Furusawa et al., 1993; Furusawa et al., 2000), but has seen relatively little use in the application-oriented, fisheriesacoustic literature (MacLennan and Simmonds, 1991). It is the goal of this paper to introduce the SNR and to demonstrate its usefulness for fisheries applications. Communications theory tells us that the SNR in its simplest form is defined as the ratio of signal power to noise power. We will develop this definition and describe the practical measurement of the SNR from split-beam data. The importance of the SNR for TS measurements and splitbeam modelling will be briefly highlighted and the routine use of the SNR for data-quality assurance will be recommended. Finally we propose an equation for measuring TS at low signal to noise. In practice, noise is recognized on the echogram as a general background of random marks. These can be removed by choosing a threshold that will provide an interference-free image but does not significantly reduce the desired echo signals in the depth range of interest. Foote (1991) and others have discussed the bias that may arise from thresholding in echo integration (EI). Split-beam measurements generally use echo-amplitude and beampattern thresholds (MacLennan and Simmonds, 1991) to reduce adverse noise effects. Thresholds provide an intuitive and practical tool, however the SNR is required to understand, quantify, minimize, and possibly correct for the bias that cannot be avoided when the SNR is too low. A distinction can be made between passive- and activenoise measurements. Passive-noise measurements are made in listening mode with the echosounder transmitter disabled. Active-noise measurements are made during normal echosounder operations for the range of interest. Both measurements will record vessel and environmental noise, but only active-noise measurements will record /$30.00 Crown Copyright Ó 2004 Published by Elsevier Ltd on behalf of International Council for the Exploration of the Sea. All rights reserved.

2 124 R. Kieser et al. reverberation, which is the noise-like, volume-backscatter signal from unwanted, interfering target distributions. Reverberation may be from bubble, silt, or plankton layers at the range of the target or from boundaries. Here, we are concerned with the noise that is observed during active measurements as it includes all noise sources that occur during typical echosounder operation. We use fisheries-acoustic standard notation (Craig, 1981; Kieser, 1981; MacLennan et al., 2002) where possible and will use two or more leading capital letters for quantities expressed in db, e.g. TS or SNR. For consistency we use SV rather than S V for the volumebackscatter coefficient and STE will stand for single-target echo as it plays a central role in TS and SNR measurements. Definition of signal-to-noise ratio The SNR is defined as signal power divided by noise power (Carlson, 1968). Inspired by Mitson (1983) we start with simulation results to illustrate the application of this definition to fisheries acoustics (Figure 1). The signal and noise are received by the transducer and processed in the echosounder to generate the filtered signal and filtered noise and their respective envelopes. Superposition of signal and noise generates a realistic echo; the filtered echo now clearly resembles a typical single-fish echo which may be seen on the oscilloscope or plotted from the digital data. Estimation of the SNR would be trivial if signal and noise could be observed separately. This simulation employs a pulse with 1-ms duration, amplitude 1 and 5-kHz carrier. The pulse envelope is composed of a flat top (0.5 ms) with cosine-shaped, leading and trailing edges (Clay and Medwin, 1977). Band-limited, Gaussian white noise (Kafadar, 1986) with random phase and an amplitude of 0.5 between 2 and 10 khz and an elliptical bandpass filter of order 4 with 4.5 to 5.5 khz pass band (Matlab, 1998) are used. Given separate realizations of the filtered signal and filtered noise, or of their envelopes, an estimate of the SNR is given by: Snr S N ð1þ where Snr is the SNR expressed as a power ratio rather than in db, S is the RMS signal power for the echo peak (Johannesson and Mitson, 1983) and N is the mean RMS noise power at the echolocation. A different approach is needed to estimate the SNR from the filtered echo that is shown at the lower right in Figure 1 as it contains signal and noise contributions. In this case the SNR is estimated from: Snr E ÿ N E ; ð2þ N E where E is the combined signal and noise power at the location of the echo peak and N E is noise power that is estimated from observations on both sides of the peak. Estimation of E and N E is described in the next section. With this definition the estimated SNR has the desirable property of approaching zero as the echo peak is reduced and becomes masked by the noise. The echo power at the peak location, E ÿ N E, approximates the steady echo signal that would be obtained from a long, nearly rectangular transmit pulse that could be used to estimate backscatter cross-section (Foote et al., 1987). Note that the use of E ÿ N E in Equation (2) is in contrast to the conventional use of E for TS estimation. We recommend that E ÿ N E be used for TS estimation, especially at low SNR provided that good noise estimates are available. This definition of the SNR matches that used for modelling the split-beam process (Ehrenberg, 1979; Kieser et al., 2000). Like TS the SNR assumes an on-axis target. It follows that off-axis targets will have a reduced SNR. For Input: Filtered: Envelop: Signal Signal Signal Noise Transducer Echosounder Noise Noise Echo = Signal + Noise Echo Echo Figure 1. A simulation of signal and noise and a typical echo that includes signal and noise as they might appear at the transducer and after the filter and envelop detection that are part of a typical echosounder.

3 Definition of signal-to-noise ratio and its role in split-beam measurements 125 example a reduction of 6 db will occur for targets at the ÿ3 db beam-pattern contour. The simple definition of the SNR used here assumes that signal and noise are measured at the output of the bandpass filters that are used in typical echosounders and therefore are limited to the same bandwidth. The definition is useful for work with a given echosounder both for comparing identical acoustic systems and for modelling. However, comparing SNR measurements from acoustic systems with different pulse duration, bandwidth, beam width, and transmit level will require a more encompassing definition of the SNR. This is also required when signal and noise are measured at the receiver input where noise will have a much wider frequency spectrum than the signal. Appropriate definitions are available (Carlson, 1968) but are beyond the scope of this paper. Measurement of signal-to-noise ratio Figure 2 shows a single-target echo (STE) that was observed with a SIMRAD EK500 echosounder. The cross and the larger points on either side of the peak highlight the maximum echo amplitude, e max, and the noise amplitudes, a target at any position in the beam, E and N E are obtained from the echo and the estimate of the SNR is: E ÿ NE SNRZ10log ÿ 2BP; ð4þ N E where SNR and BP are in db and BP is the one-way beampattern factor for the target s location in the beam. Measurement of the SNR ratio typically starts with splitbeam STE data (echo traces) which provide an estimate of the beam-pattern factor and give the location of the detected target in the sample data. The sample data are then used to estimate the signal and noise power as described above. Resampling (Lyons, 1997) or curve fitting may be required when additional data points are needed to define the peak more accurately. The regions used to estimate the noise (noise windows) must be well separated from the peak to avoid contamination from the signal envelope. A larger separation may be required at the longer range side of the echo as the echo may be extended due to ringing or target size. The noise windows also must be free of other signals and must include a sufficient number of sample points to produce reasonable estimates. The following results are obtained from the STE in Figure 2. Ping (#) Range (m) 2BP (db) E (db) N E (db) TSu (db) TSc (db) SNRu (db) SNRc (db) ÿ1.0 ÿ31.0 ÿ59.6 ÿ31.0 ÿ n j, respectively. The observed echo and mean noise power, E and N E, are: EZe 2 max ; N EZ 1 J X J jz1 n 2 j ; ð3þ where j is summed over the number of measured noise amplitudes. As stated above the SNR is defined as the ratio of signal power over noise power when the signal comes from a target that is on the beam axis (Equation (2)). For Figure 2. An echo from a single fish at 172-m range. SIMRAD EK500 sample data (40 log r) with 0.1-m range resolution are used. Pulselength is 0.75 m (1 ms). The observed signal is defined by the peak (cross) and the noise by the larger dots on both sides of the peak. where 2BP is the two-way beam-pattern factor from the split-beam target position measurement. E and N E are the peak and average noise energy, respectively, from Figure 2. As recommended we use TSu Z E ÿ N E but this makes little difference at the high SNR. TSu and TSc and SNRu and SNRc are the uncorrected (off axis) and corrected (on axis) TS and SNR, respectively. The corrected values include the beam pattern correction shown in Equation (4). TSc and SNRc are estimates of TS and SNR, respectively. Similar to TS estimation only well defined, single-target echoes will be considered for SNR estimation. Echoes may be rejected when the peak is poorly defined, when additional echoes are too close, when the variation and slope in the selected noise windows is excessive or when the estimates from the two noise windows are too different. Substantial numbers of STE will have to be examined to establish acceptable limits for particular situations. Figure 3 shows an echo trace that would not be acceptable for SNR measurement as the left-hand shoulder on the peak interferes with the noise measurement. Estimates of the SNR can be obtained from 20 or 40 log r data when the corresponding 20 or 40 log r factors are approximately constant over the range interval that includes the signal and noise samples. This will be the case when the interval is much smaller than the target range. Single-target detection and TS estimation are routinely done in split-beam echosounders. The EK500, for example, outputs an echo trace file that includes estimates of echo

4 126 R. Kieser et al. 100 khz. Although this paper focuses on the SNR for single targets we note that for the EI of a target distribution with constant volume-backscatter coefficient (e.g. a target distribution with constant average density and TS) situation i) and ii) will yield SNRs that will decrease with range as ÿ20 log r ÿ 2ar and 0, respectively. The effects of low signal to noise: evidence of TS bias from TS measurements Figure 3. An echo trace that is not acceptable for SNR measurement as the left hand shoulder, which may be from a nearby second target, interferes with the peak and the noise measurement. peak height (TSu) and information on echo quality but does not provide noise estimates. As before the latter may be obtained from sample data. However this requires that the sample data use the same units or are converted to the same units. This approach is useful when only relatively low-resolution sample data or high-resolution EI data are available. A well-known example of potential TS bias with range, and hence presumably decreasing SNR, has been described by Reynisson and Sigurdsson (1996) and Reynisson (1999) and is shown in Figure 4. Redfish of the same size (mean length 37 cm and TS ÿ40 db) are often distributed between 100 and 300-m depth. TS estimates were made with five different beam acceptance angles, only targets that are detected within the specified off-axis beam angle being accepted. Figure 4 shows that the TS estimate in general increases with range. It also increases when a larger beam acceptance Noise and SNR range dependence Evidence from echograms, plots of echo intensity vs. range, and oscilloscope observations of the echosounder output voltage generally show noise levels that increase with range. More rapid increase with range is observed for 40 log r than for 20 log r data. Two simple situations are: (i) constant noise level at the transducer face, and (ii) reverberation or volume backscatter from distributed targets in the water column. The former could be from vessel or ambient noise while reverberation could be from plankton or bubbles and suspended silt. Given a single target with constant TS and 20 or 40 log r TVG signal, noise and SNR range dependence are: TVG: 20 log r TVG: 40 log r SNR Signal ÿ20 log r Constant e i) Constant noise 20 log r C 2ar 40 log r C 2ar ÿ40 log r ÿ 2ar ii) Reverberation Constant 20 log r ÿ20 log r The last column confirms the earlier observation that the SNR is independent of the type of TVG used. Noise from the receiver front end will produce the same effect as a constant noise level at the transducer face. For a wellengineered echosounder internally generated receiver noise will generally be negligible compared to vessel and ambient noise, especially at operating frequencies below Figure 4. Redfish TS vs. depth measured with five different beam acceptance angles. At 250-m depth and from left to right TS lines use beam acceptance angles of 1.1, 1.6, 2.6, 3.6, and 4.4(. From Reynisson and Sigurdsson (1996).

5 Definition of signal-to-noise ratio and its role in split-beam measurements 127 angle is used. These effects are particularly evident below 220 m where the SNR presumably is a limiting factor. The increase in estimated TS with increasing beam acceptance angle is more traceable than the increase in TS with range as fish in a narrow depth band are more likely to be physically similar and have similar TS than fish from different depths. In addition, the effective SNR (SNRu) will certainly decrease with increasing beam angle while its decrease with range is less predictable. We will not pursue this example as measurements of the SNR are required to further explain, model, and quantify the observed TS bias and its dependence on the SNR. Work is in progress to do so, but is complicated by the fact that only echo-integration data with 1-m resolution rather than sample data with 0.1-m resolution are available. We note that the TS increase above 175-m depth is not explained by the fishing results that indicate constant fish size over the entire depth range. This is supported by trawling results from several acoustic surveys on the species in question (e.g. Magnusson et al., 1996). The increase may indicate changes in swimbladder volume or in tilt-angle distribution of the fish. The effect of these factors on target strength has been demonstrated by several authors (e.g. Nakken and Olsen, 1977; Blaxter and Batty, 1990). Effects of low SNR: target measurements and simulation of TS bias A series of split-beam target experiments was conducted in the Fraser River (Enzenhofer et al., 1998). The prevailing SNR was below 20 db which is not uncommon for riverine measurements. A split-beam angle measurement bias was observed, which was unexpected at the time and a splitbeam simulation model (Kieser et al., 2000) was developed that explained the significant bias that was observed under the prevailing low SNR. The model demonstrated that the split-beam angle measurement and the well-known TS bias become significant below similar SNR levels. We have expanded this model by including the SNR range dependence described above. The simulation uses the following echosounder parameters: beam width 7(, frequency 38 khz, a db m ÿ1, sound speed 1500 m s ÿ1,tsÿ30 db, TS threshold ÿ45 db and two-way beam-pattern threshold ÿ12 db (beam acceptance angles). Figure 2 yields an estimate of SNR db at the target range r m. Assuming constant target size and constant noise level at the transducer, the SNR range dependence is given by SNR(r) Z SNR 0 ÿ 40 log r/r 0 ÿ 2a(r ÿ r 0 ). With this the SNR drops from 33 db at 100-m to 14 db at 350-m range (Figure 5a). Pulsewidth is not included as it only enters the simulation indirectly through the SNR as a shorter pulse will require wider bandwidth and hence will admit more noise energy. Model results for the simulated SNR, the bias in the SNR, and the bias in TS are shown in Figure 5a, b, and c, respectively. Only targets that pass both the TS and twoway beam-pattern threshold are shown and used for the bias curves. SNR and TS are shown in db but calculations are done in physical units. Simulated TS vs. two-way beam pattern are shown in Figure 6a and b for target depths between 150 to 200 and 300 to 350 m, respectively. The results are summarized as: R SNR SNRbias TSbias TSbias ÿ where R is the mean range of the accepted targets, SNR is the SNR used by the simulation and SNRbias reflects the bias in the SNR that is estimated from the accepted targets. TSbias and TSbias2 give the TS bias that is estimated from all accepted targets and from those that have a two-way estimated beam pattern that is less than ÿ2 db. The bias columns indicate that measurements will tend to overestimate the SNR and TS. Significant bias is observed at SNR of less than 15 db, especially when targets from a far off-axis position are accepted. The bias in the estimated SNR is related to the well-known TS bias. It is larger than the TS bias as the TS calculations do not include the noise correction recommended earlier. The simulation model can be used to qualitatively and quantitatively explore the relation between SNR, TS, range, beam angle threshold, and other parameters. It may be used to understand a measurement of interest, to optimize measurement parameters and to possibly correct for SNR and TS bias. Good SNR measurements are a prerequisite, however. Consideration and measurement of the SNR can play an important role in developing good measurement practice and parameters and in identifying sources of measurement variability and bias. The SNR can make a significant contribution to optimize data quality and interpretation. Discussion and recommendations It is said that one person s signal is another person s noise. Generally noise can be defined as the unwanted part of the signal. Signal and noise occur at the same time and following optimal signal processing, remaining noise cannot be separated from the signal. Traditional fisheriesacoustic work focuses on the signal which may be the echo amplitude or power or the average volume-backscatter strength and it uses thresholding to eliminate noise. However noise and SNR are seldom measured. The SNR is a key quantity in any measurement and should therefore be monitored routinely to assure data quality. SNR measurements are particularly important when split-beam TS and target-position measurements are made under difficult conditions, such as at large range or on small

6 128 R. Kieser et al. Figure 5. SNR, SNR bias, and TS bias vs. range. a) The line gives the SNR that is used for the simulation and the points are from accepted targets only. Note the large scatter in the simulated values. b) SNR bias and c) TS-bias curves are from a polynomial fit to the corresponding values from the accepted targets. All calculations use physical rather than db values. targets. They also are required for modelling split-beam and other acoustic measurement processes (Ehrenberg, 1979; Kieser et al., 2000; Sawada and Furusawa, 2000; Sawada et al., 2002). The present paper stems from our earlier work that taught us that SNR measurements are required for meaningful comparison between target-position measurements and model results (Kieser et al., 2000). Although not discussed here we note that quantitative analyses require that signal and noise have well-defined statistical properties. It therefore will be important to measure signal and noise power and obtain at least some indication of their statistical properties. The model results presented here confirm the observed increase in TS bias with increased range or decreasing SNR and they highlight a corresponding bias in the measured SNR. Given good SNR measurements the split-beam model will provide a tool to optimize data-acquisition parameters and to predict and confirm data quality. In addition, it has the potential to provide corrections for SNR, TS, and other measured quantities when signal and noise are well defined. A tighter comparison between TS and other measurement and model results is desirable; however measurements from the same fish over a wide SNR will be required to conclusively compare measurement and model. This is difficult to achieve but measurements could be conducted at sea on an aggregation of single fish with different SNRs that are obtained by lowering the transducer, using different transducer beam width, changing transmit power (for nonreverberation noise only), or injecting a noise signal into the front end of the echosounder or into its digital data stream. Finally target tracking may be a useful tool to follow a fish through the beam and to relate observations to the SNR. Note that the SIMRAD EK500 can provide an absolute measurement of passive-noise power (SIMRAD, 1993; Takao and Furusawa, 1995). This is helpful in determining the minimum possible noise level for different sea conditions, water depths, vessel speeds, engine rpm, propeller pitch, etc. As it is an absolute measurement it can be used to monitor noise from a given vessel over long periods of time or to compare noise between vessels. However additional steps and a new mindset are required to readily measure the SNR from an active sonar. These include: (i) Detailed observation of noise on a standard echogram and on echograms with different thresholds and a review of TS vs. depth and TS vs. beam pattern and other plots. (ii) Quantitative observations begin with signal and noise measurements which are easily made on a few pings but routine measurements will require sophisticated software. (iii) Developers of commercial echosounders and post-processing software should encourage signal and noise measurements and their practical use by including noise measurements in their products. For example, STE

7 Definition of signal-to-noise ratio and its role in split-beam measurements 129 Figure 6. A plot of simulated TS vs. two-way beam pattern for a) 150 to 200 and b) 300 to 350-m range bins. data that now include TS, target location in the beam and depth should be complemented by noise estimates and data from windows on both sides of the echo peak, or just the latter alone, that can be used to estimate mean noise power and statistical properties. Capable and flexible instruments and software for fisheries-acoustic measurements and data analysis are available and should be used. Additional diagnostic tools for the estimation of TS bias, split-beam target detection probability, effective sampling volume (Foote, 1991), and other effects are needed. Many of these will require good SNR estimates to generate informative results and to provide possible corrections. The SNR will be a regular and rewarding topic in this context and we hope that this paper will encourage its routine measurement and use. Acknowledgements Seminal discussions and guidance from J. E. Ehrenberg and comments from R. B. Mitson and M. Furusawa are gratefully acknowledged. References Blaxter, J. H. S., and Batty, R. S Swimbladder behaviour and target strength. Rapports et Procès-Verbaux des Réunions Conseil International pour l Exploration de la Mer, 189: 233e244. Carlson, B Communication Systems: an Introduction to Signals and Noise in Electrical Communication. McGraw-Hill, New York. 495 pp. Clay, C. S., and Medwin, H Acoustical Oceanography: Principles and Applications. John Wiley & Sons, New York. 544 pp. Craig, R. E Units, symbols and definitions in fisheries acoustics. In Meeting on Acoustic Methods for the Estimation of Marine-Fish Populations, Cambridge, MA, USA, 25e29 June 1979, 2(a) pp. 23e32: Ed. by J. B. Suomala. The Charles Stark Draper Lab, Cambridge, MA, USA. Ehrenberg, J. E Effects of noise on in-situ fish target-strength measurements obtained with a dual-beam transducer system. Applied Physics Laboratory, University of Washington, APL- UW Ehrenberg, J. E A comparative analysis of in-situ methods for directly measuring the acoustic target strength of individual fish. IEEE Journal of Oceanic Engineering, OE-4(4): 141e152. Ehrenberg, J. E Analysis of split-beam, backscattering crosssection estimation and single-echo isolation techniques. Applied Physics Laboratory, University of Washington, APL-UW pp. Ehrenberg, J. E., and Weimer, R. T Effects of thresholds on the estimated fish-scattering cross-section obtained with a dualbeam transducer system. Applied Physics Laboratory, University of Washington, APL-8UW Enzenhofer, H. J., Olsen, N., and Mulligan, T. J Fixed-location riverine hydroacoustics as a method of enumerating migrating adult Pacific salmon: comparison of split-beam acoustics versus visual counting. Aquatic Living Resources, 11(2): 61e74. Foote, K. G Acoustic-sampling volume. Journal of the Acoustical Society of America, 90: 959e964. Foote, K. G., Knudsen, H. P., Vestnes, G., MacLennan, D. N., Simmonds, E. J Calibration of acoustic instruments for fish-density estimation: a practical guide. ICES Cooperative Research Report, (144):69 pp. Furusawa, M., Asami, T., and Hamada, E Detection range of echosounder. The 3rd JSPS International Seminar. Sustained Fishing Technology in Asia towards the 21st Century, p. 207e213. Furusawa, M., Takao, Y., Sawada, K., Oukubo, T., and Yamatani, K Versatile echosounding system using dual beam. Nippon Suisan Gakkaishi, 59(6): 967e980. Haykin, S Communication Systems. John Wiley & Sons, New York. 872 pp. Johannesson, K. A., and Mitson, R. B Fisheries acoustics. A practical manual for aquatic-biomass estimation FAO Fisheries Technical Paper, 240: 249 pp. Kafadar, K Gaussian white-noise generation for digitalsignal synthesis. IEEE Transactions on Instrumentation and Measurement, IM35(4): 492e495. Kieser, R Standard notation for the acoustic assessment of biological parameters. In Meeting on Acoustic Methods for the Estimation of Marine-Fish Populations, Cambridge, MA, USA, 25e29 June 1979, pp. 33e49. Ed. by J. B. Suomala. The Charles Stark Draper Lab, Cambridge, MA, USA. Kieser, R., Mulligan, T., and Ehrenberg, J Observation and explanation of systematic split-beam angle measurement errors. Aquatic Living Resources, 13(5): 275e281. Lyons, R. G Understanding Digital-Signal Processing. Prentice Hall. 517 pp. MacLennan, D. N., Fernandes, P. G., and Dalen, J A consistent approach to definitions and symbols in fisheries acoustics. ICES Journal of Marine Science, 59: 365e369. MacLennan, D. N., and Simmonds, E. J Fisheries acoustics. Fish and Fisheries Series. Chapman and Hall, London. 336 pp. Magnusson, J., Magnusson, J. V., Sigurdsson, Th., Reynisson, P., Hammer, C., Bethke, E., Pedchenko, A., Gavrilov, E., Melnikov,

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