sh_vol17_02(2)_1980.pdf (558.6Kb)

4 9 FickDir. Skr. Spr. H a v U n d ~ n . . 1 7 : 49-70.

ANGULAR MEASURES O F DORSAL ASPECT T A R G E T S T R E N G T H F U N C T I O N S O F FISH

By KENNETH G. Foo'rt:

Department of Appliecl hlathernatics, Ulliversity of Bergell

A B S T R A C T

FOOTE, K. G. 1980. Artgular measures of clorsal aspect target s t r e n g ~ h functions of fis11.FiskDir.

Skr. SPT. HnvUndcrs., 1 7 : 49-70.

T h r e e angular measures of clors;~l aspect target strength Putrc.tions in the pitch plane a r e computecl for previously gathered acoustic data o n tftrec gacloicl fishes, t\vo clupeoicl fishes,

;inel mackerel. These measures are rite angle of ntaxi~ntlrtl clorsal aspect ha( kscattel-ing cross section, the cetltral angle of the backscattering cross section, ancl the clisper-siolr of the cross section about rhe central angle. Each measure is regressetl linearly oil fish length. T h e statistical significances of the estimated regression coefficients a r e computeci. Syste~natic differences are attributed to fish anatomy: backscattering cross sections of the coilsidered s ~ v i ~ t l bladder- bearing fishes are concentr-atcci about negative tilt angles of several tiegree ntagni~ucle, \\.hich is attributeel to the inclination of the slvirn blaclcler axis. Backscattering cross sections of mackerel.

\vhich lacks a s\viin hlaclcler, are appi-oximatcly balanced about the horizontal.

I N T R O D U C T I O N

T h e general conlplexity of the orientation dependence of fish target strength functions o r backscatteriilg cross sections at ultrasonic frequencies is well known, cf. 1-efereilces in Fooai-. (1 979a). For purposes of iilterpreting the results of echo iiltegration (FORBES and N A K I ~ E N 1972), rather s i ~ n p l e relationships of target strength ancl fish length have been clerived. Two inethocls of cletermining this relationship have enlployed regression analy- sis. In one inethocl the clepenclei~t regression variable is a logarithmic measure of a special value of the backscattering cross section, e.g., maxi- nlunl clorsal aspect value (MIDTTUN and HOFF 1962, Y U D A X ~ V ^~t 01. 1966, NAKKEN and OLSEN 1977), inaxinlum near clorsal aspect value (McCAR-~NEY and STURRS 197 I ), ancl rnaximum side aspect value (Lovr;. 1969). In the other method the dependent variable is the same logarithmic measure of the average of the backscattering cross section ~vith respect to the geometric, acoustic, and behavioural circumstances of observation (FOOTE 1978, 1979a-c, 1980a). I n either case, if only through use of regression analysis to condense large quantities of' data to manageable proportions, as in the derivation of siinple target strength-to-lengtl~ relationships, much scat- tering inforn-tation is lost.

Some exanlples of other systenlatic scattering clepenclences of interest in

ac.oustic stritlies of' fish stoc.ks. ~\.hicl-i ailn ciirectl), ^01- inclirectly to inlprove abunciatlce estii~rittes, are mentioned: T h e probability density fi~nction of observeci effective scattering strerrgth of fish may facilitate classification ( F o o n 1979ci), as rtlay statistical rnor-rlenrs of echo energy from aggregatiolls ( F ~ X ~ E 198Ob). T h e effective acoustic sa~nplillg volume clepencls on the detailed scattering properties of fish ( F o o - r ~ 1979e), which is of sig~lificallce to the echo-c-ourlting nletllocl of assessing fish ahunclance (FORHI;S a11cl 9,-IKI\I..S 10'72). Car-rectiorl of echo integrator o r echo counter- cstilrlates of fish ahunctance clerivecl il-0111 rise of sector scatl~litlg sonars in the vertical plane, as in avoidance reaction strtdies, simiiarly depends o n the backscat- tering cross sectiorls of fish ( F o o - r ~ 1979e).

Several aciciitiortal exarnples of systetl~atic target strength clepenclences, which are also of use irt avoidance reaction studies (01-SEN 1979), are consid- ered in this paper. 'These are measures of the angular characteristics of the clorsal aspect target strength function in the pitch plane. 'Three quantities :ti-e consitlerecl: the angle of nlaxiirlurn backscattering cross section, the altglc of'inean co~lceiltl.ation of bat-kscattering cross section, and the clisper- sion of the hackst.;ittering cross section about this central angle. T h e length clepentiences of the several angulai- measures are clel-ived in this study for thl-ee gacloicl species, t ~ v o clupeoicl species, ancl mackerel, for 1vhic.h tneasu- I-enlents o f the clorsal aspect target strength functions at 38 and 120 k H z exist (N;\I<I<I:N ant1 0r.si.x 19'77, FOOTE itllci NAI<I<EK 1978). T h e statistical significances o f \;;trious systematic length clepe~~clences alrd lneans of the angular measures ax-e cliscusseci.

7 7

1 he source data for the computations of this scucly are the tabulatecl Ineasul.elxeI1ts of N.AKI<ES ; i i l ~ l OLSEX (1977) of the dorsal aspect target sti-e~lgth functions of six fishes at t ~ v o ultrasonic freclucncies (Foo'rt anel NAKKEK 1978). T h e number and representecl length ranges of the meas- ureci functions for each species and frequeircy are presented in Table 1.

Table 1 . Numbers ;ind ;~pplicahle length rangrs oi' measured dorsal aspcct target strength functions untlcr ;tnalvsis.

/

Data at 38 kHz

I

^{Data at 120 kHz}

Fish

1

^{I I I}

(:od (Gcrciur inoi-f~ucc) . . . . . . Saithe (Pollcirllizr r riir(~rii) . . . . . . . . . Poll;ick (Pollnihius pollcrrhirc,~) . . . . . Herring ((:liip~,rr hcirrilglis) . . . . Sprat (Sprcrit~ts .\p?r~t/ui) . . . Slac.kercl (Sroitihrr iroitrhi-uc) . . .

Number

44 6.7-67.0

48 I-). 1-68 0 39 19.7--52.0

30 8.7-32.4

24 6.6-1 7.6 24 2 9 . 7 4 1 .5 Lengtli rang?

(cm)

Number Ixngrh range (cm)

5 1

A characteristic measure of the dorsally sensed backscattering cross sec- tion is the pitch o r tilt airgle of maximuin backscattering cross section. This is defiliecl here for a particular backscattering cross section function n of tilt angle H by the foIlo\ving prescription:

o ( ~ , j = Max {a(@) for all 01, ₍₁₎

\\.here a, is the sought angle of maxitnuln backscattering cross section in the pitch plane.

T h e cetltral tilt angle of backscattering cross section is defined by the expressio~l

a , ⁼

J

^{0 u(@) (LO,}

-3214 ⁽²⁾

where a is the ~~ormalization factor,

This ~ n a k e s the likely assun~ption that, for the approximately fusiform fish of consideration, the backscattering cross section fu~lctioil is concentra- ted in the dorsal region of the pitch plane.

A measure of the dispersion in backscattering cross section about the central angle is the second c e ~ ~ t r a l moment of backscattering cross section,

T h e same assumption of approximate concentration of backscattering cross section in the dorsal region is also invoked here in the delimitation of the i~ltegration range.

Because the measurements of the dorsal aspect target strength functions

\\.ere made at one-degree intervals over the SO-degree range in tilt angles fro111 -45 to +4,5 deg, the integrals of Eqs. 2-4 are approximated by finite surnnlations. Extraction of the angle of maximum dorsal aspect backscat- terillg cross section, as in Eq. 1, is similarly approximate. In all computatiotls the length-to--\vavelength ratio is confinecl to the approximate range of 2 to 80, ~vhich 11iakes plausible the excellellce of the several approximations.

T h e several computed angular measures are regressed linearly o n fish length for similarly analyzecl scattering data of homogeneous species and frequency content accorcling to the linear expression

where a is a given characteristic a ~ i g u l a r measure expressed in degrees arid 1 is the fish length in centimetres. Estimates of the regression coefficients bo and bl , which are denoted by the respective circumflexed s y m b o l s ~ and 4 6, , are computed in accordance with the least squares criterion (WILKS 1962).

T h e corresponding standarcl errors of coefficients are computed.

T h e significances of the estimated coefficients a r e obtained from the t-statistic

where est[SE(6)] is the estimated standarcl error of regression coefficient estimate$. T h e number of degrees of freedom of the statistic, whether f o r &

o r FI, is N-2, where N is the number of independent data in each set. This number is specified in Table 1 . Significance levels corresponding to the t-statistics are also tabulated. T h e meaning of a n arbitrary significance level y , for example, is the following:

that is, the probability that the estimated regression coefficient 6 is non- vanishing is I-y. Thus the probability of wrongly rejecting the hypothesis that the regression coefficient essentially vanishes is 1-y. Small values of y therefore indicate likely non-vanishing values of the estimated regression coefficient.

A similar statistical analysis is carried out for the means of the several angular measures.

R E S U L T S

Computations of the three angular measures of dorsal aspect target strength functions are presented in Figs. 1-12. Each figure consists in a set of three scatter diagrams of the several angular measures on fish length.

T h e corresponding least squares linear regressions are shown. Statistical analyses of these regressions and of the mean angular measures are presen- ted in Tables 2 4 , which are discriminated by type of angular measure.

D I S C U S S I O N

T h e main characteristics of the angle measure data presentecl in Figs.

1-12 are the lack of a trend in the maximum and central angles of the backscattering cross section, but general negativity of the same measures in the mean, and a slight upwards trend of the dispersion angle with increasing fish length. These observations are confirmed by inspection of Tables 2 - 4 .

FOR 68 C O D L R T 3 8 KHZ

10

2 0

CENTRRL RNGLE OF B R C K S C R T T E R I N G CROSS S E C T I O N FOR 68 COO RT 3 8 KHZ

3 0 I

D I S P E R S I O N RNGLE OF BRCKSCRTTERING CROSS S E C T I O N FOR 65 COD RT 3 8 K H z

0 2 0 4 0 6 0 8 0 1 0 0

L E N G T H 1 C M 1

Fig. 1. Characteristic angular measures of measured dorsal aspect target strength functions of 68 cod at 38 kHz.

FOR 4 4 COO RT 1 2 0 K H Z

2 0

CENTRRL RNGLE OF B R C H S C R T T E R I N G CROSS

FOR 4 4 COO R T 1 2 0 K H z

3 0 ^I

D I S P E R S I O N ANGLE OF B R C K S C R T T E R I N G CROSS S E C T I O N FOR 4 4 COO AT 1 2 0 K H Z

Fig. 2. Characteristic angular measures of measured dorsal aspect target strength functions of 44 cod at 120 kHz.

20

R N G L E OF n R X I t i U N B R C K S C R T T E R I N G C R O S S F O R 5 9 S R I T H E R T 3 8 K H Z

2 0 - ^I

C E N T R R L R N G L E O F B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 5 9 S R I T H E R T 3 8 K H Z

3 0

D I S P E R S I O N R N G L E O F R R C K S C R T T E R I N G C R O S S S E C T I O N F O R 5 9 S R I T H E R T 3 8 K H Z

Fig. 3. Characteristic angular measures of measurecl dorsal aspect target strength functioils of .39 saithe at 38 kHz.

20

R N G L E O F N R X I V U M B R C K S C R T T E R I q G C R O S S S E C T I O N F O R 4 % S R I T H E R T 1 2 0 H H Z

7 1 ,

C E N T R R L R N G L E OF B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 4 8 S R I T H E R T 1 2 0 K H Z

D I S P E R S I O N R N G L E OF B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 4 8 S R I T H E R T 1 2 0 KH?

01 20 4 0 6 0 8 0 10

LENGTHL C P l l

Fig. 4. Characteristic angular measures of measured dorsal aspect target strength functions of 48 saithe at 120 kHz.

R N G L E O F n R x l n u n ~ R C K S C R T T E R I N G C R O S S S E C T I O N F O R 4 4 P O L L R C K A T 38 K H Z

A

2 0

C E N T R R L R N G L E OF B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 44 P O L L R C K R T 38 K H z

3 0 I

D I S P E R S I O N R N G L E OF B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 4 4 P O L L R C K R T 38 K H Z

A

0 1 I

2 0 4 0 6 0 8 0 100

L E N G T H ( C M 1

Fig. 5. Charac~eristic angular measures of measured dorsal aspect target strength functions of 44 pollack at 38 kHz.

I

R N G L E O F MRXIPIUM B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 39 P O L L R C K A T 1 2 0 K H Z

C E N T R R L R N G L E O F B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 3 9 P O L L R C K R T 1 2 0 K H Z

3 0 I

O I S P E R S I O N R N G L E O F B R C K S C R T T E R I t d G C R O S S S E C T I O N F O R 39 P O L L R C K R T 1 2 0 K H Z

Fig. 6. Characteristic angular measures of measured clorsal aspect target strength fntlctions of 39 pollack at 120 kHz.

20

-

^I

RNGLE OF M R X I N U M B R C K S C R T T E R I N G CROSS S E C T I O N A FOR 25 H E R R I N G RT 38 K H Z

F O R 25 H E R R I N G RT 38 KHZ

-

10

I

O I S P E R S I O N RNGLE OF B R C K S C R T T E R I N G CROSS S E C T I O N FOR 25 H E R R I N G R T 38 K H Z

0 2 0 40 6 0 8 0 100

LENGTH[ CP( I

Fig. 7. Characteristic angular measures of measured dorsal aspect target strength functions of 25 herring at 38 kHz.

20

RNGL; 0: n R x I n u n 'BAcnscRrTER;NG C R O S S sE;rIoN F O R 3 0 H E R R I N G A T 120 K H Z

2 0

-

C E N T R R L R N G L E OF B R C K S C R T T E R I N G C R O S S S E C T I O N F O R 3 0 H E R R I N G R T 1 2 0 K H Z

I

D I S P E R S I O N Q N G L E O F B R C K S C Q T T E R I N G C R O S S S E C T I O N F O R 3 0 H E R R I N G R T 1 2 0 K H z

'

--1

Fig. 8. Characteristic angular measures of measured dorsal aspect target strength functions of 30 herring at 120 kHz.

20.

R N G L E OF nRxrntin E R C K S C R T T E R I N G CROSS S E C T I O N FOR 21 SPRRT RT 38 KHZ

2 0

CEMTRRL RNGLE OF BRCKSCRTTERING CROSS SECTION FOR 21 SPRRT RT 38 K H z

3 0 I

DISPERSION RNCLE OF BRCKSCRTTERINC C R O S S SECTION FOR 21 SPRAT RT 38 K H Z

I.

Fig. 9. Characteristic angular measures of measured dorsal aspect target strength functions of 2 1 sprat at 38 kHz.

2 0

FOR 2 4 SPRRT R T 1 2 0 KHZ

2 0 I

CENTRRL RNGLE OF B R C K S C R T T E R I N C CROSS S E C T I O N FOR 2 4 SPRRT R T 1 2 0 KHZ

3 0 ^I

D I S P E R S I O N RNGLE OF B R C K S C R T T E R I N C CROSS S E C T I O N FOR 2 4 SPRRT R T 1 2 0 KHZ

S

I

0 1 I

2 0 40 6 0 5 0 100

L E N G T H I C f l I

Fig. 10. Characteristic angular measures of measured dorsal aspect target strength fi~nctions of 24 sprat at 120 kHz.

I

RNGLE OF P~RXINUM%PCKSCRTTERING CROSS S E C T I O N FOR 3 5 MRCKEREL RT 38 K H z

CEMTRRL RNGLE OF BRCKSCRT.IERING CROSS S E C T I O N FOR 35 MRCKEREL RT 38 KHZ

3 0 I

D I S P E R S I O N RNGLE B i B K K S C R T T E R I N G CROSS S E C T I O N FOR 3 5 NRCKEREL RT 38 KHZ

Fig. I 1. Characteristic angulat- measures of tueasured dorsal aspect target strength functions of 35 mackcrel at 38 kHz.

RNGLE OF R R X I t I U M B R C K S C R T T E R I N G CROSS S E C T I O N FOR 2 4 N R C K E R E L R T 1 2 0 K H z

CENTRRL RNGLE OF B R C K S C R T T E R I N G CROSS S E C T I O N FOR N R C K E R E L R T 120 KHz

A A A

A A A

A A

O I S P E R S I O N RNGLE OF B R C K S C R T T E R I N G CROSS S E C T I O N FOR 2 4 MRCKEREL R T 1 2 0 K H z

A

@A.

* A

A A A A

A A

Fig. 12. Characteristic angular measures of nieasurecl clol-sal aspect target strength fulictions of 24 mackerel at 120 kHz.

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u3u3c4&*-GWm---

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mm mmazm+mamr- 9': TL?""""

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ommi.-r-r-r-mmm~t- "qL?l:"?vy"q"- -m-~C-00-000 I I I I I I I I

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mz*mma~g&~~~ 0 0000 000000000000 I I I I I I I I

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-

000-00000-00 v v

am~~m-mmoe,mmm 9""9=?"?"=?':"" m 0 m

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8

w^ ~+o-omomwa~': .e

s

Yl r .IT?q?-:w?".Imm --oom-*mlm-mm

2

r

a2 m*mm-mum-mo*, ':"~"o-d"oq~~~ m~ommm-ammar-r- IIIIIIIIII

>,

r& 2 momomomomomo mzmzmzm~mzmz

,..,... ,..,... ,... . ,... ,... ... . ,... . ,... ,... ... ... .... mm:

:TT

. . , , w

w+*.s.s

. .aJ cc mm L;ij';;YY

zz.z.j'=,a

oGmmaaZZmmBE b b

kh%

2

Table 3 . Regression coefficients and mean. with statistical analyses. of a,. the central angle of the dorsal aspect backscattering cross section in the pitch plane .

I I

Regression coefficient b,

I

Regression coefficient

I

^{Mean al}

Cod . . . Cod . . . . . . Saithe

Saithe . . . Pollack . . . . . . Pollack

Herring . . . . . . Herring

Sprat . . . Sprat . . . Mackerel . . . Mackerel . . .

Fish Frequency

(kHz) est est(SE) t Y est est(SE) t Y est est(SE) t Y

-Table 4. Regression coefficients a n d mean, with statistical analyses, of a,, the angular dispersion of the backscattering cross section about the central angle in the pitch plane.

Cod . . . . . . . . . . . 38

Cod . . . . . . . . . . . 120

Saithe . . . . . . 38 Saithe . . . . . . . . . . . 120 Pollack . . . . . . 3 8 Pollack . . . . . . . . 120 Herring . . . . . . 3 8 Herring . . . . . . 120 Sprat . . . . . . . . . . 3 8 Sprat . . . . . . . . . . 120 Mackerel . . . . . 38 Mackerel . . . . . . 120

Fish Frequency

(kHz)

Regression coefficient b, Regression coefficient b, Mean a,

est -

est est(SE) t Y est ^est(SE) t Y est(SE) ^t Y

They are I-epreseiltetl f~tl-thel- by tile conciensations o f results pr-esentecl in Tables 5 atltl 6.

I n T a l ~ l e .? the I-egt-ession coefficients a n d means of the several angle measures are classifiecl by their consisteilcy with one of t\\-o hypotheses. T h e null hypothesis N o asserts the identity o r indistinguishability of the cluanti- ties with zero. T h e alternative hypothesis HA denies this, asserting the non- vanishing natul-e of tile quantities. 'l'lre criterion fcoi- classificatioli is that the significance level y shall exceed 0.05 to upholcl H o ancl be less than 0.05 to s ~ ~ p p o r t H A .

Table 3 . Kunibers of regression coefficients ancl liie;xtis of aliglc measures consiste~it ~ v i t h thc null o r alternative hypotl~rses at thc 0.05 level.

Tablc 6. Discri~uination of regression coefficients and nicalis of angle rileasures by their sigris.

T h e lack of a trencl in the ~ n a x i m u m ancl central angles is eviclent from the results fox the regression slope coefficient 0, in 'Table 5 . T h e null hypothesis is stl-ongly uphelcl. Simple application of the b i ~ ~ o m i a l test attaches a confi- dence level of 0.997 to the cotlsistelicy of b, ~ \ - i t h zero in the case of aO ancl a c-onficlenc-e of 0.98 in the case of a , .

T h e salrle t ~ v o angle measul-es a r e gellerally negative, however, as indica- tecl by the sign analyses of Table 6. T h e negative character of maximum a n d centl-a1 angle measures is evident from the results for the mean angle

Angle measure

sgll&1)

+

^-

sggn&, ) sgn(ii)

+

^-

+

^-

rneasure??. Siinilar results for the regression intercept coef'ficieilt bo support this conclusioil. T h e single exceptional datum for

a

in Table 6 is that for

-k ^> - 1

a t c~ t l a t 120 kHz. Given the general up~iarcls i~lclination, it1 the tail-to- heacl clirectiou, of the gatloid ailel clupeoitl s\iim bladder, .ivhich is probably the clominant scattei-ing o 1 - p n of these fishes, airti the absence of a s ~ i i ~ n blaclcle~ in mackerel, it seeins reasonable to clistinguish the clata by the pi-esence o r absei~cc of a s~vim blaclcler. That the angles of maximum ant1 ceiltral backsciittering cl-oss section are slightly negative, in the mean, for each no11-mackerel fish, but apparently vanishing in the case of inackci-el, may be regarded as a direct acoustical consequence of the described anatom- ical difference. A11 early observatioll of the acoustic nlanifestatioll of s~virn blaclcler incliilatio~i ~ i i t h respect to the imaginary fish centerliiie, to ~vhic.11 the s.iiim hlaclcler axis is referred, iias lllacle by MIII-r-1-c~ and I-IOFF ( 1 962).

T h e intrinsically positive character of'the dispersion angle a, is confil-med by the sign analysis of

Zi

i l l Table 6. This is suppoi-tecl b ~ r the positive regression intercept coeffic-ient r\ Oo. T h e up~vards treilcl of's;, is observecl in the positive regression slope coeff'icient 0 , in T;ibIe 6, although not in the 4

inore stringent, brtt n.eaker analysis of Table 3. T h e physical interpretation of the iilcreasillg ti-encl of nlean tlispei-sion angle ~ i i t h ilicl-easing fish length is that tile t1ors;tl aspect hackscatterii~g cross sect ion oi- target stt-ength in the pitc-h plane terltls to be less concentl-atecl as fish length illcreases. This conclusion appears plausible fi-om inspection of the source clata FOOT^ ant1 N.AI<I<EN 1978), although the n~agilitutle of the length clepellclc~~ce o f ' c x 2 is not easil\ cliscel lieel fi o m the datd 111 this form

Ylfeasures of the angular characteristics of target strength futlctions ;is computetl iii this paper clo not seer11 t o have beell previousl~. consiclerecl.

T h e priiicipal ~tsefulrless of the coinputat ions is espectetl to lie in c o ~ ~ s i t l e r a - tioils of the sori aclt~anc-etl in (>LSFS ( 1 979). Colnput;ltioils ofangle ~rlvasures cannot, I-to~iever, supplant such measures of fish scattering strength as those coi~siderecf in FOOTF. ( 1978, 1979a-e, 1980a). These averaged measures of effective hackscattering strength are essential to cluantitative stuclies of fish abundance, whether assessed by typical echo sou~lclei-s o r by sector scailnillg

KEFk:KE.S(:I:.S

FOC)TF., K. C . 1078. Effect o f f i s h heh;lvio~u- o n e c h o e n c r g r : t h e ncccl f ; ) ~ - nle;k5urc.1riclirs of o r i e ~ ~ t a t i i , ~ i clistrihntions. J. (:o~i.t. ill/, E-cl,/o~. .Mrr, 3 9 12). (111 press.)

F i ~ o ~ f . I<. G . iY7Cia. Systcii~;iti( \pccic\ i i ~ i c i ~ I - ( Y ~ ~ I ~ I I C J ~ i c p ~ ~ ~ i c i c i i t c l i f f c ~ . c ~ ~ ( c~ ~ I I ~ I I I I ~ gacloicl tnrgct stl.eng-rh f ' ~ i i i c tions. . l l i ~ r / i ~ i g or? I~~elroccci~~ettrrctl 111vtho11t / o f - t h ~ ct/i~rrrc/~cii~ of I I ~ ~ I - ~ I I ~ , frth poi)l~lntio~rc. ( : o I I I / I I - ~ I ~ ~ I ~ . .\lnttcr~h~ctc~/~c, Jnrrc 1979. (,c~litl-ihirtio~l no. 8: 1-22. [ \ l i n i c c ~ . j

Foo-I-F, I<. C;. Ic)7!)h. O n r e p ~ - e \ e i ~ t i n g the Ictigtli t l e p e n c l e ~ ~ c c of';~cc,tl\tic target srl.engrlis o t fi\h.

1 . Eitll. Rrc. Bonrcl C ~ I I I . . 3 6 : ILOO-l4!)(i.

FOOTE, K. G. 197%. Fish target s~rength-to-length regressions for application in fisheries research. Pp. 327-332 in ANON. eri. U1trasorzic.s Irzf~rr7otionrcl 7 9 Co17f. Pl-or. IPC: Sci.

a n d Tech. Press, Guilclforcl, Englantl.

FOOTE, K. G. 1979d. Simulation of distributions of observed effective scattering strengths of individual fish. J. Acowt. Soc. Am., 6 5 : S88 (A).

FOOTE, K. G. 1979e. Biasing of fish abu~ldance estimates derived from use of the sector sca~lnitlg sonar in the vertical plane. Pp. 44-52 in ANON. ecl. Progrr~ss in sector s m n ~ z i n g SOIZUT, C O ~ J Proc. Loior~st(?ft, D ~ r ~ r n b ~ r 1 9 7 9 .

FOOTE, I<. G. 1980a. Averagingof fish rarget strength functions:]. Arolut. Soc. Ana. 6 7 : 504-5 15.

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Received 3 1 October 1979 PI-intecl 2 J L I I I ~ 1980