Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Quantitative measurements of marine acoustic scattering from zooplanktonic organisms Beamish, Peter 1969

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1969_A1 B43.pdf [ 5.25MB ]
Metadata
JSON: 831-1.0084751.json
JSON-LD: 831-1.0084751-ld.json
RDF/XML (Pretty): 831-1.0084751-rdf.xml
RDF/JSON: 831-1.0084751-rdf.json
Turtle: 831-1.0084751-turtle.txt
N-Triples: 831-1.0084751-rdf-ntriples.txt
Original Record: 831-1.0084751-source.json
Full Text
831-1.0084751-fulltext.txt
Citation
831-1.0084751.ris

Full Text

QUANTITATIVE MEASUREMENTS OF MARINE ACOUSTIC SCATTERING FROM ZOOPLANKTONIC ORGANISMS by PETER CHARLES BEAMISH B . A . S c , U n i v e r s i t y o f T o r o n t o , 1962 S.M., M a s s a c h u s e t t s I n s t i t u t e o f Technology, 196 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department of PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1969 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for, r e f e r e n c e and Study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f PHYSICS The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date: J a n u a r y 196 9 ABSTRACT The purposes o f t h i s r e s e a r c h have been t o d e t e r m i n e a) t h e b a s i c p h y s i c a l causes o f a c o u s t i c s c a t t e r i n g from z o o p l a n k t o n i c organisms and b) n e c e s s a r y c r i t e r i a f o r f u t u r e a c o u s t i c s t u d i e s i n v o l v i n g t h e s e a n i m a l s . I n s i t u measurements a t 102 kHz have been made o f t h e s c a t t e r i n g o f sound from a v o l u m e t r i c d i s t r i b u t i o n o f a z o o p l a n k t o n i c o r g a n i s m , t h e e u p h a u s i i d . Q u a n t i t a t i v e i n f o r m a t i o n was r e c o r d e d on a n a l o g magnetic t a p e and s u b s e q u e n t l y c o n v e r t e d t o d i g i t a l form f o r a n a l y s i s . Based on s i m u l t a n e o u s measurements o f s i d e and back s c a t t e r i n g from e u p h a u s i i d s and on a m a t h e m a t i c a l model, f o u r - f i f t h s o f t h e s c a t t e r e d sound i s c o n s i d e r e d t o be caused by t h e c o m p r e s s i b i l i t y c o n t r a s t between the a n i m a l s and t h e sea w a t e r . The r e m a i n i n g o n e - f i f t h i s a t t r i b u t e d t o d e n s i t y c o n t r a s t . A c o u s t i c energy d i s t r i b u t i o n c u r v e s a r e c h a r a c t e r i s t i c o f t h e number and s i z e o f t h e a n i m a l s c o n t a i n e d i n t h e s m a l l volume of t h e ocean t h a t was s t u d i e d . A c o u s t i c c o u n t i n g of t h e a n i m a l s gave r e s u l t s t h a t compared f a v o u r a b l y w i t h s i m u l t a n e o u s c o n t r o l l e d n e t s a m p l i n g . The back s c a t t e r i n g c r o s s - s e c t i o n o f a t y p i c a l -4 2 e u p h a u s i i d a t 102 kHz has been found t o be 1.4 x 10 cm . Based on t h i s v a l u e i t i s p o s s i b l e t o p r e d i c t t h e optimum f r e q u e n c y and i n t e n s i t y o f i n c i d e n t sound f o r f u t u r e a c o u s t i c s t u d i e s i n v o l v i n g t h e s e a n i m a l s . TABLE OF CONTENTS PAGE ABSTRACT i i i TABLE OF CONTENTS i v LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS i x CHAPTER I . INTRODUCTION . 1 Statement o f t h e Problem 1 Importance o f t h e Study 2 Resume o f t h e H i s t o r y 2 E a r l y o b s e r v a t i o n s o f sound s c a t t e r i n g by marine organisms 2 Resonant s c a t t e r i n g 3 Recent o b s e r v a t i o n s o f p l a n k t o n s c a t t e r i n g ... 4 T h e o r e t i c a l s t u d i e s r e l a t i n g t o p l a n k t o n s c a t t e r i n g . . ; 5 E x p e r i m e n t a l s t u d i e s r e l a t i n g t o p l a n k t o n s c a t t e r i n g 5 O u t l i n e o f t h e T h e s i s 6 I I . THEORETICAL DISCUSSION 8 The S c a t t e r i n g o f Sound from a F l u i d Sphere .... 8 I n t r o d u c t i o n 8 The problem 9 The g e n e r a l s o l u t i o n 11 The E n c a s i n g o f a Sphere i n a T h i n E l a s t i c S h e l l 13 Sound S c a t t e r i n g from B i o l o g i c a l Organisms 14 V CHAPTER PAGE I I I . EXPERIMENTAL METHODS 16 Sea-going A p p a r a t u s 16 A c o u s t i c System 18 Location o f Experiment 24 C r u i s e D e s c r i p t i o n s 25 C a l i b r a t i o n 27 IV. DATA ANALYSIS 29 Data D e s c r i p t i o n 29 A n a l y s i s A p p a r a t u s 30 A n a l o g A n a l y s i s 32 D i g i t a l A n a l y s i s 34 Volume A n a l y s i s 34 V. RESULTS AND CONCLUSIONS 36 R e s u l t s 3 6 C o n c l u s i o n s 46 BIBLIOGRAPHY 50 APPENDICES APPENDIX I . SOUND SCATTERING FROM A FLUID SPHERE: THE SOLUTION OF SCHOCH 52 I I . ACOUSTIC ENERGIES FROM ADDED SPHERES 53 v i APPENDIX PAGE I I I . COMPUTER STUDIES OF BIOLOGICAL SCATTERING 56 I n t r o d u c t i o n 56 The Number o f S i g n i f i c a n t Spheres 56 The I n f l u e n c e o f S i z e o f Spheres 57 The I n f l u e n c e o f V e r t i c a l O r i e n t a t i o n 57 IV. FORTRAN IV PROGRAMS RELATING TO THEORETICAL STUDIES 58 V. ACOUSTIC OUTPUT AND RECEIVER SYSTEMS 67 V I . RECORDING AND MONITORING SYSTEMS 70 V I I . REPRODUCE AND ANALOG SYSTEMS 71 V I I I . A/D CONVERSION AND DIGITAL PROCESSING SYSTEMS .. 73 IX. FORTRAN IV PROGRAMS RELATING TO DATA ANALYSIS .. 76 X. VOLUME ANALYSIS FOR ISOTROPIC SCATTERING 85 X I . VOLUME ANALYSIS FOR COSINE SCATTERING 86 X I I . RESULTS 87 X I I I . ERROR ANALYSIS 88 v i i LIST OF TABLES TABLE PAGE I . Energy R a t i o s and A u x i l l i a r y Data 37 I I . D i g i t a l and A n a l o g Tape L i s t i n g s 87 v i i i LIST OF FIGURES FIGURE PAGE 1. The E u p h a u s i i d 14 2. B l o c k Diagram o f Sea-going A p p a r a t u s . 17 3. A p p a r a t u s 19 4. L o b a l P a t t e r n s , A t t e n u a t i o n Contours f o r Lower Hydrophone and Ap p a r a t u s i n t h e X - Z P l a n e .... 20 5. L o b a l P a t t e r n s and A t t e n u a t i o n Contours f o r Upper Hydrophone i n t h e X - Z P l a n e 22 6. L o b a l P a t t e r n s and A t t e n u a t i o n C o n t o u r s f o r Lower Hydrophone i n t h e Y - Z P l a n e . 23 7. L o c a t i o n o f t h e Experiment 26 8. B l o c k Diagram o f A n a l y s i s A p p a r a t u s 31 9. S i g n a l Photographs 33 10. D i s t r i b u t i o n Curves f o r Data U n i t s 1 and 2 39 11. D i s t r i b u t i o n Curves f o r Data U n i t s 3 and 4 40 12. D i s t r i b u t i o n Curves f o r Data U n i t s 5 and 6 41 13. D i s t r i b u t i o n Curves f o r Data U n i t s 7 and 8 42 14. D i s t r i b u t i o n Curves f o r Data U n i t s 9 and 10 .... 43 15. G r a p h i c a l Sounding Records 45 16. A c o u s t i c E n e r g i e s from Added Spheres 53 17. Schematic o f A n a l o g Network 72 ACKNOWLEDGMENTS The author wishes to express s i n c e r e thanks to Dr. R.W. Stewart and Dr. B.McK. Bary who have given guidance and encouragement during t h i s research. Grat i t u d e i s a l s o expressed to the c a p t a i n s , o f f i c e r s and men of the C.N.A.V. Endeavour, the C.S.S. Vector and the H.M.C.S. Miramachi. S p e c i a l thanks are expressed to W.E. Barraclough and R. Pieper who have helped w i t h b i o l o g i c a l aspects, to R. Wilson f o r computing a s s i s t a n c e , to D. Hume f o r the photographs i n f i g u r e 3 and to the many f a c u l t y , students and s t a f f who have aided w i t h the experimental program. CHAPTER I INTRODUCTION I. STATEMENT OF THE PROBLEM For many years a c o u s t i c echoes have been obtained from b i o l o g i c a l organisms i n the sea. Often-some or a l l of these echoes were considered to be caused by a c o u s t i c s c a t t e r i n g from zooplanktonic organisms. The main purpose of t h i s study has been to determine the b a s i c p h y s i c a l causes of echoes from zooplanktonic organisms. A second purpose has been to be able to e s t a b l i s h necessary c r i t e r i a f o r fu t u r e a c o u s t i c s t u d i e s i n v o l v i n g these animals. The phenomenon of s c a t t e r i n g occurs because some of the p h y s i c a l p r o p e r t i e s of the s c a t t e r e r s are d i f f e r e n t from the corresponding p r o p e r t i e s of the surrounding medium. For a c o u s t i c s c a t t e r i n g from zooplanktonic organisms i n the ocean, the s c a t t e r e r s have an a c o u s t i c impedance c o n t r a s t w i t h the f l u i d medium. This c o n t r a s t , i n i t s b a s i c form, c o n s i s t s of a d i f f e r e n c e i n c o m p r e s s i b i l i t y (the f r a c t i o n a l change i n volume per u n i t p r e s s u r e ) , a d i f f e r e n c e i n d e n s i t y , or a combination of both f a c t o r s . The primary purpose of t h i s study was to determine the degree to which these f a c t o r s c o n t r i b u t e to plankton echoes. Furthermore i t becomes p o s s i b l e to p r e d i c t the s c a t t e r i n g strength of 2 z o o p l a n k t o n i c organisms as a f u n c t i o n o f t h e i r s i z e and of t h e f r e q u e n c y o f t h e i n c i d e n t sound and t h e r e b y t o p r e d i c t t h e optimum f r e q u e n c y and i n t e n s i t y o f i n c i d e n t sound f o r f u t u r e a c o u s t i c s t u d i e s o f t h e s e a n i m a l s . I I . IMPORTANCE OF THE STUDY A c o u s t i c s c a t t e r i n g by b i o l o g i c a l organisms i n t h e ocean i s o f imp o r t a n c e i n the f i e l d o f sound n a v i g a t i o n and r a n g i n g (SONAR). I t i s a l s o i m p o r t a n t f o r i n v e s t i g a t i o n o f t h e d i s t r i b u t i o n , i d e n t i f i c a t i o n and b e h a v i o u r o f t h e marine a n i m a l s . T h i s s t u d y has l e d t o q u a n t i t a t i v e knowledge o f the p h y s i c a l p r o c e s s e s w h i c h cause s c a t t e r i n g from a p a r t i c u l a r z o o p l a n k t o n i c o r g a n i s m , t h e e u p h a u s i i d . Data o b t a i n e d a r e c o n s i d e r e d t o have a b e a r i n g on t h e d e s i g n o f f u t u r e e x p e r i m e n t s i n v o l v i n g t h e s e and s i m i l a r a n i m a l s . The main i m p o r t a n c e , however, i s t h e e x p a n s i o n o f e m p i r i c a l knowledge r e g a r d i n g the fundamental p h y s i c a l p r o c e s s e s o c c u r r i n g d u r i n g a c o u s t i c s c a t t e r i n g from z o o p l a n k t o n i c organisms i n t h e s e a . I I I . RESUME OF THE HISTORY E a r l y o b s e r v a t i o n s o f sound s c a t t e r i n g by marine  organisms. The s t u d y o f sound s c a t t e r i n g by marine organisms began about 1930, m a i n l y i n B r i t a i n and Norway. 3 F o l l o w i n g t h e r a p i d development o f a c o u s t i c e c h o - r a n g i n g d e v i c e s , f o r i c e b e r g d e t e c t i o n a f t e r t h e T i t a n i c d i s a s t e r and f o r submarine d e t e c t i o n d u r i n g World War I , a number o f f i s h i n g t r a w l e r s were equipped w i t h such d e v i c e s , i n a r d e n t a n t i c i p a t i o n o f i n c r e a s i n g t h e i r c a t c h . More t h a n a decade passed b e f o r e a s e r i o u s s t u d y began c o n c e r n i n g t h e i n t r i g u i n g phenomenon of v e r t i c a l d i u r n a l m i g r a t i o n . S c a t t e r i n g l a y e r s moved upwards toward th e s u r f a c e a t s u n s e t and downwards from th e s u r f a c e a t dawn. These l a y e r s t h e r e f o r e , had a d i s t i n c t l y b i o l o g i c a l c h a r a c t e r ; t h e y have s i n c e been found t h r o u g h o u t the w o r l d ' s oceans. F o r a d e s c r i p t i o n o f t h e e a r l y h i s t o r y and o t h e r a s p e c t s o f a c o u s t i c s c a t t e r i n g by marine o r g a n i s m s , t h e r e a d e r i s r e f e r r e d t o Hersey and Backus (1962). Resonant s c a t t e r i n g . I n 1952, Hersey, Johnson and D a v i s r e p o r t e d t h a t r e v e r b e r a t i o n from deep s c a t t e r i n g l a y e r s was s t r o n g l y frequency-dependent. Many o b s e r v a t i o n s have been made o f t h e sudden appearance o r d i s a p p e a r a n c e o f m i g r a t i n g l a y e r s on t h e r e c o r d i n g s o f s i n g l e f r e q u e n c y sounding d e v i c e s . These o b s e r v a t i o n s s uggest t h a t t h e a b i l i t y t o d e t e c t some l a y e r s a c o u s t i c a l l y may be a r e s u l t o f a resonance phenomenon. The resonance i s c o n s i d e r e d t o be a s s o c i a t e d w i t h t h e a c o u s t i c response o f g a s - f i l l e d s wim-bladders o f f i s h (Hersey and Backus 1954, Andreeva 1964). S i n c e 1952, a g r e a t many s t u d i e s have been made i n v o l v i n g 4 a c o u s t i c s c a t t e r i n g from f i s h , b o t h i n t h e ocean and i n t a n k s . Most o f t h e s e e x p e r i m e n t s have been c a r r i e d o u t a t s o n i c f r e q u e n c i e s i n t h e v i c i n i t y o f 12 kHz. What con c e r n s us i s t h a t some i n t e r p r e t a t i o n s o f e x p e r i m e n t s c a r r i e d o u t a t t h e s e f r e q u e n c i e s a t t r i b u t e p a r t o r a l l o f t h e r e c e i v e d s c a t t e r e d sound t o z o o p l a n k t o n i c o r g anisms. Recent o b s e r v a t i o n s o f p l a n k t o n s c a t t e r i n g . Bary (1966) r e p o r t e d t h a t t h e r e was no c o n s i s t e n t r e l a t i o n s h i p found between t h e biomass,.or between the numbers o f z o o p l a n k t o n i c o r g a n i s m s , and mid-water s c a t t e r i n g r e c o r d e d a t 12 kHz i n S a a n i c h I n l e t , B r i t i s h Columbia. He t h u s c o n c l u d e d t h a t i t was p r o b a b l e " t h a t z o o p l a n k t o n organisms of l e n g t h s up t o about 2 cm were not c a u s i n g back s c a t t e r i n g o f t h e 12 k c / s p u l s e s o f s u f f i c i e n t i n t e n s i t y t o be r e c o r d e d " . Barham (1966) has r e p o r t e d t h a t t h e r e was no s p a t i a l r e l a t i o n s h i p between 12 kHz soundings and e u p h a u s i i d s t h a t were ob s e r v e d from a d i v i n g s a u c e r . S i n c e 1966, echo-soundings have been made i n S a a n i c h I n l e t u s i n g 44 kHz, 108 kHz and 197 kHz (Bary, p e r s o n a l communication). Data o b t a i n e d by Bary suggest t h a t z o o p l a n k t o n i c organisms o f l e n g t h s up t o about 2 cm p r o b a b l y cause back s c a t t e r i n g o f s u f f i c i e n t i n t e n s i t y t o be r e c o r d e d a t t h e h i g h e r f r e q u e n c i e s . S u p p o r t i n g e v i d e n c e was p r o v i d e d i n August 1967, when an echo was r e c o r d e d from a l i v i n g e u p h a u s i i d ( l e n g t h about 2 cm) a t 102 kHz, i n a f r e s h water tank a t t h e I n s t i t u t e o f Oceanography, U n i v e r s i t y o f B r i t i s h C o l umbia. T h e o r e t i c a l s t u d i e s r e l a t i n g t o p l a n k t o n s c a t t e r i n g . Two decades a f t e r t h e f i r s t s t u d i e s o f sound s c a t t e r i n g by marine o r g a n i s m s , Anderson (1950) and Schoch (1950) p r e s e n t e d a g e n e r a l s o l u t i o n t o a boundary v a l u e problem d e p i c t i n g a model a p p r o p r i a t e f o r non-resonant s c a t t e r e r s i n t h e oceans. They e s s e n t i a l l y expanded the t h e o r y o f R a y l e i g h (1873) t o i n c l u d e s c a t t e r e r s w h i c h a r e comparable i n s i z e t o t h e w a v e - l e n g t h o f t h e i n c i d e n t sound. Both a d e t a i l e d d e s c r i p t i o n o f t h e i r papers and a h i s t o r y o f r e l a t e d t h e o r e t i c a l s t u d i e s a r e g i v e n i n c h a p t e r I I . E x p e r i m e n t a l s t u d i e s r e l a t i n g t o p l a n k t o n s c a t t e r i n g . H a r t o g and Knollman (1962) have c a r r i e d o ut measurements o f underwater sound s c a t t e r i n g from f l u i d s p h e r e s . They have found s u b s t a n t i a l agreement w i t h the t h e o r y o f Anderson (1950) f o r an i n c i d e n t - w a v e f r e q u e n c y o f 30 kHz. E n r i g h t (1963) has made measurements o f t h e compress-i b i l i t y o f some marine c r u s t a c e a n s by u s i n g a m i c r o p i e z o m e t e r t o d e t e r m i n e t h e f r a c t i o n a l change i n a s m a l l volume, f o r p r e s s u r e changes o f a few atmospheres. I n a l l c a ses he found t h e c o m p r e s s i b i l i t y o f t h e a n i m a l s t o be l e s s t h a n t h e c o m p r e s s i b i l i t y o f sea w a t e r . Measurements o f t h e t i s s u e c o m p r e s s i b i l i t y o f b o t h p r e s e r v e d and l i v i n g i s o p o d s were c o n s i s t e n t . Measurements o f t h e c o m p r e s s i b i l i t y o f p r e s e r v e d 6 e u p h a u s i i d s i n d i c a t e d v a l u e s a p p r o x i m a t e l y 15 p e r c e n t lower t h a n t h e c o m p r e s s i b i l i t y o f sea w a t e r . Lebedeva (1964) has used an a c o u s t i c a l method f o r measuring t h e b u l k modulus o r i n c o m p r e s s i b i l i t y (the i n v e r s e o f c o m p r e s s i b i l i t y ) o f l i v e prawns. The a n i m a l s were suspended on a f i l a m e n t a t an a n t i n o d e o f a r e s o n a n t f r e q u e n c y s t a n d i n g wave i n an a i r - t i g h t water column. The r e s u l t i n g s h i f t s i n r e s o n a n t f r e q u e n c y were used t o compute t h e b u l k modulus o f t h e a n i m a l t i s s u e s . I t was n e c e s s a r y t o de-gas b o t h t h e sea water and t h e specimens. T h i s was a c c o m p l i s h e d b o t h by e v a c u a t i o n and by p e r i o d i c d i s c h a r g e s o f p r e s s u r e . Lebedeva found t h e b u l k modulus o f prawns t o be 7 per c e n t l o w e r t h a n t h a t o f sea w a t e r . R.W. Sheldon ( p e r s o n a l communication) a t t h e B e d f o r d I n s t i t u t e i n Dartmouth, Nova S c o t i a , has measured th e d e n s i t y o f l i v e e u p h a u s i i d s . He has found t h e a n i m a l s t o be a p p r o x i m a t e l y 3 p e r c e n t denser t h a n sea w a t e r . IV. OUTLINE OF THE THESIS The remainder o f t h i s t h e s i s c o n s i s t s o f f o u r c h a p t e r s and t h i r t e e n a p p e n d i c e s . The main body o f t h e t h e s i s i s i n t e n d e d t o be a condensed, f a c t u a l p r e s e n t a t i o n of t h e t h e o r y , e x p e r i m e n t , a n a l y s i s , r e s u l t s and c o n c l u s i o n s . The a p p e n d i c e s a r e d e s i g n e d f o r a r e s e a r c h e r who d e s i r e s t o c o n t i n u e o r expand upon t h e i n v e s t i g a t i o n s p r e s e n t e d h e r e w i t h . 7 Chapter I I contains the main developments of the t h e o r e t i c a l background. A model of experimental c o n d i t i o n s i s presented i n a boundary value problem. The general s o l u t i o n i s s t a t e d . Summaries are then presented of two i n v e s t i g a t i o n s designed to improve the model. Chapter I I I e x p l a i n s the experimental methods used. I t contains a d e s c r i p t i o n of the sea-going apparatus and i n c l u d e s the a c o u s t i c system as i t p e r t a i n s to the models described i n the previous chapter. Location of the experiment, c r u i s e d e s c r i p t i o n and c a l i b r a t i o n techniques are discussed. Chapter IV e x p l a i n s the a n a l y s i s methods used. I t contains d e s c r i p t i o n s of the data, the a n a l y s i s apparatus and the analog and d i g i t a l methods of studying tbe echo pulses. This chapter a l s o contains a d i s c u s s i o n of the a n a l y s i s of a t t e n u a t i o n e f f e c t s i n the water due to transducer l o b a l p a t t e r n s . Chapter V presents the r e s u l t s and c o n c l u s i o n s . The experimental r e s u l t s are c l o s e l y t i e d to chapters I I I and IV which des c r i b e the experimental techniques. The conclusions are obtained by a c l o s e examination of the r e s u l t s i n chapter V and the t h e o r e t i c a l d i s c u s s i o n i n chapter I I . A l l i n f o r m a t i o n t h a t i s considered n o n - e s s e n t i a l i n a i d i n g the reader to understand the l a t t e r r e l a t i o n s h i p between the conclusions and t h e o r e t i c a l concepts of the p h y s i c s , i s placed i n the v a r i o u s appendices. 8 CHAPTER I I THEORETICAL DISCUSSION T h i s c h a p t e r w i l l b e g i n w i t h a d e s c r i p t i o n o f t h e problem and g e n e r a l s o l u t i o n f o r s c a t t e r i n g o f sound from a f l u i d s p h e r e . i t w i l l t h e n d e s c r i b e t h e e f f e c t s o f : a) e n c a s i n g t h e sphere i n a t h i n e l a s t i c s h e l l , and b) complex shapes more c l o s e l y r e s e m b l i n g t h e b i o l o g i c a l organisms s t u d i e d d u r i n g t h e e x p e r i m e n t . I . THE SCATTERING OF SOUND FROM A FLUID SPHERE I n t r o d u c t i o n . The s c a t t e r i n g o f p l a n e waves o f sound by spheres was f i r s t i n v e s t i g a t e d m a t h e m a t i c a l l y by A. C l e b s c h (1863) . Other c o n t r i b u t o r s i n c l u d e w e l l known m a t h e m a t i c a l p h y s i c i s t s such as R a y l e i g h , L o r e n z , Thomson, Love, Bromwich, Debye and many o t h e r s . 1 L o r d R a y l e i g h was t h e f i r s t t o s t u d y t h e s c a t t e r i n g from a f l u i d sphere but h i s a n a l y s i s was l i m i t e d t o spheres of s m a l l d i a m e t e r compared w i t h t h e w a v e - l e n g t h . Anderson (1950) and Schoch (1950) have i n v e s t i g a t e d spheres o f d i a m e t e r comparable t o t h e w a v e - l e n g t h , w h i l e Machlup (1952) has s t u d i e d t h e i n f l u e n c e o f e n c a s i n g t h e spheres i n t h i n e l a s t i c s h e l l s . The e f f e c t o f t h e v i s c o s i t y o f t h e f l u i d s has been n e g l e c t e d . l F o r a comprehensive summary o f e a r l y papers t h e r e a d e r i s r e f e r r e d t o Logan (1965). 9 The problem. Consider a s p h e r i c a l o b ject of radi u s 'a' immersed i n an i n f i n i t e f l u i d medium, approximated by the ocean. Consider a l s o plane a c o u s t i c waves of pressure amplitude A and angular frequency to, t r a v e l l i n g i n the -z d i r e c t i o n and i n c i d e n t upon the ob j e c t . The problem to be solved i s t h a t of f i n d i n g the r e l a t i o n s h i p between a) the excess pressure of the sc a t t e r e d wave P s emergent at d i f f e r e n t d i r e c t i o n s from the o b j e c t and b) the p h y s i c a l p r o p e r t i e s of the object i t s e l f t h a t cause the s c a t t e r i n g . The p r o p e r t i e s of i n t e r e s t are de n s i t y pj_, i n c o m p r e s s i b i l i t y Kj_ and sound v e l o c i t y c^. They are 2 r e l a t e d by c^ = K\/p^. The corresponding p r o p e r t i e s of the surrounding i n f i n i t e f l u i d medium w i l l be designated p, K and c. Let the centre of the ob j e c t be the o r i g i n of the po l a r coordinate system ( r , 6, <j>) , where the r e l a t i o n s h i p to the C a r t e s i a n z-axis i s z = rcose ( f i g u r e 16, appendix I I ) . Because of s p h e r i c a l symmetry we may e l i m i n a t e the tj)-dependence l e a v i n g only the two independent v a r i a b l e s r and 6. The excess pressure w i l l be a s o l u t i o n of the 2 2 2 2 three-dimensional wave equation V P = 1/c 3 P / 3 t f o r which the time dependence i s of the form e l a )^* The general s o l u t i o n i s obtained by separation of v a r i a b l e s 10 i n s p h e r i c a l c o o r d i n a t e s and f o r a x i a l symmetry i s g i v e n . i n terms o f t h e Legendre f u n c t i o n s P n (cose) and t h e s p h e r i c a l B e s s e l and Neumann f u n c t i o n s j n and n n r e s p e c t i v e l y . The g e n e r a l s o l u t i o n i s an i n f i n i t e s e r i e s o f s p h e r i c a l harmonics and f o r the i n c i d e n t p l a n e p r e s s u r e wave, becomes P ( r , 0 ) = A e " l a r t ] T ( - i ) n ( 2 n + l ) P n ( c o s e ) j n ( k r ) n=0 where k i s t h e i n c i d e n t wave number, r e l a t e d t o the w a v e l e n g t h A and t h e v e l o c i t y o f sound i n the f l u i d c, by t h e e q u a t i o n s k = 2II/A and k = w/c The i n c i d e n t wave g i v e s r i s e t o an e x t e r n a l s c a t t e r e d wave P s and an i n t e r n a l wave P-^  w h i c h when expanded i n s p h e r i c a l harmonics become: P s ( r , 8 ) = e ~ l u t A n P n ( c o s 6 ) h n ( k r ) and n= -iwt °° P i ^ e ) = e ^ " ^ r B n p n ( c o s e ) j n ( k i r ) where h n ( k r ) = j n ( k r ) + i n n ( k r ) , k^ i s t h e i n t e r n a l wave number and A n and B n a r e t h e unknown c o e f f i c i e n t s t o be d e t e r m i n e d from t h e boundary c o n d i t i o n s . A t t h e boundary, r = a, t h e r e must be: a) c o n t i n u o u s p r e s s u r e o r P(a) + P s ( a ) = P i (a) (1) b) c o n t i n u o u s r a d i a l p a r t i c l e v e l o c i t y o r V n(a) + V s n ( a ) = V i n ( a ) ( 2 ) 11 The r a d i a l v e l o c i t y can be d e r i v e d from t h e p r e s s u r e u s i n g V = e _ 1 ( i ) t and 3V/3t = -1/p 3P/3r t o g i v e t h e dynamic e q u a t i o n V n = - i / p c 3P/3r The t a n g e n t i a l v e l o c i t y has been assumed t o have n e g l i g i b l e i n f l u e n c e . S u b s t i t u t i n g t h e d e s c r i b e d q u a n t i t i e s i n t o (1) and (2) t h e r e s u l t i n g e q u a t i o n s may be s o l v e d f o r A n , the unknown c o e f f i c i e n t s o f t h e s c a t t e r e d p r e s s u r e wave. The g e n e r a l s o l u t i o n . The r e s u l t a n t g e n e r a l s o l u t i o n o f t h e wave e q u a t i o n as o b t a i n e d by Anderson (1950) f o r t h e s c a t t e r e d wave i s - i w t Ps = e A n P n ( c o s e ) h n ( k r ) n = i where and *n = - A ( - l )n ( 2 n + l ) j i ( k a ) j i ( k ± a ) Z j n ( k a ) j n ( k i a ) h n ( k a ) j n ( k ± a ) Z h n ( k a ) j n ( k ± a ) = (Kp/K i P ; L) 1/2 U s i n g t h e above s o l u t i o n , t h e d e s i r e d dependence o f P s on t h e d e n s i t y and i n c o m p r e s s i b i l i t y c o n t r a s t s between t h e o b j e c t and t h e s u r r o u n d i n g f l u i d w i l l be d e s c r i b e d . S u b s t i t u t i o n o f t h e s e r i e s a p p r o x i m a t i o n s f o r j n ( k a ) , h n ( k a ) and t h e i r d e r i v a t i v e s , w i l l produce t h e f o l l o w i n g a p proximate s o l u t i o n o f Schoch(1950) (see appendix I ) . 12 P s. = - A k 2 a 3 The above r e l a t i o n s h i p between the s c a t t e r e d p r e s s u r e and t h e d e n s i t y and i n c o m p r e s s i b i l i t y c o n t r a s t i s t h e key r e l a t i o n s h i p upon w h i c h t h e model i s based. I t w i l l now be used t o d e s c r i b e t h e p h y s i c s i n v o l v e d . I f t h e i n c o m p r e s s i b i l i t y o f t h e o b j e c t i s i d e n t i c a l t o t h a t o f t h e f l u i d K (but pj_^p),, t h e n th e f i r s t term becomes i d e n t i c a l l y z e r o and t h e s c a t t e r e d p r e s s u r e i s t h e n p r o p o r t i o n a l t o t h e c o s i n e o f t h e a n g l e measured t o t h e l i n e o f i n c i d e n t p r e s s u r e . The o b j e c t i s compressed and r a r i f i e d e x a c t l y as i s t h e s u r r o u n d i n g w a t e r but because o f t h e d e n s i t y c o n t r a s t and t h e f l u c t u a t i n g p r e s s u r e g r a d i e n t , t h e o b j e c t has a d i f f e r e n t a c c e l e r a t i o n t h a n th e s u r r o u n d i n g w ater m o l e c u l e s and t h e r e f o r e a c t s l i k e a r a d i a t i n g d i p o l e w i t h maximum energy s c a t t e r e d a l o n g t h e l i n e 9 = 0 and z e r o energy r a d i a t e d a l o n g 9 = -§-. I f t h e d e n s i t y o f t h e o b j e c t i s i d e n t i c a l t o t h a t o f t h e f l u i d p (but Kj_ ^ K) , t h e n the second term becomes i d e n t i c a l l y z e r o w i t h t h e r e s u l t t h a t t h e s c a t t e r e d p r e s s u r e i s i s o t r o p i c . F o r s m a l l ka t h e p r e s s u r e g r a d i e n t o f t h e i n c i d e n t wave w i l l have l i t t l e r e - r a d i a t i o n e f f e c t b u t t h e f l u c t u a t i n g p r e s s u r e w i l l cause s p h e r i c a l o s c i l l a t i o n s o f t h e o b j e c t and t h u s i s o t r o p i c r e - r a d i a t i o n . The o b j e c t r a d i a t e s K i - K + Pi-P 1+i i (kr-cot) 3 K ± - K ( k a ) 2 ( 1 + i k a ) 2p±+p \ fe, cosf (3) 13 energy e q u a l l y i n a l l d i r e c t i o n s . F o r t h e case where = K and = p i t becomes app a r e n t t h a t t h e o b j e c t i s t r a n s p a r e n t t o t h e i n c i d e n t sound wave and P s = 0. Fo r r l a r g e , t h e phase s h i f t w i t h r e s p e c t t o t h e i n c i d e n t p r e s s u r e o f b o t h t h e i s o t r o p i c and c o s i n e terms w i l l be l e s s t h a n a few de g r e e s . T h e r e f o r e , i f b o t h terms a r e u s e d , t h e r e a l p a r t s may be added t o g i v e a good a p p r o x i m a t i o n o f t h e t o t a l s c a t t e r e d p r e s s u r e . 2 I f ka<<l and K(ka) <<3K^ th e n f o r l a r g e k r t h e s o l u t i o n r e duces t o t h a t o f R a y l e i g h (1873). i (kr-cot) 2 3 P = -Ak a s Ki - K P i _ p + ~ :— c o s i 3K I 2pj_+p e T h i s e x p r e s s i o n shows t h e well-known r e s u l t o f R a y l e i g h s c a t t e r i n g . I I . THE ENCASING OF A FLUID SPHERE IN A THIN ELASTIC SHELL Machlup (1952) has shown t h a t t h e r e f l e c t i o n b e h a v i o u r o f a f l u i d sphere encased i n a t h i n e l a s t i c s h e l l i s v e r y n e a r l y i d e n t i c a l t o t h a t o f a f l u i d sphere a l o n e , f o r i n c i d e n t w a velengths o f t h e o r d e r o f t h e magnitude o f t h e sphere. F o r low e r f r e q u e n c i e s he has shown t h e i n c r e a s i n g i n f l u e n c e o f t h e s h e l l due t o i t s r i g i d i t y as w e l l as t h e c o n t r a s t s i n d e n s i t y and c o m p r e s s i b i l i t y w i t h t h e f l u i d s . However f o r z o o p l a n k t o n i c o r g a n i s m s , t h e i n f l u e n c e o f t h e SCALE IN M M 0 1 2 3 4 5 THE EUPHAUSIID r i g i d i t y w i l l be decreased s i n c e the animal cross s e c t i o n s are not c i r c u l a r and some bending of the s h e l l occurs. I I I . SOUND SCATTERING FROM BIOLOGICAL ORGANISMS The expression f o r the s c a t t e r e d pressure from a f l u i d sphere as a f u n c t i o n of the p r o p e r t i e s of the incoming sound and of the object i t s e l f has been shown. This s o l u t i o n i s r e p r e s e n t a t i v e of a s p h e r i c a l animal whereas the b i o l o g i c a l organisms w i t h which we deal have a number of d i f f e r i n g shapes and o r i e n t a t i o n s . Figure 1 i s a drawing of an euphausiid, the l a r g e s t and most abundant of the p l a n k t o n i c organisms thought r e s p o n s i b l e f o r the experimental s c a t t e r i n g . Various shapes have been constructed from spheres of d i f f e r e n t s i z e 15 I n a ppendix I I t h e Born a p p r o x i m a t i o n has been used i n c a l c u l a t i n g t h e s c a t t e r e d energy from added s p h e r e s . I n appendix I I I , t h e c o m p u t a t i o n o f t h e number o f s i g n i f i c a n t spheres and t h e i n f l u e n c e o f s i z e and o r i e n t a t i o n have been d i s c u s s e d f o r t h e s p e c i f i c c h a r a c t e r i s t i c s o f t h e e x p e r i m e n t . I t i s shown by t h e s e c o m p u t a t i o n s t h a t , f o r t h i s e x p e r i m e n t , t h e i n f l u e n c e s o f s i z e and o r i e n t a t i o n a r e s m a l l , p r o v i d e d t h a t enough echoes a r e a n a l y s e d t o j u s t i f y u s i n g s t a t i s t i c a l c o n c e p t s t o reduce t h e i n f l u e n c e o f o r i e n t a t i o n o f t h e a n i m a l s . N e v e r t h e l e s s , t h e computed c o r r e c t i o n f a c t o r , even though s m a l l , w i l l be a p p l i e d d u r i n g t h e i n t e r p r e t a t i o n o f t h e r e s u l t s . 16 CHAPTER I I I EXPERIMENTAL METHODS This chapter i n c l u d e s a d i s c u s s i o n of the sea-going apparatus as w e l l as a d e t a i l e d d e s c r i p t i o n of the a c o u s t i c parameters. Discussions of the l o c a t i o n of the experiment, the c r u i s e s during which data were c o l l e c t e d and c a l i b r a t i o n techniques, are in c l u d e d . Sea-going apparatus. Figure 2 i s a block diagram of the sea-going experimental apparatus. D e t a i l e d d e s c r i p t i o n s are given i n the appendices. The output and r e c e i v e r systems (see appendix V) c o n s i s t of a narrow beam, 102 kHz t r a n s m i t t e r and two broadband c y l i n d r i c a l r e c e i v e r s , o m n i d i r e c t i o n a l i n the plane normal to the l o n g i t u d i n a l a x i s . The r e c e i v e r outputs are connected to tuned p r e a m p l i f i e r s and f i v e hundred f e e t of low-noise c o a x i a l c a b l e . The monitoring and reco r d i n g systems (see appendix VI) c o n s i s t of a fourteen-channel, simultaneous-replay tape recorder and a storage o s c i l l o s c o p e connected to the reproduce a m p l i f i e r s of the recorder. The t i m i n g c o n t r o l c o n s i s t s of a t h i r t y v o l t peak-to-peak square wave which both t r i g g e r s the output t r a n s c e i v e r and i s d i f f e r e n t i a t e d , attenuated and recorded to act as a t r i g g e r s i g n a l f o r the monitor and a n a l y s i s systems. ROSS GRAPHIC RECORDER 7 \ ROSS TRANSCEIVER 7f\ TFT TR TUNED PREAMPLIFIER TUNED PREAMPLIFIER GGER TRANSDUCER C A B L E 6 ATLANTIC LC-32 RECEIVER ROSS TRANS-DUCER WAVETEK 116 FUNCTION GENERATOR ATLANTIC LC-32 RECEIVER OSCILLOSCOPE CAMERA RECEIVER C A B L E RECEIVER C A B L E TEKTRONIX 5 4 9 STORAGE OSCILLOSCOPE 3k. RECORD. MODE AMPEX F R - 1300 14 CHANNEL TAPE RECORDER REPLAY MODE TRIGGER FILTER FILTER FIGURE 2 BLOCK DIAGRAM OF SEA-GOING APPARATUS 18 A c o u s t i c system. The a p p a r a t u s i s shown i n t h e photographs o f f i g u r e 3 and drawn t o s c a l e i n f i g u r e 4. The e x p e r i m e n t a l method d e c i d e d upon was t o i n s o n i f y t h e a n i m a l s w i t h 14 c y c l e s o f a 102 kHz p r e s s u r e wave (see appendix V f o r d e s c r i p t i o n o f p u l s e shape) and t o aim t h e r e c e i v e r s and g a t e t h e r e c e i v e d s i g n a l so t h a t a s m a l l volume, w h i c h would u s u a l l y c o n t a i n o n l y a few a n i m a l s , was s t u d i e d . A f r e q u e n c y near 100 kHz was chosen f o r t h e f o l l o w i n g r e a s o n s . The s i z e d i s t r i b u t i o n o f marine z o o p l a n k t o n l i k e l y t o produce th e back s c a t t e r e d sound was w e l l known. H i g h e r f r e q u e n c i e s would cause g r e a t e r d i f f i c u l t y i n r e l a t i n g t h e m a t h e m a t i c a l models d e s c r i b e d i n c h a p t e r I I t o t h e e x p e r i m e n t a l r e s u l t s . S i g n a l r e c e p t i o n and p r o c e s s i n g would be more d i f f i c u l t . F r e q u e n c i e s below 100 kHz might not produce a measurable s c a t t e r e d p r e s s u r e from t h e s m a l l e s t p l a n k t o n o f i n t e r e s t (Bary, 1966). The e x a c t f r e q u e n c y was chosen by t u n i n g t h e t r a n s m i s s i o n o s c i l l a t o r a t sea i n o r d e r t o g e t t h e h i g h e s t s i g n a l - t o - n o i s e r a t i o f o r the s p e c i f i c a c o u s t i c system o f t h i s e x p e r i m e n t . The n e c e s s a r y e l e c t r o n i c s were s e a l e d a g a i n s t t h e e f f e c t o f p r e s s u r e so t h a t the equipment c o u l d be lowered i n t o s u i t a b l e l a y e r s o f t h e a n i m a l s . I t was assumed t h a t a f t e r s e t t l i n g f o r a few m i n u t e s , t h e a p p a r a t u s had l i t t l e FIGURE 3 APPARATUS 20 z t 3.15 MILLISECONDS -3.58 MILLISECONDS FIGURE 4 LOBAL PATTERNS, ATTENUATION CONTOURS FOR LOWER HYDROPHONE AND APPARATUS IN THE X - Z PLANE 21 i n f l u e n c e on t h e b e h a v i o u r o f t h e p l a n k t o n . Underwater t e l e v i s i o n was used t o s t u d y t h i s i n f l u e n c e . The a c o u s t i c a p p a r a t u s was a t t a c h e d t o t h e t e l e v i s i o n h o u s i n g and f o r near s u r f a c e o b s e r v a t i o n s , where t h e r e was s u f f i c i e n t i l l u m i n a t i o n from t h e ambient l i g h t , t h e z o o p l a n k t o n i c a n i m a l s seemed l i t t l e p e r t u r b e d by t h e a p p a r a t u s . O b s e r v a t i o n s o f t h e e f f e c t a t g r e a t e r depths were i n t e r f e r e d w i t h by t h e n o t i c e a b l e response o f t h e a n i m a l s t o t h e a r t i f i c i a l i l l u m i n a t i o n n e c e s s a r y f o r t h e s e o b s e r v a t i o n s . No such i l l u m i n a t i o n was used d u r i n g d a t a c o l l e c t i o n w i t h t h e a c o u s t i c a p p a r a t u s . The d i m e n s i o n s o f t h e r e c e i v e r p o s i t i o n s were such t h a t a) t h e d i r e c t p u l s e had c o m p l e t e l y passed t h e l o w e r hydrophone b e f o r e t h e f i r s t m e a n i n g f u l p l a n k t o n echo a r r i v e d and b) t h e t o t a l p a t h l e n g t h s t o t h e two hydrophones were a p p r o x i m a t e l y e q u i v a l e n t . A b s o r p t i o n o f t h e sound f o r t h e range under c o n s i d e r a t i o n i s l e s s t h a n 0.04 db per metre ( T o l s t o y and C l a y , 1966). The r e c e i v e r s were p o s i t i o n e d such t h a t t h e a n g l e s between t h e i n c i d e n t and r e c e i v e d sound, f o r a p o i n t a t t h e c e n t r e o f the volume, were n/12 and n/2 r a d i a n s . The p u l s e r e p e t i t i o n r a t e was 250 m i l l i s e c o n d s The volume under c o n s i d e r a t i o n ( f i g u r e s 4 t o 6) i s d e l i n e a t e d by a t r a n s m i t t i n g cone and by f o u r e l l i p s o i d s o f r e v o l u t i o n , two f o r each hydrophone. Contours o f e q u a l 22 LOBAL PATTERNS AND ATTENUATION CONTOURS FOR UPPER HYDROPHONE IN THE X - Z PLANE 23 FIGURE 6 LOBAL PATTERNS AND ATTENUATION CONTOURS FOR LOWER HYDROPHONE IN THE Y - Z PLANE 24 a t t e n u a t i o n (due t o the t r a n s m i t t e r and r e c e i v e r l o b a l patterns which are p l o t t e d i n db i n f i g u r e s 4 and 6) as w e l l as the g a t i n g e l l i p s o i d s are shown. Figure 4 i l l u s t r a t e s , f o r the lower hydrophone, the area contained by the i n t e r s e c t i o n of t h a t surface f o r which the pressure a t t e n u a t i o n i s 6 db above th a t at the o r i g i n 0, and the X - Z plane which contains the o r i g i n , the sound source and both r e c e i v e r s . Figure 5 gives a s i m i l a r volume f o r the upper hydrophone. Figure 6 shows the i n t e r s e c t i o n of the 6 db a t t e n u a t i o n surface f o r the lower hydrophone w i t h the Y - Z plane. In order to get the maximum overlap between the two volumes, the e l l i p s o i d s f o r each r e c e i v e r were defined by d i f f e r e n t opening and c l o s i n g times f o r the r e c e i v e r gates. A numerical i n t e g r a t i o n to c a l c u l a t e the i n f l u e n c e of the t r a n s m i t t e r and r e c e i v e r attenuations was performed using p o i n t s on a 20 cm g r i d throughout the volumes (see chapter IV and appendix X). This r e s u l t permits the c a l c u l a t i o n of a c o r r e c t i o n f a c t o r , dependent on the volume c h a r a c t e r i s t i c s , f o r the r a t i o between the t o t a l r e f l e c t e d energy r e c e i v e d i n the upper hydrophone to the t o t a l r e c e i v e d energy i n the lower. I t was decided to use t h i s r a t i o of energies as the primary q u a n t i t a t i v e measurement tha t would i n d i c a t e the nature of the s c a t t e r i n g d i s t r i b u t i o n . L o c a t i o n of experiment. One cannot be c e r t a i n t h a t 25 t h e c a t c h i n g o f marine z o o p l a n k t o n and t h e subsequent p r e s e r v a t i o n and s t o r i n g o f t h e a n i m a l s i n t h e l a b o r a t o r y does n o t a l t e r p r o p e r t i e s o f t h e a n i m a l s ( f o r example t h e c o n d i t i o n o f t h e p r o t e i n s ) and t h e r e b y a l t e r t h e a c o u s t i c s c a t t e r i n g i t s e l f . I t was d e c i d e d t h e r e f o r e t h a t t h e a c o u s t i c measurements s h o u l d be c a r r i e d o u t i n s i t u . The s e l e c t e d e x p e r i m e n t a l l o c a t i o n was S a a n i c h I n l e t on Vancouver I s l a n d , B r i t i s h Columbia (see f i g u r e 7 ) . I t was n e c e s s a r y t o d e c i d e upon a l o c a t i o n where: (1) b i o l o g i c a l s t u d i e s i n d i c a t e d t h e e x i s t e n c e o f h i g h c o n c e n t r a t i o n s o f marine z o o p l a n k t o n , and (2) where a c o u s t i c measurements c o u l d be made i n c o n j u n c t i o n w i t h b i o l o g i c a l s a m p l i n g programs. The l o c a t i o n o f S a a n i c h I n l e t was i d e a l f o r t h e s e two c o n d i t i o n s . The oceano-graphy o f t h i s i n l e t has been d e s c r i b e d by H e r l i n v e a u x (1962). C r u i s e d e s c r i p t i o n s . Four c r u i s e s were made d u r i n g 1967 and 1968. The f i r s t two, on board C.N.A.V. Endeavour, l a s t e d from May 19 t o May 24. and from August 1 t o August 7, 1967. B o t h o f t h e s e s e a - e x p e r i m e n t s p r o v i d e d v a l u a b l e i n f o r m a t i o n on b i o l o g i c a l s t r u c t u r e , q u a n t i t a t i v e r e f l e c t i v i t y and t h e s p e c i f i c n a t u r e o f t h e e x p e r i m e n t a l o b j e c t i v e s . The t h i r d and f o u r t h c r u i s e s were made by t h r e e s h i p s , i n o r d e r t o o b t a i n p h y s i c a l and b i o l o g i c a l d a t a s i m u l t a n e o u s l y . The f i r s t o f t h e s e s e a - e x p e r i m e n t s t o o k p l a c e from November 27 t o December 8, 1967. The a c o u s t i c e x p e r i m e n t was c a r r i e d 26 FIGURE 7 LOCATION OF THE EXPERIMENT 27 out from C.N.A.V. Endeavour w h i c h moored t o t h e buoys i n t h e c e n t r a l p a r t o f t h e i n l e t (see f i g u r e 7) w h i l e s c i e n t i s t s on b o a r d t h e C.S.S. V e c t o r and M.V. A.P.Knight t r i e d t o g e t b i o l o g i c a l d a t a i n t h e t e e t h o f a h o w l i n g g a l e ! The f i n a l c r u i s e l a s t e d from June 17 t o June 28, 1968 and c o n s i s t e d o f two p a r t s . D u r i n g t h e f i r s t week, aboard C.S.S. V e c t o r , q u a l i t a t i v e g r a p h i c a l r e c o r d s o f s c a t t e r i n g were made. D u r i n g t h e second week t h e a c o u s t i c a l equipment was assembled on board t h e H.M.C.S. M i r a m a c h i , w h i c h moored t o t h e buoys, w h i l e C.S.S. V e c t o r and t h e M.V. A.P.Knight performed d e t a i l e d b i o l o g i c a l s a m p l i n g under t h e d i r e c t i o n o f Dr. B.McK. Bary and Mr. W.E. B a r r a c l o u g h . A l l q u a n t i t a t i v e d a t a were c o l l e c t e d d u r i n g t h e second week and, whenever p o s s i b l e , echoes were r e c o r d e d s i m u l t a n e o u s l y and a t t h e same depths as t h e b i o l o g i c a l s a m p l i n g . The tows passed w i t h i n 50 t o a few hundred metres o f t h e r e f l e c t i o n a p p a r a t u s . C a l i b r a t i o n . The o u t p u t t r a n s d u c e r was c a l i b r a t e d i n a tank a t t h e Underwater Weapons Range L a b o r a t o r y , P a t r i c i a Bay, Vancouver I s l a n d , i m m e d i a t e l y f o l l o w i n g t h e c r u i s e , and u s i n g t h e f r e q u e n c y a t w h i c h t h e d a t a were t a k e n . The l o b a l p a t t e r n s a r e shown i n db i n f i g u r e s 4 and 6. T r a n s m i t t i n g c h a r a c t e r i s t i c s a r e g i v e n i n appendix V. C a l i b r a t i o n o f t h e r e c e i v e r s was performed by t h e manufacturers, while c a l i b r a t i o n s of the. preamplifiers both the submersible units and the input stages of the tape recorder, were performed repeatedly at sea during data c o l l e c t i o n . Specifications appear i n appendix V 29 CHAPTER IV DATA ANALYSIS T h i s c h a p t e r i n c l u d e s d e s c r i p t i o n s o f t h e d a t a , t h e a n a l y s i s a p p a r a t u s and t h e a n a l o g and d i g i t a l methods o f s t u d y i n g t h e echo p u l s e s . A d i s c u s s i o n o f t h e g e o m e t r i c a n a l y s i s o f t h e volumes and t h e subsequent i n t e r p r e t a t i o n o f b o t h i s o t r o p i c and c o s i n e s c a t t e r i n g i s i n c l u d e d . Data d e s c r i p t i o n . The a c o u s t i c d a t a c o n s i s t e d o f th e c o n t i n u o u s l y r e c o r d e d r e c e i v e d s i g n a l s i n t h e upper and l o w e r hydrophones. The echo p u l s e s o f i n t e r e s t were r e c o r d e d , f o r t h e upper hydrophone, from 2.94 t o 3.7 9 m i l l i s e c o n d s a f t e r t h e o u t p u t p u l s e , and f o r t h e lower hydrophone, from 3.15 t o 3.58 m i l l i s e c o n d s a f t e r t h e o u t p u t p u l s e ( f i g u r e s 4 and 5 ) . R e c o r d i n g s d u r i n g t h e s e i n t e r v a l s w i l l be c a l l e d s i g n a l b l o c k s . The echo p u l s e s had t h e same r i s e t i m e , p u l s e d u r a t i o n and decay t i m e as d i d t h e o u t p u t p u l s e (appendix V ) . Echo p u l s e s from z o o p l a n k t o n i c organisms a r e shown a t o n e - f o u r t h r e a l t ime i n f i g u r e 9A. I t was n e c e s s a r y t o compute t h e t o t a l a c o u s t i c energy r e c e i v e d a t each hydrophone d u r i n g t h e above mentioned time i n t e r v a l s . F o r t h e m a j o r i t y o f t h e r e c e i v e d s i g n a l s , w h i c h i n d i c a t e d t h e p r e s e n c e o f o n l y a few z o o p l a n k t o n i c organisms w i t h i n t h e d e s c r i b e d volume, t h i s i n f o r m a t i o n was c o n t a i n e d i n t h e envelope o f each s i g n a l b l o c k . I t was found t h a t 30 a n a l o g t e c h n i q u e s o f f e r e d t h e b e s t methods of p r o d u c i n g t h e e n v e l o p e s . D i g i t a l t e c h n i q u e s however o f f e r e d t h e b e s t methods o f c a r r y i n g out t h e l a r g e number of c o m p u t a t i o n s r e q u i r e d f o r t h e a n a l y s i s o f t h e a n a l o g s i g n a l s . A n a l y s i s a p p a r a t u s . F i g u r e 8 i s a b l o c k diagram o f t h e a n a l y s i s a p p a r a t u s . D e t a i l e d d e s c r i p t i o n s a r e g i v e n i n a p p e n d i c e s V I I and V I I I . The r e p r o d u c e and a n a l o g systems (see appendix V I I ) c o n s i s t e d o f r e p r o d u c e t a p e r e c o r d e r a m p l i f i e r s , band pass f i l t e r s and o p e r a t i o n a l a m p l i f i e r networks w h i c h i n c l u d e d r e c t i f i e r s f o l l o w e d by c i r c u i t s f o r t r a c i n g t h e e n v e l o p e s o f t h e echo p u l s e s . The s i g n a l s t h e n passed i n t o an a n a l o g t o d i g i t a l c o n v e r s i o n system, were r e c o r d e d d i g i t a l l y by a C.D.C. 8092 computer and were f u r t h e r a n a l y s e d by an I.B.M. 7044 computer (see appendix V I I I ) . B o t h computers form p a r t of t h e f a c i l i t i e s o f t h e U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e . The t i m i n g s i g n a l s f o r t h e a n a l o g t o d i g i t a l c o n v e r s i o n were i n i t i a t e d by a p u l s e from t h e a n a l o g t a p e . T h i s p u l s e t r i g g e r e d t h e d e l a y c i r c u i t o f t h e o s c i l l o s c o p e w h i c h was a d j u s t e d t o g i v e a t i m i n g s i g n a l c o r r e s p o n d i n g t o t h e f i r s t e l l i p s o i d o f t h e "volume of i n t e r e s t " . T h i s s i g n a l t r i g g e r e d t h e f u n c t i o n g e n e r a t o r t o i m m e d i a t e l y AMPEX FR - 1300 14-CHANNEL TAPE RECORDER REPLAY MODE TRIGGER OSCILLOSCOPE CAMERA TEKTRONIX 549 STORAGE OSCILLOSCOPE DELAY TRIGGER GENERAL RADIO 1554-A FILTER GENERAL RADIO 1554-A FILTER WAVETEK 116 FUNCTION GENERATOR CONTROL DATA 8092 COMPUTER ANALOG NETWORK ANALOG NETWORK F I G U R E 8 B L O C K DIAGRAM OF A N A L Y S I S A P P A R A T U S ANALOG TO DIGITAL CONVERTER I. B- M. 7044 COMPUTER 32 produce s i x t y - f o u r square waves a t 14.0 kHz, w h i c h i n i t i a t e d seven a n a l o g t o d i g i t a l c o n v e r s i o n s on each s i g n a l i n p u t c h a n n e l d u r i n g each m i l l i s e c o n d . A n a l o g a n a l y s i s . The echo p u l s e s were r e p r o d u c e d a t f i f t e e n i n c h e s per second w h i c h i s o n e - f o u r t h o f t h e r e c o r d i n g speed. Reproduce a m p l i f i e r g a i n s were a d j u s t e d so t h a t t h e r e c o r d e d and r e p r o d u c e d c a l i b r a t i o n s i g n a l s were i d e n t i c a l i n a m p l i t u d e . The band pass f i l t e r s were tuned f o r a c e n t r a l f r e q u e n c y o f 25.5 kHz ( c o r r e s p o n d i n g t o 102.0 kHz i n r e a l r e c o r d i n g time) and were c a r e f u l l y matched f o r i d e n t i c a l g a i n s . F i g u r e s 9A and 9B a r e o s c i l l o s c o p e photographs o f s i g n a l s d u r i n g t h e a n a l y s i s p r o c e s s . D e s c r i p t i o n s a r e as f o l l o w s : 9A) Upper and l o w e r hydrophone s i g n a l s a t t h e i n p u t s i d e o f t h e a n a l o g networks and t h e t r i g g e r p u l s e d i r e c t l y from t h e t a p e r e c o r d e r . Hydrophone s i g n a l s have been f i l t e r e d and show p l a n k t o n s c a t t e r i n g f o l l o w i n g t h e d i r e c t a c o u s t i c p u l s e s (under D.U. and D.L. i n f i g u r e 9) t o t h e r e c e i v e r s . The h o r i z o n t a l t i m e s c a l e i s 2 m i l l i s e c o n d s p e r c e n t i m e t r e . The v e r t i c a l s c a l e i s 2 v o l t s p e r c e n t i m e t r e . 9B) R e c t i f i e d and RC f i l t e r e d hydrophone s i g n a l s a t t h e i n p u t s i d e o f t h e a n a l o g t o d i g i t a l c o n v e r t e r and t h e square wave p u l s e s used t o i n i t i a t e t h e c o n v e r s i o n s (the 64 p u l s e s appear as a s o l i d l i n e a t t h e l o w e r r i g h t ) . The h o r i z o n t a l t ime s c a l e i s 2 m i l l i s e c o n d s p e r c e n t i m e t r e . The v e r t i c a l s c a l e i s 0.5 v o l t s p e r c e n t i m e t r e . The RC f i l t e r s cause a t i m e d e l a y o f t h e e n v e l o p e s w h i c h has been compensated f o r by s h i f t i n g t h e t i m i n g marks t h a t c o r r e s p o n d t o t h e boundary e l l i p s o i d s . UPPER HYDROPHONE LOWER HYDROPHONE TRIGGER FIGURE 9A SIGNAL PHOTOGRAPHS 34 D i g i t a l a n a l y s i s . Seven d i g i t a l programs a r e d e s c r i b e d i n d e t a i l i n appendices V I I I and IX. The main programs d e s i g n e d t o compute r e s u l t s t h a t a r e g i v e n i n t h e f o l l o w i n g c h a p t e r a r e as f o l l o w s . The p r i n c i p a l d i g i t a l a n a l y s i s c o n s i s t e d o f s q u a r i n g each v a l u e o f t h e c o n v e r t e d v o l t a g e and summing a c r o s s t h e t i m i n g i n t e r v a l s f o r each hydrophone. The " e n e r g i e s " t h u s o b t a i n e d were summed over many thousands o f echoes and a r a t i o o f energy i n t h e upper hydrophone t o t h a t i n t h e lower hydrophone was computed. Having o b t a i n e d t h e s e v a l u e s , a second d i g i t a l a n a l y s i s c o n s i s t e d o f computing and p l o t t i n g t h e d i s t r i b u t i o n c u r v e s f o r each hydrophone. A t h i r d a n a l y s i s c o n s i s t e d o f c o u n t i n g t h e number o f p u l s e s r e c e i v e d a t each hydrophone f o r each t r a n s m i t t e d p u l s e . Volume a n a l y s i s . From a s t a t i s t i c a l v i e w p o i n t , i t i s r e a s o n a b l e t o assume t h a t t h e i n s i t u p l a n k t o n , when averaged o v e r many l o c a t i o n s and t i m e s , a r e homogeneously d i s t r i b u t e d w i t h i n t h e "volume o f i n t e r e s t " . U s i n g t h i s a s s u m p t i o n , as w e l l as t h a t o f i s o t r o p i c s c a t t e r i n g , i t i s th e n m e a n i n g f u l t o c a l c u l a t e t h e r a t i o o f t h e e x p e c t e d r e c e i v e d p r e s s u r e s a t t h e hydrophones f o r t h e two volumes under c o n s i d e r a t i o n . Such a r a t i o becomes an i m p o r t a n t c o r r e c t i o n f a c t o r when i n t e r p r e t i n g t h e e x p e r i m e n t a l r e s u l t s . F i g u r e s 4, 5 and 6 show a t t e n u a t i o n c o n t o u r s i n db 35 above z e r o a t t e n u a t i o n a t t h e o r i g i n 0, f o r t h r e e c r o s s s e c t i o n s o f t h e volumes under c o n s i d e r a t i o n . T i m i n g e l l i p s o i d s have been a d j u s t e d f o r maximum o v e r l a p o f s t h e volumes. An a n a l y s i s was c a r r i e d o ut t o e s t i m a t e t h e e x p e c t e d amount o f s c a t t e r e d sound from each volume, f o r a homogeneous d i s t r i b u t i o n o f i s o t r o p i c s c a t t e r e r s . O b j e c t s o f u n i t r e f l e c t i v i t y were assumed t o e x i s t a t t h e c o r n e r s o f a twenty c e n t i m e t r e g r i d . A n u m e r i c a l i n t e g r a t i o n o f r e c e i v e d s i g n a l was p e r f o r m e d , e x t e n d i n g t o t h e margins o f t h e volumes where the r e c e i v e d s i g n a l was 0.1 p e r c e n t o f t h e s i g n a l a t t h e o r i g i n . The r a t i o o f t h e t o t a l r e c e i v e d p r e s s u r e a t t h e upper hydrophone t o t h a t a t t h e l o w e r hydrophone i s 1.07 ± 0.01 (see appendix X ) . T h i s f i g u r e w i l l be used as a c o r r e c t i o n f o r t h e e x p e r i m e n t a l r e s u l t s . A second a n a l y s i s was c a r r i e d o ut t o e s t i m a t e t h e e x p e c t e d amount o f s c a t t e r e d sound f o r each volume, f o r a homogeneous d i s t r i b u t i o n o f c o s i n e s c a t t e r e r s . O b j e c t s w i t h u n i t r e f l e c t i v i t y a l o n g t h e p r o p a g a t i o n a x i s were assumed t o e x i s t a t t h e c o r n e r s o f a twenty c e n t i m e t r e g r i d . A n u m e r i c a l i n t e g r a t i o n s i m i l a r t o t h e i s o t r o p i c case was performed. The r a t i o o f t h e t o t a l r e c e i v e d p r e s s u r e a t t h e upper hydrophone t o t h a t a t t h e lower hydrophone i s 14.30 ± 0.01 (see appendix X I ) . 36 CHAPTER V RESULTS AND CONCLUSIONS I . RESULTS 84,077 s i g n a l b l o c k s on each hydrophone were a n a l y s e d . 77,454 o f t h e s e had e n e r g i e s t h a t were c o n s i d e r e d r e p r e s e n t a t i v e o f t h e p r e s e n c e o f up t o a few z o o p l a n k t o n i c organisms w i t h i n t h e d e s c r i b e d volumes. The r e m a i n i n g echoes were c o n s i d e r e d r e p r e s e n t a t i v e o f t h e presence, o f e i t h e r a g r e a t e r number of z o o p l a n k t o n i c organisms o r of l a r g e r a n i m a l s . The a c o u s t i c d a t a were c o l l e c t e d i n t e n " u n i t s " , each h a v i n g s e p a r a t e time and d epth c h a r a c t e r i s t i c s . A l l s i g n a l s were r e c o r d e d from June 25 t o June 27, 1968, d u r i n g d a y l i g h t hours and a t depths r a n g i n g from 28 t o 45 m e t r e s . The b i o l o g i c a l d a t a were o b t a i n e d c o n c u r r e n t l y . The f o l l o w i n g t a b l e g i v e s a d a t a summary. The d a t a u n i t s l i s t e d w i t h t h e i r a p p r o p r i a t e a n a l o g and d i g i t a l t a p e s a r e g i v e n i n appendix X I I . The mean o f t h e energy r a t i o s shown i n t a b l e I i s 1.52 ± 0.09 (see e r r o r a n a l y s i s , appendix X I I I ) . The r a t i o o f t h e t o t a l energy r e c e i v e d i n t h e upper hydrophone t o the t o t a l energy r e c e i v e d i n the lower hydrophone i s 1.54 ±0.09. T h i s l a t t e r f i g u r e i s o b t a i n e d by summing t h e e n e r g i e s r e c e i v e d a t each hydrophone f o r a l l d a t a u n i t s ; i t i n c l u d e s DATA UNIT DEPTH (metres) DATE OF RECORDING TIME OF RECORDING SIGNAL BLOCKS ANALYSED FOR DISTRIBUTION SIGNAL BLOCKS-ANALYSED FOR ENERGY RATIO RATIO OF TOTAL ENERGI] 1 28 25/6/68 0940-1057 8619 7680 1.27 2 33 25/6/68 1120-1222 8681 8357 1.49 3 38 25/6/68 1410-1514 8162 7948 1.55 4 43 25/6/68 1530-1639 8379 6743 1.76 5 33 26/6/68 1020-1129 7237 6738 1.15 6 43 26/6/68 1325-1432 8603 8366 1.69 7 45 26/6/68 1505-1618 8624 7025 1.70 8 40 26/6/68 1637-1931 8720 8554 1.57 9 44 27/6/68 1509-1621 8727 8673 1.53 10 31 27/6/68 1836-1952 8325 7370 1.53 TABLE I ENERGY RATIOS AND AUXILLIARY DATA 38 i n f o r m a t i o n from the echoes r e p r e s e n t a t i v e of up to a few zooplanktonic organisms i n the volume of i n t e r e s t . These r e s u l t s have been computed using the f o l l o w i n g three c o r r e c t i o n f a c t o r s (see page references) f o r the r a t i o of the upper to lower hydrophone, received v o l t a g e s . page 1) Ratio of "volumes" 1.07 ± 0.01 35 2) I n t e r f e r e n c e e f f e c t s 1.02 ± 0.01 57 3) Receiver gains 1.045 ± 0.005 68 The t o t a l c o r r e c t i o n f a c t o r used was thus 1.14. Representative d i s t r i b u t i o n curves f o r each u n i t are shown i n f i g u r e s 10 to 14. They r e l a t e the numbers of echoes at any given value w i t h the corresponding energy i t s e l f . The purpose of these p l o t s was to see i f they were c h a r a c t e r i s t i c of b i o l o g i c a l c o n d i t i o n s w i t h i n the small volume of the ocean th a t was s t u d i e d . These graphs were made by the Calcomp Plo.tter at the U n i v e r s i t y of B r i t i s h Columbia Computing Centre. The animals caught from C.S.S. Vector were mostly euphausiids but i n c l u d e d some amphipods, copepods, chaetognaths and a few l a r v a l f i s h . This was t r u e at the depth of a c o u s t i c data c o l l e c t i o n f o r a l l nets used i n c l u d i n g those commonly employed f o r catching l a r g e r animals. D e t a i l s of the c o n s t r u c t i o n and operation of the sampling device used f o r the q u a n t i t a t i v e estimates of the biomass can be s u p p l i e d by Dr. B.McK. Bary of the I n s t i t u t e of Oceanography, • A A A . m).o A, -~A 20.0 SO.O 100.0 .120.0 ENERGY UPPER HYDROPHONE 1B0.0 ZOO 1 200 1 1 1 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE FIGURE 10A ^ " i " 1 1 80.0 100.0 120.0 ENERGY UPPER HYDROPHONE DISTRIBUTION CURVES FOR DATA UNITS 1 AND 2 80.0 ENERGY 100.0 120.0 UPPER HYDROPHONE —I 200 1 1 1 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE l 200 FIGURE 11A 80.0 100.0 120.0 ENERGY UPPER HYDROPHONE 200 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE FIGURE 11B DSITRIBUTION CURVES FOR DATA UNITS 3 AND 4 80.0 100.0 IZO.O ENERGY UPPER HYDROPHONE zoo 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE FIGURE 12A 20.0 1 1 1 80.0 100.0 120.0 ENERGY UPPER HYDROPHONE 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE i 1B0.0 FIGURE 12B D I S T R I B U T I O N CURVES FOR DATA UNITS 5 AND 6 1 1 1 1 I I I I I I 0 20 0 IJO.O 50.0 80.0 100.0 120.0 IMO.O 160.0 1B0.0 200.0 ENERGY UPPER HYDROPHONE o 200.0 ENERGY LOWER HYDROPHONE FIGURE 13A FIGURE 13B DISTRIBUTION CURVES FOR DATA UNITS 7 AND 8 43 1 1—: 1 80.Q 100.0 120.0 ENERGY UPPER HYDROPHONE U J m R-—1 1 1 I T 60.0 80.0 1O0.D 120.0 140.0 ENERGY LOWER HYDROPHONE FIGURE 14A az U J CD A-f\r 80.0 100.0 120.0 ENERGY UPPER HYDROPHONE - i WO.Q 80.0 100.0 120.0 ENERGY LOWER HYDROPHONE FIGURE 14B DISTRIBUTION CURVES FOR DATA UNITS 9 AND 10 44 U n i v e r s i t y of B r i t i s h Columbia. This instrument c o n s i s t e d of a c y l i n d r i c a l housing which contained a 40 mesh per i n c h net and a flow meter i n the t r a i l i n g end. S i g n a l s t r a n s m i t t e d from the ship through an e l e c t r i c towing cable were used to open a c i r c u l a r gate-valve i n the mouth of the sampler at the depth of i n t e r e s t , and c l o s e i t again before r e t r i e v a l of the apparatus. Continuous monitoring of the flow meter, pressure and temperature was achieved v i a s i g n a l s t r a n s m i t t e d up the cable. The mean number of euphausiids i n the volume of a c o u s t i c i n t e r e s t , computed from 20 hauls of the sampling device described above, was 1.0. The mean number of r e c e i v e d a c o u s t i c pulses (see chapter IV) at each hydrophone f o r each output t r a n s m i s s i o n was 1.1. Separate but supporting r e s u l t s are given i n f i g u r e 15 which shows three g r a p h i c a l sounding records obtained simultaneously on Wednesday June 26, 1968 at 0900 P a c i f i c standard time. These recordings were made by Ross sounders at frequencies of 44, 108, and 197 kHz; they show the strong frequency dependence of the s c a t t e r i n g l a y e r t h a t was studied (20-45 metres). The peak amplitude a c o u s t i c pressure from the t r a n s m i t t e r m e a s u r e d at the centre of the volumes by suspending a c a l i b r a t e d hydrophone at t h i s p o i n t , was 5 2 1.33 x 10 dynes/cm . The peak amplitude of a t y p i c a l FIGURE 15A 44 KHZ 41. MINUTES. FIGURE 15B 108 KHZ FIGURE 15C 197 KHZ GRAPHICAL SOUNDING RECORDS 46 euphausiid echo measured at the upper hydrophone, a dis t a n c e r =2.5 metres from the s c a t t e r e r , was 2 1.74 dynes/cm . Because the angle i s small between the l i n e of i n c i d e n t sound and the l i n e of sound r e f l e c t e d to the upper hydrophone, the back s c a t t e r e d peak amplitude pressure w i l l be very n e a r l y the same as the value given above f o r the upper hydrophone. The s c a t t e r i n g c r o s s - s e c t i o n i s defined by the formula: 4 n r 2 I s cr =•— where I s i s the i n t e n s i t y of the s c a t t e r e d wave at a dis t a n c e r from the s c a t t e r e r and I i s the i n t e n s i t y of the i n c i d e n t plane wave. The back s c a t t e r i n g c r o s s - s e c t i o n -4 2 of a t y p i c a l euphausiid at 102 kHz i s thus 1.35 x 10 cm . The i s o t r o p i c s c a t t e r i n g c r o s s - s e c t i o n (based on the p r e v i o u s l y described r a t i o of the t o t a l r e c e i v e d energies) -4 2 i s thus 0.88 x 10 cm . I I . CONCLUSIONS A p r i n c i p a l c o n c l u s i o n based on back and side s c a t t e r i n g from euphausiids and on the mathematical model, i s t h a t the p h y s i c a l cause of the s c a t t e r i n g c o n s i s t s of both a c o n t r a s t i n c o m p r e s s i b i l i t y between the animals and the surrounding water and a d i f f e r e n c e i n the r e s p e c t i v e d e n s i t i e s . 47 C o n c l u s i o n s o b t a i n e d from th e r a t i o o f the t o t a l energy r e c e i v e d i n t h e upper hydrophone t o t h e t o t a l energy r e c e i v e d i n t h e l ower hydrophone and e q u a t i o n (3) i n c h a p t e r I I a r e as f o l l o w s : two p o s s i b i l i t i e s e x i s t . A) I f Kj_ - K i s o f the same a l g e b r a i c s i g n as P i - p, t h e i n c o m p r e s s i b i l i t y c o n t r a s t i s r e s p o n s i b l e f o r 78-83 p e r c e n t (see e r r o r a n a l y s i s , appendix X I I I ) o f t h e s c a t t e r e d sound. The d e n s i t y c o n t r a s t i s r e s p o n s i b l e f o r t h e r e m a i n i n g 17-22 per c e n t . B) ' I f t h e d i f f e r e n c e s mentioned i n case A a r e o f o p p o s i t e s i g n , t h e i n c o m p r e s s i b i l i t y c o n t r a s t i s r e s p o n s i b l e f o r 3 0-31 p e r c e n t o f t h e s c a t t e r e d sound; th e d e n s i t y c o n t r a s t f o r 69-70 p e r c e n t . E n r i g h t (1963) has found t h a t the i n c o m p r e s s i b i l i t y o f e u p h a u s i i d s i s 15 p e r c e n t g r e a t e r t h a n th e i n c o m p r e s s -i b i l i t y o f sea w a t e r . F o r t h i s r e s u l t , o n l y case A c o u l d a ccount f o r a r e a l i s t i c v a l u e o f t h e d e n s i t y c o n t r a s t . Sheldon (page 6) has found t h a t l i v e e u p h a u s i i d s a r e a p p r o x i m a t e l y 3 per c e n t more dense t h a n sea w a t e r . H i s r e s u l t , f o r case A, agrees w i t h t h e i n c o m p r e s s i b i l i t y c o n t r a s t o f E n r i g h t . By s u b s t i t u t i n g i n t o e q u a t i o n (3) i n c h a p t e r I I 3 a f r e q u e n c y of 102 kHz, a volume o f 20 mm , t r a n s m i t t e d and r e c e i v e d p r e s s u r e s as d e s c r i b e d i n t h i s c h a p t e r and a mean range o f 2.5 m e t r e s , t h e r e s u l t a n t i n c o m p r e s s i b i l i t y 48 c o n t r a s t i s 8 per c e n t . Once a g a i n , o n l y case A c o u l d a c c o u n t f o r a r e a l i s t i c v a l u e o f t h e d e n s i t y c o n t r a s t . Lebedeva (1964) has e x p r e s s e d c o n c e r n about t h e p o s s i b l e p r e s e n c e o f gaseous f o r m a t i o n s w i t h i n t h e a n i m a l s d u r i n g h er e x p e r i m e n t . These b u b b l e s may have been caused by t h e e v a c u a t i o n p r o c e s s ; t h e y c o u l d i n d e e d a c c o u n t f o r her low v a l u e f o r t h e i n c o m p r e s s i b i l i t y o f the a n i m a l s . The d i s t r i b u t i o n c u r v e s shown i n f i g u r e s 10-14 a r e c h a r a c t e r i s t i c a t low energy v a l u e s o f t h e mean number o f r e c e i v e d echo p u l s e s i n each s i g n a l b l o c k and t h e r e f o r e w i t h t h e number o f a n i m a l s p e r c u b i c metre. F o r example, d a t a u n i t s 1, 4, 7, and 10 have mean v a l u e s o f g r e a t e r t h a n 1.5 d i s t i n c t echoes a t each hydrophone,, f o r each t r a n s m i t t e d p u l s e . The c u r v e s c o r r e s p o n d i n g t o t h e s e u n i t s a r e s i g n i f i c a n t l y d i f f e r e n t from t h o s e o f d a t a u n i t s 2, 3, 5, and 9 w h i c h have mean v a l u e s o f l e s s t h a n 1.0 d i s t i n c t echoes f o r each t r a n s m i t t e d p u l s e . I s o l a t e d s e c t i o n s o f t h e d i s t r i b u t i o n c u r v e s a t v e r y h i g h energy v a l u e s c o u l d o f t e n be a s s o c i a t e d w i t h s e q u e n t i a l echoes and perhaps t h e r e f o r e were caused by t h e p r e s e n c e w i t h i n t h e volume,of a n i m a l s l a r g e r t h a n e u p h a u s i i d s , perhaps f i s h . These s e c t i o n s o f d a t a were not used i n t h e energy r a t i o c a l c u l a t i o n s d e s c r i b e d p r e v i o u s l y . The sounding r e c o r d s i n f i g u r e 15 show, q u a l i t a t i v e l y , t h e s t r o n g dependence o f t h e s c a t t e r e d a c o u s t i c p r e s s u r e on 49 t h e f r e q u e n c y o f t r a n s m i s s i o n , as d e s c r i b e d by e q u a t i o n (3) i n c h a p t e r I I . The s c a t t e r i n g c r o s s - s e c t i o n i s p r o p o r t i o n a l t o t h e f o u r t h , p o w e r o f t h e i n c i d e n t f r e q u e n c y f o r s m a l l k a ( e q u a t i o n ( 3 ) , c h a p t e r I I ) . T h e r e f o r e th e commonly used sounders i n oceanography w i t h f r e q u e n c i e s a p p r o x i m a t e l y o n e - e i g h t h of t h e v a l u e used i n t h i s e x p e r i m e n t w i l l p r oduce, f o r an average s i z e z o o p l a n k t o n i c o r g a n i s m , a s c a t t e r i n g c r o s s -— 8 2 s e c t i o n o f t h e o r d e r o f 3 x 10 cm . Hersey and Backus (1962) s u g g e s t t h a t i t i s n e c e s s a r y t o have a t o t a l a c o u s t i c back s c a t t e r i n g c r o s s - s e c t i o n o f a t -4 2 l e a s t 2 x 10 cm f o r each c u b i c metre o f ocean, i n o r d e r t o a c c o u n t f o r "observed s c a t t e r i n g " . F i s h c o n c e n t r a t i o n s i n t h e ocean a r e o f t e n h i g h enough t h a t t h e i r a c o u s t i c c r o s s -s e c t i o n s a t 12 kHz exceed t h i s v a l u e ; i n d e e d t h e i r echoes a r e o f t e n o b s e r v e d a t t h i s f r e q u e n c y . On t h e o t h e r hand, based on t h e s c a t t e r i n g c r o s s - s e c t i o n o f e u p h a u s i i d s , i t now becomes d o u b t f u l t h a t e i t h e r t h e c o n c e n t r a t i o n s o f t h e s e a n i m a l s o r t h e s i g n a l - t o - n o i s e r a t i o s o f commonly used 12 kHz sounders a r e h i g h enough t o p e r m i t t h e a c o u s t i c d e t e c t i o n o f e u p h a u s i i d s a t t h i s f r e q u e n c y . I t now becomes p o s s i b l e , however, t o p r e d i c t t h e s c a t t e r i n g c r o s s - s e c t i o n o f z o o p l a n k t o n i c organisms as a f u n c t i o n o f t h e i r s i z e and o f t h e f r e q u e n c y of t h e i n c i d e n t sound and t h e r e b y t o p r e d i c t t h e optimum f r e q u e n c y and i n t e n s i t y o f i n c i d e n t sound f o r f u t u r e a c o u s t i c s t u d i e s o f t h e s e a n i m a l s . 50 BIBLIOGRAPHY Anderson, V.C., 1950: Sound s c a t t e r i n g from a f l u i d s p h e re. J . -Acoust".' Soc. Am., 22, 426-431. Andreeva, I.B., 1964: S c a t t e r i n g o f sound by a i r b l a d d e r s o f f i s h i n deep s o u n d - s c a t t e r i n g ocean l a y e r s . A k u s t . Zhur., 10 (1) , 20-24 ( i n R u s s i a n - t r a n s l . , 1964: S o v i e t P h y s i c s - A c o u s t i c s , 1 0 ( 1 ) , 17-20). Barham, E.G., 1966: Deep s c a t t e r i n g l a y e r m i g r a t i o n and c o m p o s i t i o n : o b s e r v a t i o n s from a d i v i n g s a u c e r . S c i e n c e , 151, 1399-1403. B a r y , B.McK., 1966: Back s c a t t e r i n g a t 12 k c / s i n r e l a t i o n t o biomass and numbers o f z o o p l a n k t o n i c organisms i n S a a n i c h I n l e t , B r i t i s h Columbia. Deep^-Sea Res., 13, 655-666. C l e b s c h , A., 1863: Uber d i e R e f l e x i o n an e i n e r K u g e l f l a c h e . J . , f u r Math., 61, 195-262. E n r i g h t , J.T., 1963: E s t i m a t e s o f t h e c o m p r e s s i b i l i t y o f some marine c r u s t a c e a n s . L i m n o l . & Oceanogr., 8 ( 4 ) , 382-387. H a r t o g , J..J. and G.C. K n o l l m a n , 1963: Measurement of underwater sound s c a t t e r e d from a f l u i d s p h e r e . J . A c o u s t . Soc. Am., 35, 538-541. H e r l i n v e a u x , R.H., 1962: Oceanography of S a a n i c h I n l e t i n Vancouver I s l a n d , B r i t i s h Columbia. J . F i s h .  Res. Bd. Canada, 1 9 ( 1 ) , 1-37. Hersey, J.B. and R.H. Backus, 1954: New e v i d e n c e t h a t m i g r a t i n g gas b u b b l e s , p r o b a b l y t h e swimbladders o f f i s h , a r e l a r g e l y r e s p o n s i b l e f o r s c a t t e r i n g l a y e r s on t h e c o n t i n e n t a l r i s e s o u t h o f New England. Deep-Sea Res., 1, 190-191. Hersey, J.B. and R.H. Backus, 1962: Sound s c a t t e r i n g by marine o r g a n i s m s . No.13 I n : The Sea: Ideas and O b s e r v a t i o n s on P r o g r e s s i n t h e Study o f t h e Sea. V o l . I , 498-539. M. H i l l ( E d i t o r ) , I n t e r s c i e n c e , New York. Hersey, J.B., H.R. Johnson and L.C. D a v i s , 1952: Recent f i n d i n g s about t h e deep s c a t t e r i n g l a y e r . J . Mar. Res. , 11, 1-9. Lebedeva, L.P., 1964: Measurement o f t h e b u l k modulus o f e l a s t i c i t y o f a n i m a l t i s s u e s . A k u s t . Zhur., 10 ( 4 ) , 479-480 ( i n R u s s i a n - t r a n s l . 1965: S o v i e t P h y s i c s - A c o u s t i c s , 1 0 ( 4 ) , 410-411). Logan, N.A., 1965: Survey o f some e a r l y s t u d i e s o f t h e s c a t t e r i n g o f p l a n e waves by a sphere. P. IEEE., 53 (2) , 773-785. Machlup, S., 1952: A t h e o r e t i c a l model f o r sound s c a t t e r i n g by marine c r u s t a c e a n s . J . A c o u s t . Soc. Am., 24, 290-293. R a y l e i g h ( S t r u t t , J.W.), 1878: The Theory o f Sound. M a c m i l l a n (Dover P u b l i c a t i o n s , I n c . , New Y o r k , 1945, 2, 282-284). Schoch, A., 1950: S c h a l l r e f l e x i o n , S c h a l l b r e c h u n g und S c h a l l b e u g u n g . Ergeb. E x a k t . Naturw., 23, 206-20 T o l s t o y , I . and C.S. C l a y , 1966: Ocean A c o u s t i c s . M c G r a w - H i l l , New York. 52 APPENDIX I SOUND SCATTERING FROM A FLUID SPHERE: THE SOLUTION OF SCHOCH 2 U s i n g c = K/p, x = ka and y = k-^a, A n becomes A = -A(2n+1) ( - i ) n P°Jn(x)JA(y) - PjCj Jn ( x) Jn (y) pch n(x)JA(y) - P i C i h ^ x ) j n ( y ) We now use t h e s e r i e s e x p a n s i o n s f o r j n and h n . S o l v i n g f o r Ag and u s i n g J n ( z ) = n/z J n ( z ) '~ J n + i ^ 2 ) A = -A(-pcy/3 + pjCjx/3) - p c ( l - i / x ) y / 3 + p i C i ( - i / x 2 ) = - A i x 2 ( p i C i x - pcy) 3piCj_ - pcxy(l+ix) S u b s t i t u t i n g x = wa/c and y = oia/c . 3 , 2 2, A 0 _ - A i x ( p i C i - pc ) 3 P i c i ~ p c 2 x 2 ( 1 + i x ) S o l v i n g f o r A, and u s i n g j * <z) = j . (z) - (n+ l ) / z j„(z) i " n-1 1 1 3 A = -Ax (pcx - P i C i y ) 2p^c^y + cx and s i m i l a r l y 3 = -Ax (p - pj) 2pi + p U s i n g t h e a s y m p t o t i c form o f h n ( k r ) and s u b s t i t u t i n g i n t h e g e n e r a l s o l u t i o n , t h e d e s i r e d r e s u l t i s o b t a i n e d . 53 APPENDIX I I ACOUSTIC ENERGIES FROM ADDED SPHERES Let P^ be the a c o u s t i c pressure s c a t t e r e d from one f l u i d sphere, as described i n chapter I I . P-^  may be w r i t t e n as Aa^e"""^^ where 'a' i s the sphere r a d i u s . Let the sphere be l o c a t e d at the centre of the right-hand coordinate system x - y - z , . o r i e n t e d such t h a t the i n c i d e n t plane wave approaches along the z - a x i s . Let R be the po i n t of r e c e p t i o n , l o c a t e d i n the x-z plane, a di s t a n c e r from the centre of the sphere and i n c l i n e d to the z-axis by angle 6. Consider a second sphere a di s t a n c e d-^  from the f i r s t and i n c l i n e d to the z-axis by angle a|'. Let 01 be the sum Z FIGURE 16 ACOUSTIC ENERGIES FROM ADDED SPHERES 54 o f t h e a n g l e s o f i n c i d e n c e and r e f l e c t i o n f o r t h e second sphere and r^_ t h e d i s t a n c e from t h e sphere c e n t r e t o t h e p o i n t o f r e c e p t i o n . The a c o u s t i c p r e s s u r e r e f l e c t e d from t h e two spheres ( n e g l e c t i n g t h e mutual a c o u s t i c impedance o f t h e spheres) may be w r i t t e n : P 2 = A a 3 e i ( w t - k r ) + A i a J e i ( u t - k E l + k d l C O S a l > I t i s assumed t h a t d]_<<r, 6j_~ 6 and 1/r-^ - 1/r so t h a t A^ - A. " T h e r e f o r e : P 2 = Ae i (cot-kr) 3 , 3 i k ( r - r i + d i c o s a T ) a + a]_e 1 1 1 (1) The d i s t a n c e R - S± can be w r i t t e n : 2 2 2 2 2 2 r-j_ = (d^sinacos<f)^+rsine) +d£sin a-j_sin <t>]_+ (d^cosa-rcosO) and f o r d^ s m a l l , can be reduced t o : r - = d}_ ( c o s a ^ c o s e - sina-j_cos<f>-]_sin6) S u b s t i t u t i n g (2) i n t o (1) (2) P 2 = Ae i (cot-kr) 3.3 i k d n (cosa, +cosa n cos8-sina, cosd), s i n e ) a +a-je ± 1 1 1 Y l S i m i l a r l y : n+l : ^ A e i (cot-kr) a3 + ^ L ^ a 3 e i k d n (cosa n+cosa ncose-sina ncos<(> nsin6) The energy E n + 1 i s t h e p r o d u c t o f P n + 1 and i t s complex c o n j u g a t e . For random orientation i n the x - y plane the average energy received at point R from (n+1) spheres becomes: k d n (cosa n+cosa ncos 6-sinancos<j>nsin0) +1 a s i n j n ,n=.J kd (cosa +cosa cos0-sina cosd> sine) n n ; .n n Y n d* ( A l l of the following discussions and re s u l t s are concerned with the r a t i o of two energies at two d i f f e r e n t values of 6. The computations i n appendix III involve these energy r a t i o s for various values of the r a d i i a n , distances d and orientation angles a . n n 56 APPENDIX I I I COMPUTER STUDIES OF BIOLOGICAL SCATTERING I n t r o d u c t i o n . F i g u r e I i n c h a p t e r I I shows t h e shape o f t h e e u p h a u s i i d and i n c l u d e s t h e geometry used f o r t h e f o l l o w i n g c o m p u t a t i o n s . T h i s s e c t i o n w i l l i n c l u d e d e s c r i p t i o n s and r e s u l t s o f programs d e s i g n e d t o compute: I . The number o f s i g n i f i c a n t spheres I I . The i n f l u e n c e o f s i z e o f spheres I I I . The i n f l u e n c e o f v e r t i c a l o r i e n t a t i o n Each a n a l y s i s c o n c e r n s i n t e r f e r e n c e phenomena t a k i n g p l a c e d u r i n g i s o t r o p i c s c a t t e r i n g and i n c l u d e s d a t a c o r r e s p o n d i n g t o t h e e x p e r i m e n t a l c o n f i g u r a t i o n o f r e c e i v e r s and t o t h e i n c i d e n t f r e q u e n c y . The r a t i o o f energy r e c e i v e d a t 0^ = 0.262 t o t h e r e c e i v e d a t 0 2 = -1.57 i s computed f o r i n c i d e n t wave number k = 4.28 ( c . g . s . ) . I . THE NUMBER OF SIGNIFICANT SPHERES F o r t r a n IV program SCTREI (see appendix IV) has been used t o s t u d y t h e energy r a t i o s f o r from 2 t o 26 spheres a c c o r d i n g t o f o r m u l a ( 3 ) r a p p e n d i x I I . The f i r s t 11 spheres comprise t h e body o f t h e e u p h a u s i i d , t h e r e m a i n i n g spheres r e p r e s e n t t h e p l e o p o d s . The r e s u l t s o f t h e s e c o m p u t a t i o n s i n d i c a t e t h a t spheres o t h e r t h a n t h o s e l o c a t e d w i t h i n t h e main body have n e g l i g i b l e i n f l u e n c e on t h e energy r a t i o . 57 II . THE INFLUENCE OF SIZE OF SPHERES Program SCTRE2 has been used to study the energy r a t i o for the number of s i g n i f i c a n t spheres, found i n the previous section, using d i f f e r i n g sizes of animals. Distances d n are adjusted so that the largest separation d-^, from the eye to the t a i l , varies from 20 to 2000 millimetres. The results indicate that the energy r a t i o remains less than 1.24 when the animals' cephalothorax l i e s i n the horizontal plane. II I . THE INFLUENCE OF VERTICAL ORIENTATION Program SCTRE3 has been used to study the influence of v e r t i c a l orientation of each animal. The size corresponding to the maximum r a t i o i n section II was used. The values of a were incrimented by a few degrees. The re s u l t s indicate that for a d i s t r i b u t i o n of orientations, normal about the horizontal, with a standard deviation of 15 degrees, the energy r a t i o mean for animals centred i n the volumes i s 1.08 ± 0.01. By numerical integration throughout the volumes, the energy r a t i o mean i s 1.04 ± 0.01. The pressure r a t i o mean i s therefore 1.02 ± 0.01. This figure w i l l be used as a correction for the experimental r e s u l t s . . APPENDIX IV FORTRAN SOURCE LIST 58 [ SN SOURCE STATEMENT 0 * $IBFTC SCTRE1 * C- -B =' RADIUS* C = WAVE NO. , G = LIMIT OF INTEGRATION * C -D = DISTANCE TO SPHERE CENTRE E = INCLINATION OF SPHERE 1 DIMENSION B128), THETA(2), D{28), E(28) 2 * COMMON L . . 3 * READ 4000 »BZ t ( B ( J ) » J = l , 2 8) »C, G ,THETA ( 1 ) t THETA ( 2 ) 10 READ 4000,, (D(J),J-1,28) »(E(J),J=1»28) 21 * 3 J = 1 22 * L = 1 23 PRINT 4010 24 5 1 = 1 . . .. . * C — — -START OF INTEGRATION 25 10 M = 10. * G 26 * M = M/2 : 27 M = 2 * M 30 FZERO= (BZ**3 + SUM1(0. ,B, C D , E, THETA))**2+SUM2(0.,B,C,DtE,THETA)**2 31 * XM = M 32 * H = G/XM 33 * X = H 34 T = 0. 35 * F = 0. 36 * K ' = 1 37 * 40 F0FX=(BZ##3+SUM1(X,B,CD,E,THETA) ) **2+SUM2J X» 8»Ci D.» E» THETA ) **2 40 F = F + FOFX 41 * X = X + H 42 * FOFX = < BZ**3 + SUM1(X,B,C,D,E,THETA) ) **2+SUM2(X,B,C,D,E,THETA)**2 43 T = T + FOFX 44 * X = X + H 45 * K = K + l . . . .. 46 * IF (K.LE.M/2) GO TO 40 51 * GO TO (60,70), I i 52 45 IF (I.EQ.2) GO TO 50 55 * RN = ((FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 56 * THETA ( 1 ) = THETA (.2J 57 * 1 = 2 . . . . ........ 60 * GO TO 10 61 50 RD = {(FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 62 * R = RN/RD 63 GO TO 80 64 * 60 EMINU= (BZ*,*3 + SUM1 (0. , B ,C D , E , THETA ) )**2+SUM2(0. , B, C D , E , THETA ) **2 65 GO TO .45 _ . . . 66 70 EMINL=(BZ**3 + SUMH0., B,C,D,E,THETA))**2+SUM2(0.,B,CD,E,THETA)**2 67 * GO TO 45 70 * 80 J = J+l 71 * PRINT 4005,J,R,RN,RD,EMINU,EMINL 72 L=L + 1 73 THETA(1) = 0.175 74 IF (L.EQ.29) GO TO 90 77 * GO TO 5 100 90 STOP 101 * 4000 FORMAT (12F6.0) 102 4005 FORMAT (1H0,I10,F20.3,2X,4F20.10) 103 4010 FORMAT (1H1,2X,14HN0. OF SPHERES,5X,12HENERGY RATIO,10X, 1.8HE. UPPER,12X,8HE. LOWER,14X,5HEMINU,15X,5HEMINL) 104 END ISN SOURCE STATEMENT FORTRAN SOURCE LIST 0 * $IBFTC SUM1 1 * FUNCTION SUM1<X,B,C,D,E,THETA)  2 * COMMON L 3 * DIMENSION B ( 6 ) , 0 ( 6 ) , E ( 6 ) , THETA(2) 4 * SUM1 = 0 . 5 * DO 20 N = l t L 6 * 20 SUM1 = SUM1 + B(N)**3*C0S(C*D(N)*.(C0S(E{N> ) * 1+C0S(E(N))»C0S(THETA(1))-SIN(E(N))*COS(X)*SIN(THETA ( 1 ) ) ) ) 10 * RETURN 11 * END NO MESSAGES FOR ABOVE ASSEMBLY 08MIN 23.ASEC ISN SOURCE STATEMENT FORTRAN SOURCE LIST 60 0 * $I8FTC SUM2 1 * FUNCTION SUM2(X,B,C,D,E,THETA)  2 * COMMON L 3 * DIMENSION 8 ( 6 ) , D ( 6 ) , E ( 6 ) , THETA(2) 4,* SUM2 = 0 . 5 * DO 30 N = 1,L 6 * 30 SUM2 = SUM2 + B(N)**3*SI N(C*D(N)*(COS(E<N) ) * 1+C0S(E(NH*C0S(THETA(1) )-SIN(E(N) )*COS(X)*SIN(THETAt 1 ) ) ) ) 10 * RETURN 11 * END *N0 MESSAGES FOR ABOVE ASSEMBLY 00 PB450 i ISN SOURCE STATEMENT FORTRAN SOURCE LIST 61 0 * $IBFTC SCTRE2 C- — . — B = RADIUS, C = WAVE NO., G = LIMIT OF INTEGRATION C- D = DISTANCE TO SPHERE CENTRE E = INCLINATION OF SPHERE 1 DIMENSION B( 50) ,D( 50) , E( 50 ) ,STUF1.( 50 ) ,STUF2( 50) ,STUF3(50), 1_STUF4(50) ,01 (50) ,R(200) 2 * COMMON L 3 READ 1000f.BZt (B( J) , J = l,10) 10 READ 1001,C,G,THETA1,THETA2 11 READ . 1002 »(D(J),J=l,10) 16 READ-1002,(E(J),J=1,10) 23 * BZ3 = BZ*BZ*BZ . . . . 24 5 L = 10 25 * SIZE =. 0.0 26 * DO 7 J = 1,L 27 7 D K J ) = D(J) 31 * EMA = 0. ; 32 DO 8 N = 1 , L • • . 3 3 8 EMA = EMA + BCN)*B(N)*B(N). 35 EMAX = (B Z 3 + EMA)*(BZ3 + EMA) 36 PRINT 1005,BZ„(B(J),J=l, 10) 43 * PRINT 1006,C,G,THETAl,THETA2 44 * PRINT 1007,(D(J),J=1,10) . 51 PRINT 1008, (E( J) , J = 1,10) _ .... . .... . ... ._ . 56 * PRINT 1009,(EMAX) • 63 * PRINT 1010 64 NN = 1 65 * 10 DO 15 N = 1,L 66 STUFKN) =. C*D(N)*(COS(E (N) )+COS(E(N) ) *COS ( THET A1) > 67 STUF2(N) = C*D(N)*SIN(E(N))*SIN{THETAl) 70 * STUF3(N) =. C*0(N)*{COS(E(N) )+C'0S(E(N))*C0S(THETA2) ) 71 * 15 STUF4(N) = C*D(N)*SIN(E(N)) *SIN(THETA2) 73 * 30 1 = 1 * C- •START OF INTEGRATION ; 7 A * 35 M = 10. * G 75 M = M/2 ...... . . . . . 76 * M = 2 * M 77 FZERO =(BZ3 +SUM1 (0. ,-B, S TUF1, STUF2 ) ) **2 + SUM2(0.,8, STUF 1, STUF2 ) **2 100 * XM = M 101 H = G/XM 102 * X = H 103 T = 0. 104 * F = 0. 105 K = 1 106 * 40 FOFX = (BZ3+SUM1(X,B,STUFl,STUF2))**2+SUM2(X,B,STUF1,STUF2)**2 107 * F = F + FOFX 110 * X = X + H 111 * FOFX = (BZ3+SUM1(X,B,STUF1,STUF2))**2+SUM2(X,B,STUF1,STUF2)**2 112 * T = T + FOFX 113 * X = X + H 114 K = K + 1 115 IF (K.LE.M/2) GO TO 40 120 t GO TO (60,70), I 121 * 45 IF ( I.EQ.2) GO TO 50 124 RN = ((FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 125 * DO 48 N = 1,L FORTRAN SOURCE LIST SCTRE2 62 ISN SOURCE STATEMENT 126 STUFKN) = STUF3(N) 127 48 STUF2IN) = STUF4(N) 131 * I = 2 132 GO TO 35 133 50 RO = {{FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 134 * R(NN) = RN/RD 135 * RR = RD/RN 136 * GO TO 80 137 60 EMAXU = (BZ3+SUM1(0.,B,STUF1,STUF2))**2+SUM2(0.,B,STUF1 ,STUF2)**2 140 * GO TO 45 141 * 70 EMINL = (BZ.3 + SUMl{p.»B,STUF.l,STUF2) )**2+SUM2(0. ,B,STUF1 ».STUF2)**2. 142 RMAX =. EMAXU/EMINL 143 * GO TO 45 144 80 SIZE = SIZE + 0.2 > 145 * PRINT 1020,SIZE,R(NN),RR,RN,RD,EMAXU,EMINL,RMAX 146 90 NN = NN + 1 147 IF (NN.EQ.25) GO TO 110 V 152 * DO 100 J = 1,L 153 100 D(J) = D1I.J) * FLOAT (NN) 155 GO TO 10 > 156 110 STOP 157 * 1000 FORMAT (11.F6.0) 160 * 1001 FORMAT (4F6.0) 161 * 1002 FORMAT (10F6.0) 162 * 1005 FORMAT (1H0,8HRADII = ,11F8.2) 163 1006 FORMAT (1H0.11HWAVE NO. = ,F5.2,2X,4HG = ,F5.2,2X, * 1 9HTHETA1 = , F5.3,2X,9HTHETA2 = ,F5.2) 164 1007 FORMAT (1H0,21HDISTANCE TO CENTER = ,10F8.4) 165 * 1008 FORMAT (1H0,14HINC LINATION = ,10F8.2) 166 1009 FORMAT (1H0,54HMAXIMUM ENERGY FROM 11 SPHERES WITH NO INTERFERENCE - * 1 = ,F8.3) 16 7 1010 FORMAT (1H0,9HLENGTH CM,3X,15HE.UPPER/E.LOWER, 1 2X,15HE.LOWER/E.UPPER,2X,7HE.UPPER,2X,7HE.LOWER,2X,7HE .MAX.U,2X, * 2 7HE.MIN.L,2X,15HE.MAX.U/E.MIN.L) 170 * 1020 FORMAT. (1H0,F6.1,2F17.3,6X,4F9.3,F11.3) 171 t END USER FUNCTION SUBPROGRAM REFERENCES SUM2 •NO MESSAGES FOR ABOVE ASSEMBLY 09MIN 07.0SEC FORTRAN SOURCE LIST 63 ISN SOURCE STATEMENT 0 $IBFTC SUM1 . 1 FUNCTION SUM1(X,B,STUF1,STUF2) > i 2 t- COMMON L j 3 DIMENSION B(20),STUF1(20),STUF2(20) . SUM1 = 0. 1 5 * DO 500 N = 1,L i 6 * 500 SUM1 = S U M 1 + B ( N ) * B ( N ) * B ( N ) * C 0 S ( S T U F 1 ( N ) - S T U F 2 ( N ) * C 0 S ( X ) ) 10 * RETURN 11 END NO MESSAGES FOR ABOVE ASSEMBLY > 09MIN 21.7SEC SOURCE STATEMENT FORTRAN SOURCE LIST 64 0 * SIBFTC SUM2 1 * FUNCTION SUM2(X,B,STUF1,STUF2)  2 * COMMON L 3 * DIMENSION B(20),STUF1(20),STUF2(20) 4 * SUM2 = 0. 5 * DO 600 N = 1,L 6 * 600 SUM2 = SUM2+B(N)*B(N)*B(N)*SIN<STUF1(N)-STUF2(N)*C0S(X)) 10 * RETURN  11 * END NO MESSAGES FOR ABOVE ASSEMBLY 00 PC120 FORTRAN SOURCE LIST 65 1 SN SOURCE STATEMENT 0 * $IBFTC SCTRE3 C- B = RADIUS, C = WAVE NO., G = LIMIT OF INTEGRATION * C- D = DISTANCE TO SPHERE CENTRE E = INCLINATION OF SPHERE 1 DIMENSION 8(50) ,0(50) iE-( 50) fSTUF 1.(50 ),STUF2( 50) ,STUF3(50), 1STUF4(50).,D1 (50) ,R(200) 2 COMMON L 3 READ 1C00,BZ, (B( J) , J=l ,10) 10 * READ 1001,C,G,.THETA1,THETA2. 11 READ 100 2 , ( D ( J ) , J = l , 1 0 ) 16 * READ 1002,(E(J),J=1,10) 23 BZ3 '= BZ*BZ*BZ . ... ... . 24 5 L = 10 25 * DO 7 J •= 1,L 26 7 D(J) = OU) * 9. 30 * EMA = 0. 31 DO "8 N = 1.,L 32 8 EMA = EMA + B(N)*B(N)*B(N ) 34 * EMAX = (BZ3 + EMA)*(BZ3 + EMA) 35 PRINT 1005,BZ,(B(J),J=1,10) 42 PRINT 1006,C,G,THETA1,THETA2 43 * PRINT 1007,<D(J),J=1,10) 50 PRINT 1008,(E(J),J=1,10) 55 * PRINT 1009, (EMAX) 62 PRINT 1010 63 NN = 1 64 * 10 DO 15 N = 1,L 65--* STUFKN) = C*D(N)*(COS(E (N ) )+COS(E(N) ) *COS(THETA1) ) 66 STUF2(N) = C*D(N)*SIN(E(N))*SIN(THETA1) 67 STUF3(N) =. C*D(N)*(COS(E(N) )+COS(E.(N) )*COS(THETA2) ) 70 * 15 STUF4(N) =. C*D(N)*SIN(E( N ) ) * S I N ( THE T A2 ) 72 30 I = 1 * C- START OF INTEGRATION 73 * 35 M = 10. * G 74 * M = M/,2 -75 * M = 2 * M . ... - _ ..... .. 76 * FZERO =(BZ3 + SUMKO. , B , S TU F1, S TUF2 ) )**2 + SUM2(0. , B, STUF 1 , STUF2 ) **2 77 * XM = M 100 H = G/XM 101 * . X = H 102 * T = 0. 103 F = 0. 104 * K = 1 105 * 40 FOFX = (BZ3 + SUM1(X,B,STUF1,STUF2).)**2+SUM2(X,B,STUF1,STUF2)**2 106 * F = F + FOFX 107 X = X + H 110 FOFX = (BZ3+SUM1(X,B,STUF1,STUF2))**2+SUM2(X,B,STUF1,STUF2)**2 111 * T = T. + FOFX 112 X = X + H 113 K = K + 1 114 * IF (K.LE.M/2) GO TO 40 117 * GO TO (60,70) ,. I 120 * 45 IF (I.EQ.2) GO TO 50 123 * RN = ((FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 124 DO 48 N = 1,L 125 STUFKN) =. STUF3(N) FORTRAN SOURCE LIST SCTRE3 66 ISN SOURCE STATEMENT 126 * 48 STUF2(N) = STUF4(N) 130 * I = 2  131 * GO TO 35 132 * 50 RD = {(FZERO + 4.*F + 2.*T - FOFX)*H/3.)/G 133..* R.(NN) = RN/RD 134 * RR = RD/RN 135 * GO TO 80 136 * 60 EMAXU = (BZ3+SUM1(0.,B,STUF1,STUF2))**2+SUM2(0.,6,STUF1,STUF2)**2 137 * GO TO 45 140 * 70 EM INL = (BZ3+SUM1(0.,B,STUF1,STUF2))**2+SUM2(0.,B,STUF1,STUF2)**2 141 * RMAX = EMAXU/EMINL 142 * GO TO 45 143 * 80 ANG = E l l ) * 57.3 144 * PRINT 1020,E(1),ANG,R(NN),RR,RN,RD,EMAXU,EMINL,RMAX  145 * 90 NN = NN + 1 146 * IF (NN.EQ.25) GO TO 110 151 * DO 100 J = 1 ,L 152 * 100 E{J > = E(J) + 0.2618 154 * GO TO 10 155 * 110 STOP  156 * 1000 FORMAT ( U F 6 . 0 ) 157 * 1001 FORMAT (4F6.0) 160 * 1002 FORMAT (10F6.0) 161 * 1005 FORMAT (1H0,8HRADII = ,11F8.2) 162 * 1006 FORMAT (1H0.11HWAVE NO. = ,F5.2,2X,4HG = ,F5.2,2X, * 1 9HTHETA1 = , F5.3,2X,9HTHETA2 = ,F5.2) 163 * 1007 FORMAT (IHO,2IHDISTANCE TO CENTER = ,10F8.4) 164 * 1008 FORMAT (IHO,14HINCLINATION = ,10F8.2) 165 * 1009 FORMAT {IHO,54HMAX I MUM ENERGY FROM 11 SPHERES WITH NO . INTERFERENCE * 1 = ,F8.3) 166 * 1010 FORMAT <IHO,6HANG-S1,2X,14HANG-S1 DEGREES,2X,15HE.UPPER/E.LOWER, * 1 2X,15HE.LOWER/E.UPPER,2X,7HE.UPPER,2X,7HE.LOWER,2X,7HE.MAX.U,2X, USE * 2 7HE.MIN.L,2X,15HE.MAX.U/E.MIN.L) 167 * 1020 FORMAT (IHO,F6.2,F10.0,2F17.3,6X,4F9.3,F11.3) 170 * END . . . ... R FUNCTION SUBPROGRAM REFERENCES SUM2 NO MESSAGES FOR ABOVE ASSEMBLY 00 LB230 67 APPENDIX V ACOUSTIC OUTPUT AND RECEIVER SYSTEMS Output system. The a c o u s t i c p u l s e s a r e g e n e r a t e d by a c r y s t a l t r a n s d u c e r , d e s i g n e d f o r depths up t o 500 f e e t , and a model 200 " f i n e l i n e " t r a n s c e i v e r and r e c o r d e r , b u i l t by Ross L a b o r a t o r i e s , I n c . , S e a t t l e , Washington. On coinmand by a t h i r t y v o l t square wave, from a Wavetek f u n c t i o n ,6 g e n e r a t o r , t h e t r a n s c e i v e r d e l i v e r s a 300 w a t t , 102 kHz e l e c t r i c a l p u l s e t o t h e t r a n s d u c e r . The c r y s t a l s respond w i t h a r i s e t i m e o f 35 m i c r o s e c o n d s , a p u l s e d u r a t i o n o f 70 m i c r o s e c o n d s and a decay time o f 35 m i c r o s e c o n d s , d e l i v e r i n g a t o t a l power o f a p p r o x i m a t e l y 100 a c o u s t i c w a t t s t o t h e w a t e r . F o l l o w i n g t h e main a c o u s t i c b u r s t i s a low energy r i n g i n g w h i c h l a s t s f o r 22 0 m i c r o s e c o n d s but w h i c h c o n t r i b u t e s o n l y a few p e r c e n t t o t h e t o t a l a c o u s t i c energy o f t h e t r a n s m i t t e d s i g n a l . The t r a n s d u c e r was c a l i b r a t e d a t t h e Underwater Weapons Range L a b o r a t o r y , P a t r i c i a Bay, B.C., u s i n g a s t a n d a r d c a l i b r a t e d LC-32 r e c e i v e r a t a t e s t d i s t a n c e o f n i n e f e e t , i n an a n e c h o i c t a n k . The t r a n s m i t t i n g s e n s i t i v i t y 2 a t 102 kHz i s 106.3 db w i t h r e f e r e n c e t o 1 dyne/cm /ampere a t 1 y a r d . L o b a l diagrams were o b t a i n e d by r o t a t i n g t h e t r a n d u c e r about each o f two p e r p e n d i c u l a r f i x e d a x e s , 68 w h i l e r e c o r d i n g t h e r e c e i v e d s i g n a l on a p o l a r p l o t t i n g d e v i c e c o u p l e d t o t h e r o t a t i o n motor. The l o b a l p a t t e r n s t h u s o b t a i n e d a r e shown i n f i g u r e s 4 and 6. R e c e i v e r system. The LC-32 hydrophone r e c e i v e r s were manufactured by A t l a n t i c R e search C o r p o r a t i o n , A l e x a n d r i a , V i r g i n i a . The r e c e i v i n g s e n s i t i v i t i e s a t t h e end o f 7.6 metres o f c o a x i a l c a b l e , c a l i b r a t e d by the m a n u f a c t u r e r and i n a t a n k a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , a r e b o t h -109 db w i t h r e f e r e n c e t o 1 v o l t / d y n e / c m (open c i r c u i t v o l t a g e ) , a t 102 kHz. Hydrophone #609 was always used i n t h e upper p o s i t i o n , #6 08 always used i n t h e l o w e r . The r e c e i v e r s were co n n e c t e d t o A t l a n t i c R e s e a r c h C o r p o r a t i o n tuned LG-1030 p r e a m p l i f i e r s , s e r i a l numbers 101 and 102, w h i c h have v o l t a g e g a i n s o f 61.1 and 60.7 db r e s p e c t i v e l y , a t 102 kHz. The a m p l i f i e r s a r e two-stage p o t t e d u n i t s each powered w i t h two 6.75 v o l t mercury b a t t e r i e s . The o u t p u t t e r m i n a l s a r e connected t o 145 metres o f #908 - 25, 42 ohm, 40 p f / f t . , low n o i s e c o a x i a l c a b l e , w h i c h i s t e r m i n a t e d a c r o s s 2020 ohms. Gains o f the p r e a m p l i f i e r s and c a b l e s were measured r e p e a t e d l y d u r i n g t h e e x p e r i m e n t u s i n g a 102 kHz s i n e wave i n p u t . The o u t p u t o f t h e c a b l e s , a c r o s s 202 0 ohms, was measured on a c a l i b r a t e d T e k t r o n i x 549 o s c i l l o s c o p e . A m p l i f i e r #101 was always used w i t h the upper hydrophone ( s e r i a l #609). Amplifier #102 was always used with the lower hydrophone ( s e r i a l #608). 70 APPENDIX VI RECORDING AND MONITORING SYSTEMS R e c o r d i n g system. A c o u s t i c , t r i g g e r and c a l i b r a t i o n s i g n a l s were r e c o r d e d on an Ampex FR-1300, 14 c h a n n e l tape r e c o r d e r . D i r e c t r e c o r d and re p r o d u c e a m p l i f i e r s were used i n a l l c a s e s . Tape speed was 60 i n c h e s p e r second. A one v o l t peak-to-peak, c a l i b r a t i o n s i g n a l was r e c o r d e d on a l l c h a n n e l s and t h e r e c o r d a m p l i f i e r s were t h e r e a f t e r always used w i t h t h e same c h a n n e l s . Record a m p l i f i e r g a i n s were untouched d u r i n g t h e ex p e r i m e n t . The upper hydrophone s i g n a l - appears on c h a n n e l s 1, 4, 7, and 10, t h e lo w e r on c h a n n e l s 2, 5, 8, and 11. The t r i g g e r s i g n a l was r e c o r d e d on c h a n n e l s 3, 6, 9, and 12. M o n i t o r i n g system. Near t h e r e c o r d heads o f the FR-1300 a r e s i t u a t e d r e p r o d u c e heads. I t was t h e r e f o r e p o s s i b l e t o r e p l a y and m o n i t o r a l l s i g n a l s d u r i n g t h e r e c o r d i n g p r o c e s s . A t e k t r o n i c 549 o s c i l l o s c o p e , t o g e t h e r w i t h a p o l a r o i d o s c i l l o s c o p e camera, were used f o r m o n i t o r i n g . 71 APPENDIX V I I REPRODUCE AND ANALOG SYSTEMS Reproduce system. The c a l i b r a t i o n s i g n a l , r e c o r d e d d u r i n g d a t a c o l l e c t i o n , on each c h a n n e l o f t h e c a l i b r a t i o n t a p e , i s a one v o l t peak-to-peak,.102.0 kHz s i n e wave. The r e p r o d u c e a m p l i f i e r s were a d j u s t e d f o r each c h a n n e l such t h a t t h e c a l i b r a t i o n s i g n a l was i d e n t i c a l i n a m p l i t u d e t o t h e s i g n a l r e c o r d e d a t sea. The re p r o d u c e tape speed was f i f t e e n i n c h e s p e r second. S t a n d a r d p r e c a u t i o n s and t e c h n i q u e s were used d u r i n g h a n d l i n g o f a l l a n a l o g t a p e s . A n a l o g system. The s i g n a l s from t h e FR-1300 re p r o d u c e modules were con n e c t e d t o t h e i n p u t phone j a c k s o f GR 1554-A band pass f i l t e r s . The n a r r o w e s t band was used w i t h a c e n t r e f r e q u e n c y o f 25.5 kHz and f r e q u e n c y r e s p o n s e c h a r a c t e r i s t i c s o f -10 db a t 23.0 and 28.0 kHz. The o u t p u t s i g n a l s from each o f t h e GR f i l t e r s were t h e n connected t o t h e c i r c u i t i n f i g u r e 17, c o n s t r u c t e d u s i n g P 85 AU o p e r a t i o n a l a m p l i f i e r s and a P h i l b r i c h RP - M a n i f o l d . GR FILTER O.OI/jf O.OIyUf IOK 85 AU 2K IOK P 8 5 AU A/D CONVERTER FIGURE 17 SCHEMATIC OF ANALOG NETWORK 73 APPENDIX V I I I A/D CONVERSION AND DIGITAL PROCESSING SYSTEMS The output s i g n a l s from the analog networks as shown i n f i g u r e 9B were the input to channels 1 and 2 of the U.B.C. I n s t i t u t e of Oceanography analog to d i g i t a l converter. This instrument c o n s i s t s of a D i g i t a l Equipment Corporation 10-bit u n i p o l a r a n a l o g - d i g i t a l converter and the appropriate i n t e r f a c i n g necessary t o d e l i v e r the d i g i t a l i n f o r m a t i o n to the computer. The conversion pulses from the Wavetek 116 Function generator were i n i t i a t e d by the +Gate A delay t r i g g e r from the o s c i l l o s c o p e . S i x t y - f o u r 10 v o l t square waves were produced at 14.0 kHz and used to i n i t i a t e t h i r t y - t w o conversions on each channel. The output from the converter was r e c e i v e d by a C o n t r o l Data 8092 computer at the U n i v e r s i t y of B r i t i s h Columbia Computing Centre. The d i g i t a l i n f o r m a t i o n was stored i n the 8092 and then p r i n t e d on three d i g i t a l tapes at r a t e s of 556 b i t s per i n c h and seven echoes per block. The d i g i t a l tapes were read by the 7044 computer using the Map Ocean Subroutine w r i t t e n by J.R. Wilson f o r reading Ocean format d i g i t a l tapes produced by the CDC 8092 during A t o D conversion runs. Aspects of the c a l l i n g sequences t h a t are important f o r the remainder of the d i g i t a l 74 programs a r e as f o l l o w s . C a l l Ocean 1 s e a r c h e s f o r t h e d e s i r e d f i l e o f t h e d a t a t a p e and t e r m i n a t e s t h e p r o c e s s i n g a f t e r a s e t number of e r r o r s . C a l l Ocean 2 r e a d s t h e d i g i t a l d a t a , r e t u r n s a s i g n a l (IND = 1) when an end o f f i l e mark i s e n c o u n t e r e d and r e t u r n s a second s i g n a l (IND = 2) f o r u n r e c o v e r a b l e p a r i t y e r r o r s on t h e d a t a t a p e . C a l l RWUNLD causes the d i g i t a l t a p e t o be rewound and unloaded. The f o l l o w i n g s i x F o r t r a n IV d i g i t a l programs have been used t o p r o c e s s the d a t a (see appendix IX f o r d e t a i l s ) . 1. Hydrophone I n p u t (HYINPT). T h i s program f i r s t c a l l s Ocean 1 t o cause the d a t a tape t o be p o s i t i o n e d a t t h e f i r s t echo o f t h e f i l e t o be p r o c e s s e d . I t t h e n c a l l s Ocean 2 t o r e a d t h e t h i r t y - t w o d i g i t i z e d v a l u e s f o r each s i g n a l c h a n n e l and w i l l do so f o r s e q u e n t i a l echoes f o r each time o f c a l l i n g . 2. Hydrophone P r i n t e r P l o t (HYPLOT). H y p l o t causes a graph t o be p r i n t e d o f t h e d i g i t a l v a l u e o f each c o n v e r t e d v o l t a g e a g a i n s t the s e q u e n t i a l numbers o f t h e c o n v e r s i o n s . I t i s used f o r d i g i t a l m o n i t o r i n g . The p r i n t e r p l o t s t h u s o b t a i n e d can be c o r r e l a t e d w i t h a n a l o g m o n i t o r i n g on t h e o s c i l l o s c o p e . 3. Energy L i s t i n g s ( E L I S T ) . T h i s program l i s t s t h e f i l e number, echo number and "energy" i n t h e upper and l o w e r hydrophone s i g n a l s , f o r each d i g i t i z e d echo. I t has 75 been u s e f u l f o r c o r r e l a t i o n w i t h t h e hydrophone p r i n t e r p l o t s as w e l l as a l l f o l l o w i n g programs w h i c h compute v a r i o u s p r o p e r t i e s o f t h e d i g i t i z e d echoes. 4. R a t i o s o f E n e r g i e s (RATIOS). R a t i o s causes t h e c o m p u t a t i o n o f t h e r a t i o o f t h e t o t a l "energy" i n t h e upper hydrophone t o t h e t o t a l "energy" i n t h e l o w e r • hydrophone f o r d i g i t a l c o n v e r s i o n s c o r r e s p o n d i n g t o echoes r e c e i v e d from w i t h i n t h e s p e c i f i e d volumes o f the ocean. I t a l s o i s used t o produce s t a t i s t i c a l p r o p e r t i e s o f t h e i n f o r m a t i o n . 5. D i s t r i b u t i o n o f E n e r g i e s (DISTRN). T h i s program causes c o m p u t a t i o n o f t h e numbers o f echoes whose " e n e r g i e s " f a l l w i t h i n s p e c i f i e d l i m i t s . I t c a l l s a s u b r o u t i n e which p l o t s t h i s i n f o r m a t i o n u s i n g t h e Calcomp P l o t t e r a t t h e U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e . These graphs a r e shown i n c h a p t e r V. 6. C o u n t i n g o f I n d i v i d u a l Echoes (COUNT). T h i s program causes t h e c o m p u t a t i o n o f t h e number o f maxima i n t h e hydrophone p r i n t e r p l o t graphs f o r each s i g n a l c h a n n e l . APPENDIX IX . . FORTRAN SOURCE LIST 76 ISN SOURCE STATEMENT 0 * SIBFTC HYINPT 1 SUBROUTINE HYINPT (NA,NB,IND,INIT,NFILE,NUN IT) 2 DIMENSION N(10),NA(1),NB (1 ) 3 * COMMON NCOUNT 4 IF.(INIT.EO.O) GO TO 20 7 * DO 10 1=1,32 10 CALL 0CEAN2 I IND,KBLOCK,N) 11 * IF (IND.EQ.l) RETURN 14 NA(I) = N(1) 15 10 NB(I) = N(2) 17 NCOUNT = NCOUNT + 1 20 IF (NCOUNT.LT.7) RETURN 23 * DO 15 1=1,32 24 15 CALL 0CEAN2 (I DUMMY,IDUMMY,N) 26 * NCOUNT = 0 27 RETURN 30 * 20 NCOUNT = 0 31 CALL 0CEAN1 (2,NUN IT,100,NFILE,2,0) 32 RETURN 33 END NO MESSAGES FOR ABOVE ASSEMBLY FORTRAN SOURCE LIST ISN SOURCE STATEMENT 0 * $IBFTC HYPLOT * C THE FOLLOWING CONTROL CARD IS REQUIRED WITH THE PROGRAM * C 1) KFILE ,KSTART,KSTOP,KU,KL,KTWO,KRULE ( 3 I 5, 3(4X,A 1),I 5 ) * C WHERE, * C KFILE = NO. OF FILE TO BE PLOTTED ON OCEAN TAPE * C KSTART = NO. OF FIRST ECHO TO BE PLOTTED * C KSTOP = NO. OF LAST ECHO TO BE PLOTTED * C KU = CHARACTER TO BE PLOTTED FOR UPPER HYDROPHONE  * C KL = CHARACTER TO BE PLOTTED FOR LOWER HYDROPHONE * C KTWO = CHARACTER TO BE PLOTTED WHEN TWO POINTS COINCIDE * C KRULE = 1 FOR A ROW OF PERIODS/INCH ON, THE OUTPUT . * C = 0 IF THIS IS NOT DESIRED * C THE INPUT TAPE IS ON S.SU04 * C UPPER AND LOWER HYDROPHONE PRINTER PLOT  1 * DIMENSION NA(32),NB(32),KPLOT(101),NPLOT(101) 2 * COMMON NCOUNT * C READ CONTROL PARAMETERS 3 * NFILE = 0 4 * KPOS = 1 5 * NCOUNT = 0  6 * 5 READ (5,2001) KFILE,KSTART,KSTOP,KU,KL,KTWO,KRULE 16 * IF (KFILE.EQ.O) GO TO 79 * C OPEN OCEAN FILE AND POSITION DATA TAPE _ 21 # IF (NFILE. EQ.KFILE) GO TC 7 24 * 8 CALL HYINP.T (NA ,NB , IND ,0 , KF I LE , 4 ) 25 * NFILE = KFILE  26 * KPOS = 1 27 * 7 KSKIP = KSTART - KPOS 30 * IF (KSKIP.LT.O) GO TO 8 33 * IF (KSKIP.EQ.O) GO TO 15 36 * DO 10 I = 1,.KSKIP 37 * CALL HYINPT (NA,NB,IND,1,KFILE,4)  40 * KPOS = KPOS + 1 41 * 10 IF (IND.EQ.l) GO TO 80 * C SET UP PRINTER PLOT ARRAY ...... 45 * . 15 DO 20 1=1,101 46 * 20 CALL REPLCE (KPL0T(I),1H ) 50 * IF (KRULE.EQ.O) GO TO 40  53 * DO 30 I = l,.101,10 54 * 30 CALL REPLCE (KPERD,IH.) 56 * 40 CALL REPLCE (KPERD,IH.) 57 * CALL REPLCE (KBLANK.1H ) 60 * CALL REPLCE (KX,1HX) 61 * KPLOT(l) = KPERD  62 * KPLOT ( 101 ) =• KPERD * C SKIP TO TOP OF FIRST PAGE 63 * . NPAGE = 0 64 * CALL GPHEAD (100,NPAGE) * C DO PRINTER PLOT 65 * DO 70 I=KSTART,KSTOP  66 * WRITE (6,4001) 67 * CALL GPHEAD (1,NPAGE) 70 * CALL HYINPT (N A, NB, IND,1 ,KFILE,4) ... ... 71 * IF (IND.EQ.l ) GO TO 80 74 * KPOS = KPOS + 1 FORTRAN SOURCE LIST HYPLOT 78 ISN SOURCE STATEMENT 75 * 00 65 J=l,32 76 K l = NA(J) 77 * K2 = NB(J) 100 VI = FL0AT(K1-511)/100. 101 V2 = FL0AT(K2-51l)/100. 102 * KERROR = KBLANK 103 * KE1 = 0 104 * KE2 = 0 105 * K l = ( K l - 5 1 0 ) / 3 106 * IF (KI.GT.0.AND.K1.LT.102) GO TO 42 i l l * KERROR = KX 112 * KE 1 = 1 113 * GO TO 44 114 42 KSAVE1 = KPLOT(Kl) 115 * KPLOT(Kl) = KU 116 * 44 K2 = (K2-510J/3 117 IF (K2.GT.0.AND.K2.LT.102) GO TO 46 122 * KERROR = KX 123 * KE2 = 1 124 * GO TO 48 125 46 IF (K1.EQ.K2) GO TO 90 130 * KSAVE2 = KPLOT(K2) 131 * KPL0T1K2) = KL 132 * 48 IF ( J . N E . l ) GO TO 50 135 * WRITE (6,4002) I,J,VI,V2,KPLOT,KERROR 136 GO TO 60 137 * 50 WRITE (6,4003) J,V1,V2,KPLOT,KERROR 140 * 60 IF (KE1.EQ.1) GO TO 62 143 KPLOT(Kl) = KSAVE1 144 62 IF (KE2.EQ.1) GO TO 65 147 * KPLOT(K2) = KSAVE2 150 * 65 CONTINUE 152 70 CALL GPHEAD (100.NPAGE) 154 * 75 CALL GPHEAD (100,NPAGE) 155 WRITE (6,4001) 156 * CALL 0CEAN3 157 * GO TO 5 160 * 79 CALL RWUNLD 161 * CALL EXIT 162 * 80 WRITE (6,4004) 163 * NFILE = NFILE + 1 164 KPOS = 1 165 GO TO 75 166 90 KSAVE2 = KSAVE1 167 * KPL0T(K2) = KTWO 170 * GO TO 48 171 * 2001 FORMAT (3I5,4X,A1,4X,A1,4X,A1,15) 172 4001 FORMAT (1H ) 173 * 4002 FORMAT (15,I4,2F7.2,2X,101A1,4X,Al) 174 * 4003 FORMAT (5X,I 4,2F7.2,2X,101A1,4X,A1) 175 4004 FORMAT (38H0END OF FILE ENCOUNTERED ON OCEAN TAPE) 176 * END SN SOURCE STATEMENT FORTRAN SOURCE LIST 79 0 $I8FTC ELI ST * C -HYDROPHONE ENERGIES LISTED BY FILE AND ECHO NUMBER ' 1 * DIMENSION NV1(50),NV2(50),KSHOT(3000) ,ENGYUP(3000),ENGYLO( 3000) 2 * 3 READ (5,4001) KFILE,KSTOP,KATAPE,KARUN,KDTAPE,KDATE,KDEPTH 12 Y=CLOCK(0. ) _ . .. : 13 * IF (KFILE.EQ.O) GO TO 40 | 16 * PRINT 4007, KFILE,KSTOP,KATAPE,KARUN,KDTAPE,KDATE,KDEPTH ! 17 * PRINT 4010 ! 20 * PRINT 4020 | 21 PRINT 4010 .; 22 K = 0 23 * DO 5 J = 1,3000 1 24 * KSHOT(J) = 0 25 ENGYUP(J) = 0. 26 * 5 ENGYLO(J) = 0. i 30 CALL HYINPT (NV1,NV2,IND,0,KFILE,4) , 31 * DO 20 J = 1,3000 : 32 * K = K + 1 33 * ENGYUP(J) = 0 . ' 34 ENGYLO(J) = 0. : 35 * CALL HYINPT (NV1,NV2,IND,1,KFILE,4) * C -LIST BLOCKS CONTAINING PARITY ERRORS WITH A -0. 36 * IF (IND.EQ.2) GO TO 19 . ... * C -END CALCULATIONS WHEN END OF FILE MARK ENCOUNTERED j 41 IF ( IND.EQ.1) GO TO 25 1 44 * DO 10 I = 2,25 1 45 * V i =( FLOAT (NVK I ) ) / 100 .-5 . 11 ) / 1. 14 ! 46 10 ENGYUP(J) = ENGYUP(J) + VI * VI i 5 0 DO. 15 I = 8,19 ! 5 1 V2 = (FL0AT(NV2(I)J/100.-5.11) 52 15 ENGYLO(J) = ENGYLO(J) + V2 * V2 i 54 GO TO 20 ! 55 * 19 ENGYUP(J) = -0. i 5 6 * ENGYLO(J) = -0. ! 57 20 KSHOT (J) = J ...... ! 61 * 25 DO 36 I = 1,K,.5 ; 62 L = I + 4 I 63 36 PRINT 4004, (KFILE,KSHOT(N),ENGYUP(N),ENGYLO(N),N=I,L) ! 71 Z=CLOCK(Y)/60. ! 72 * PRINT 6001,Z ! 7 3 * GO TO 3 1 74 * 40 CALL RWUNLD I 75 * CALL EXIT ! 76 * 4001 FORMAT (515,110,15) , 77 * 4004 FORMAT (13,I5,F7.1,F7.1,4(5X,I3,I5,F7.1,F7.1) ) 100 * 4007 FORMAT ( 1H-,12HDIGITAL FILE,I3,3X,22HECH0 NUMBERS 1 THROUGH, 15,2X * 111HANA LOG TAPE,13,3X,10HANAL0G RUN,I 2,4X,12HDIGITAL TAPE,14, 2.X, I 24HDATE , I 8,2X,5HDEPTH,13) : 101 * 4010 FORMAT (1H-) ' 102 * 4020 FORMAT (1H0,4(9HFILE/ECH0,2X,3HUPR,4X,3HL0R,6X),9HFILE/ECHO, 2X, 13HUPR,4X,3HL0R) 103 6001 FORMAT (1H0,18H7044 TIME FOR F I LE,F9.2,2X,4HSECS) 104 •* END ISN SOURCE STATEMENT FORTRAN SOURCE LIST 80 0 $I8FTC RATIOS * C- -ENERGY RATIO CALCULATIONS 1 DIMENSION NVU 50) ,NV2< 50),VI SUM<3000), 1V2SUM(3000),V1SQ(3000),V2SQ(3000) 2 * 3 READ (5,4001) KFILE,KSTOP,KATAPE,KARUN,KDTAPE,KDATE,KDEPTH 12 * IF (KFILE.EQ.O) GO TO 40 15 * Y=CLOCK(0.) 16 * PRINT 4007, KFILE,KSTOP,KATAPE» KARUN» KDTAPE» KDATE» KDEPTH 17 CALL HYINPT (NV1,NV2,IND,0,KFILE,4) 20 * K = 0 21 * DO 20 J = 1,3000 22 * K = K + 1 23 6 VISUM(J) = 0. 24 * V2SUM(J) = 0. 25 * 8 CALL HYINPT (NV1,NV2,IND,1,KFILE,4) C- -ELIMINATE PARITY ERRORS 26 IF { IND.EQ.2) GO TO 8 c - -END CALCULATIONS WHEN END OF FILE MARK ENCOUNTERED 31 * IF ( IND.EQ.l) GO TO 37 34 DO 10 I = 2,25 35 VI =(FLOAT<NV1(I))/100.-5.11)/1.14 36 * 10 VISUM(J) = VISUM(J) + VI * VI 40 * IF (VISUM(J).GT.15.) GO TO 6 43 * DO 15 I = 8,19 44 * V2 = (FL0AT(NV2(I))/100.-5.11) 45 * 15 V2SUM (J) = V2SUMU) + V2 * V2 47 IF (V2SUM(J).GT.15.) GO TO 6 52 * 20 CONTINUE 54 * 37 E1SUM = 0. 55 E2SUM = 0. 56 V1SQSM = 0. 57 V2SQSM = 0. 60 * DO 38 J = 20,K 61 E1SUM = E1SUM + VISUM(J) 62 * E2SUM = E2 SUM + V2SUMIJ) 63 V1SQ(J) = VISUM(J) * VISUM(J) 64 * V2SQU) = V2SUMU) * V2SUM (J ) 65 ViSQSM = V1SQSM + V1SQ(J) 66 38 V2SQSM = V2SQSM + V2SQU) 70 KK = K - 20 71 RSUM = E1SUM/E2SUM 72 * E1AVG = E1SUM/FL0ATIKK) 73 * E2AVG = E2 SUM/FLOAT(KK) 74 * V1SQBR = VISQSM/FLOATtKK) 75 V2SQ8R = V2SQSM/FL0AT(KK) 76 * E1BRSQ = E1AVG * ElAVG 77 E2BRSQ = E2AVG * E2AVG 100 * VARE1 = V1S0BR - E1BRSQ 101 * VARE2 = V2SQBR - E28RSQ 102 * STDE1 = SQRT(ABS(VAREl)) 103 * STDE2 = SQRT(ABS(VARE2)) 104 * PRINT 4008, KK 105 PRINT 4006 106 WRITE(6,4005) RSUM,EIAVG,STDE1,E2AVG,STDE2 107 * Z=CLOCK(Y)/60. FORTRAN SOURCE LIST RATIOS 81 ISN SOURCE STATEMENT 110 * PRINT 6001,Z 111 GO TO 3 112 * 40 CALL RWUNLD 113 CALL EXIT 114 t 4001 FORMAT (515,110,15) 115 4005 FORMAT {IHO,5(F25.3)) 116 4006 FORMAT (1H-,16X,13HRATI0 OF AVGS,11X,14HAVG ENERGY UPR,11X, 114HSTD DEVN UPPER,11X,14HAVG ENERGY LWR,1IX,14HSTD DEVN LOWER) 117 4007 FORMAT (1H-,12HDIGITAL FILE,I3,3X»22HECHO NUMBERS 1 THROUGH,15,2X, 111HANAL0G TAPE,13,3X»1OHANALOG RUN,I 2,4X,12HDIGITAL TAPE,14,2X, 24H0ATE,I8,2X,5HDEPTH,13) 120 * 4008 FORMAT (1H-,35HT0TAL NUMBER OF ECHOES PROCESSED = , 15) 121 * 6001 FORMAT (1H-,18H7044 TIME FOR FILE,F9.2,2X,4HSECS) 122 END USER FUNCTION SUBPROGRAM REFERENCES NO MESSAGES FOR ABOVE ASSEMBLY 00 LB200 FORTRAN SOURCE LIST 82 I SN SOURCE STATEMENT ! o SIBFTC DISTRN * c - FREQUENCY DISTRIBUTION OF ENERGIES 1 DIMENSION NV1(50),NV2(50),VISUM{3000),V2SUM(3000), 1IUPPER(3000),I LOWER(3000) 2 CALL PLOTS . .... 3 * XORG = 0.0 4 * 3 READ (5»2001) KFILE,KSTOP,KATAPE,KARUN,KDTAPE,KDATE,KDEPTH 14 S = CLOCK(0.) 1 15 IF (KFILE.EQ.O) GO TO 40 20 PRINT 4007, KFILE,KSTOP,KATAPE,KARUN,KDTAPE,KDATE,KDEPTH 21 .. PRINT 4008 22 CALL HYINPT (NV1,NV2 ,1ND,0,KF I LE,3) 23 4 K = 0 24 * DO 20 J = 1,3000 25 * K = K + 1 26 * VISUM(J) = 0. 27- V2 SUM(J) = 0. „ 30 * 8 CALL HYINPT (NVI,NV2,IND,1,KFILE,3) C- ELIMINATE PARITY ERRORS 31 * IF (IND.EQ.2) GO TO 8 34 IF (IND.EQ.l) GO TO 37 37 * DO 10 I = 2,25 40 VI =(FL0AT(NV1(I))/100.-5.11)/1.14 41 10 V1SUM(J),= VISUM(J) + VI * VI , 43 * DO 15 I = 8,19 44 V2 = (FL0AT(NV2(I))/100.-5.11) 45 * 15 V2SUMU) = V2SUMU) + V2 * V2 47 * 20 CONTINUE 51 37 DO 38 J = 1,3000 . 52 * IUPPER(J). = 0 53 * 38 I LOWER(J) = 0 55 * KK = K - 20 56 PRINT 5000, KK 57 PRINT 4008 60 .DO 50 J = 20,K 61 + • M = ABS(VI SUM(J) ) + 1. 62 N = ABS(V2 SUM(J) ) + 1. 63 IUPPER(M) = IUPPER(M) + 1 64 ILOWER(N) = ILOWER(N) + 1 65 * 50 CONTINUE 67 DO 60 J = 1,200,12 . 70 * L = J + 11 71 60 WRITE (6,5001) ( I , I UPPER(I), I = J,L) 77 * PRINT 4008 100 DO 70 J = 1,200,12 101 * L = J +. 11 102 * 70 WRITE (6,5001) ( I, I LOWER ( I ) , I = J,L) _... ' 110 * T = CL0CK(S)/60. 111 * PRINT 6001 ,T 112 * DIMENSION X(200) ,Y(200) 113 * L = 1 114 DO 100 J = 1,200 115 * X(J) = FLOAT(J) 116 Y(J) = FLOAT (ILOWER(J)) 117 * YI200) = 0. FORTRAN SOURCE LIST OISTRN 83 ISN SOURCE STATEMENT 120 IF ( YU).GT.50. ) L = J 123 * 100 IF IY(J).GT.50.) Y ( J ) = 50. 127 * CALL GRAPH(XORG,0.0,0,1,3.00,OOR,OUN,10.00,AOR,AUN,1, 1 14H NUMBER,14,1,29H ENERGY LOWER HYDROPHONE, * 2 29,200,Y(L),X(L),1) 130 * L = 1 131 * 00 200 J = 1,200 132 * X U ) = FLOAT ( J ) 133 * Y U ) = FLOAT ( I UPPER ( J ) ) 134 Y(200) = 0. 135 IF (Y(J).GT.50.) L = J 140 * 200 IF (Y( J) .GT.50. ) Y U ) = 50. 144 CALL GRAPH(0.0,4.0,0,1,3.00,OOR,OUN,10.00,AOR,AUN,I, * 1 14H NUMBER,14,1,29H ENERGY UPPER HYDROPHONE, 2 29,2 0 0 , Y ( L ) , X ( L ) , 1 ) 145 * XORG = 12.0 146 * GO TO 3 147 40 CALL PLOTND 150 * CALL RWUNLD 151 * CALL EXIT 152 * 2001 FORMAT (515,110,15) 153 4007 FORMAT (1H-,12HDIGITAL FILE,13,3X,22HECH0 NUMBERS 1 THROUGH,I 5,2X, * 111HANALOG TAPE,I3,3X,10HANALOG RUN,I 2,4X,12HDIGITAL TAPE,14,2X, * 24HDATE,I 8,2X,5HDEPTH,13) 154 4008 FORMAT (IHO) 155 * 5000 FORMAT (1HO,42HNUMBER OF ECHOES FOR COMPUTED DISTRIBUTION,I 5) 156 5001 FORMAT (IH ,2415) 157 6001 FORMAT (1H0,18H7044 TIME FOR FILE,F9.2,2X,4HSECS) 160 * END USER FUNCTION SUBPROGRAM REFERENCES NO MESSAGES FOR ABOVE ASSEMBLY 00 QB470 ISN SOURCE STATEMENT FORTRAN SOURCE L I S T 84 0 * $ I B F T C COUNT C NUMBER OF ANIMALS IN EACH VOLUME 1 * DIMENSION N V 1 ( 5 0 ) , N V 2 ( 5 0 ) 2 * 3 READ ( 5 , 4 0 0 1 ) K F I L E . K S T O P t K A T A P E t K A R U N f K D T A P E , K D A T E , K D E P T H 12 READ ( 5 , 7 0 0 1 ) K C L I P 14 * Y = C L O C K ( 0 . ) 15 IF . ( K F I L E . E Q . O ) GO TO 40 20 * PRINT 4 0 0 7 , K F I L E , K S T O P , K A T A P E , K A R U N , K D T A P E , K D A T E , K D E P T H 21 * CALL HYINPT ( N V 1 , N V 2 , I N D , 0 , K F I L E , 4 ) 22 * K = 0 23 KUTOTL = 0 24 KLTOTL = 0 25 DO 2 0 J = 1 , 3 0 0 0 26 * K = K + 1 27 * 8 C A L L HYINPT ( N V 1 , N V 2 , I N D , 1 , K F I L E , 4 ) C E L I M I N A T E P A R I T Y ERRORS , 30 IF ( I N 0 . E Q . 2 ) GO TO 8 33 * * I F ( I N D . E Q . 1 ) GO TO 37 C - E L I M I N A T E ECHOES WITH NO DIRECT PULSE ON LOWER HYDROPHONE < 36 IF ( N V 2 ( 2 ) . L T . 611") GO TO 8 41 M = 0 . 42 * N = 0 , 43 * DO 10 I = 2 , 2 5 . . . '•• 44 IF ( N V 1 ( 1 + 1 ) . L E . N V 1 ( I ) ) GO TO 10 4 7 IF ( N V 1 ( 1 + 1) . L E . K C L I P ) GO TO 10 52 * IF. ( N V 1 ( 1 + 2 ) . L E . N V 1 ( 1 + 1) ) M = M + 1 , 55 10 CONTINUE " i 5 7 * DO 15 I = 8 , 1 9 ! 60 * IF (NV2 (1 + 1) . L E . N V 2 ( I ) ) GO TO 15 6 3 * IF ( N V 2 ( 1 + 1 ) . L E . K C L I P ) GO TO 15 66 * IF ( N V 2 ( I + 2 ) . L E . N V 2 ( I + 1 ) ) N = N + 1 1 71 * 15 CONTINUE 1 7 3 * KUTOTL = KUTOTL + M 74 20 KLTOTL = KLTOTL + N , 76 37 AVGU •= F L O A T ( K U T O T L ) / F L O A T ( K ) 1 77 AVGL = F L O A T ( K L T O T L ) / F L O A T ( K ) ' 100 PRINT 4 4 3 3 101 * PRINT 4 4 4 4 , K U T O T L , K L T O T L , K , A V G U , A V G L 1102 * Z = C L O C K ( Y ) / 6 0 . ' 103 PRINT 6 0 0 1 , Z 104 * GO TO 3 .. . . . 105 4 0 C A L L RWUNLD 106 * C A L L EX IT 107 4 0 0 1 FORMAT ( 5 1 5 , 1 1 0 , 1 5 ) 110 4 0 0 7 FORMAT ( I H - , 1 2 H D I G I T A L F I L E , I 3 , 3 X , 2 2 H E C H 0 NUMBERS 1 THROUGH, I 5 . 2 X 111HANALOG T A P E , 1 3 , 3 X , 1 0 H A N A L 0 G R U N , I 2 , 4 X , 1 2 H D I G I T A L T A P E , 1 4 , 2 X , * 2 4 H D A T E , I 8 „ 2 X , 5 H D E P T H , 1 3 ) 1 1 1 4 4 3 3 FORMAT ( I H - , 2 9 H T 0 T A L NUMBER UPPER HYDROPHONE,4X , 1 29HT0TAL NUMBER LOWER H Y D R O P H O N E , 4 X , 2 26HNUMBER OF ECHOES PROCESSED , 4 X , 1 3 H A V E R A G E U P P E R , * 3 4 X , 1 3 H A V E R A G E LOWER) 112 * 4 4 4 4 F O R M A T ( I H O , 8 X , 1 1 0 , 2 3 X , 1 1 0 , 2 I X , 1 1 0 , 1 3 X , F 1 0 . 3 , 7 X , F 1 0 . 3 ) 113 * 6 0 0 1 FORMAT ( 1 H 0 , 1 8 H 7 0 4 4 TIME FOR F I L E , F 9 . 2 , 2 X , 4 H S E C S ) 114 * 7 0 0 1 FORMAT ( 1 5 ) 115 * • - END ' 85 APPENDIX X VOLUME ANALYSIS FOR ISOTROPIC SCATTERING C o n s i d e r a homogeneous d i s t r i b u t i o n o f i s o t r o p i c s c a t t e r e r s . I n o r d e r t o compute the t o t a l r e c e i v e d p r e s s u r e i n each hydrophone t h e f o l l o w i n g a n a l y s i s was c a r r i e d o u t . A t t e n u a t i o n r e l a t i v e t o t h e o r i g i n (see f i g u r e 4) was computed a t p o i n t s on a twenty c e n t i m e t r e g r i d , on the X - Z p l a n e , w h i c h c o n t a i n s t h e o r i g i n , t h e sound s o u r c e and b o t h r e c e i v e r s . Assuming u n i t i n c i d e n t p r e s s u r e and u n i t r e f l e c t i v i t y , t h e r e c e i v e d p r e s s u r e was computed a t each hydrophone f o r each g r i d p o i n t between th e t i m i n g e l l i p s o i d s . These p o i n t s were assumed r e p r e s e n t a t i v e o f c u b i c volumes w i t h l i n e a r d i m e n s i o n s o f 20 cm. A g e o m e t r i c c o r r e c t i o n was a p p l i e d depending on t h e p r o p o r t i o n o f t h e volume between th e t i m i n g e l l i p s o i d s . These co m p u t a t i o n s were r e p e a t e d f o r e i g h t a d d i t i o n a l p l a n e s p a r a l l e l t o t h e X - Z p l a n e and f o r Y v a l u e s o f ±20, ±40, ±60 and ±80 cm. The t o t a l r e c e i v e d p r e s s u r e f o r each hydrophone was computed from t h e sum o f t h e v a l u e s f o r each p o i n t on each o f t h e n i n e p l a n e s . The r a t i o o f t h e p r e s s u r e i n t h e upper hydrophone t o t h e p r e s s u r e i n t h e lower hydro-phone was 1.07 ± 0 . 0 1 . T h i s v a l u e has been used f o r a c o r r e c t i o n f a c t o r , as e x p l a i n e d i n c h a p t e r IV. 86 APPENDIX XI VOLUME ANALYSIS FOR COSINE SCATTERING C o n s i d e r a homogeneous d i s t r i b u t i o n o f c o s i n e s c a t t e r e r s . I n o r d e r t o compute t h e t o t a l r e c e i v e d p r e s s u r e i n each hydrophone t h e f o l l o w i n g a n a l y s i s was c a r r i e d o u t . A t t e n u a t i o n r e l a t i v e t o t h e o r i g i n was computed f o r g r i d p o i n t s as d e s c r i b e d i n t h e volume a n a l y s i s f o r i s o t r o p i c s c a t t e r i n g (appendix X ) . Assuming u n i t i n c i d e n t p r e s s u r e and u n i t r e f l e c t i v i t y a l o n g t h e p r o p a g a t i o n a x i s , t h e r e c e i v e d p r e s s u r e was computed a t each hydrophone f o r each g r i d p o i n t . These p r e s s u r e s depend on t h e a n g l e measured from t h e l i n e o f i n c i d e n t p r e s s u r e t o t h e r e c e i v e r . The g e o m e t r i c c o r r e c t i o n s were a p p l i e d and t h e t o t a l r e c e i v e d p r e s s u r e s were computed as d e s c r i b e d i n t h e volume a n a l y s i s f o r i s o t r o p i c s c a t t e r i n g . The r a t i o o f t h e p r e s s u r e i n t h e upper hydrophone t o t h e p r e s s u r e i n t h e lower hydrophone i s 14.30 ± 0.01. T h i s v a l u e r e p r e s e n t s an upper l i m i t f o r p r e s s u r e r a t i o s measured w i t h t h e a p p a r a t u s o f t h i s e x p e r i m e n t . APPENDIX X I I RESULTS DATA ANALOG ANALOG DIGITAL ANALOG DIGITAL ANALOG DIGITAL UNIT TAPE RUN TAPE/FILE RUN ' T A P E / F I L E R U N ' TAPE/FILE 1 6 1 X224/13 2 X219/1 3 X222/1 2 7 1 X224/14,16 2 X219/2 3 X222/2 3 8 1 X224/18,19 2 X219/3 3 X222/3 4 9 1 X224/20 3 X222/4 4 X222/7 5 10 1 X224/21 2 X219/6 3 X224/27 6 11 1 X224/3 2 X224/5 4 X222/8 7 12 2 X219/7 3 X224/28 4 X222/9 8 13 1 X224/22 2 X219/9 3 X224/29 9 15 1 X224/25 2 X219/2 3 X222/6 10 16 1 X224/26 2 X219/13 3 X224/30 TABLE I I DIGITAL AND ANALOG TAPE LISTINGS 88 APPENDIX X I I I ERROR ANALYSIS The f o l l o w i n g a b s o l u t e and per c e n t e r r o r s have been e s t i m a t e d f o r t h e measurement o f t h e r a t i o o f t h e t o t a l energy r e c e i v e d i n t h e upper hydrophone t o t h e t o t a l energy r e c e i v e d i n t h e low e r hydrophone. ABSOLUTE PER CENT RATIO ERROR ERROR 1. R a t i o o f "volumes" 1.07 + 0.01 .93 2. I n t e r f e r e n c e e f f e c t s 1.02 + 0.01 .98 3. R e c e i v e r g a i n s 1.045 + 0.005 .48 4. Re p l a y g a i n s 1.00 + 0.001 .10 5. A n a l o g network g a i n s 1.00 + 0.002 .20 6. A/D c o n v e r t e r g a i n s 1.00 + 0.001 .10 T o t a l p e r c e n t e r r o r f o r p r e s s u r e - 2.79 T o t a l p e r c e n t e r r o r f o r energy - -,5.58 T h e r e f o r e t h e r a t i o o f t o t a l e n e r g i e s r e c e i v e d i s 1.54 +5.58% o r 1.54 ± 0.09. S i m i l a r e r r o r s a r e p o s s i b l e f o r t h e mean o f t h e energy r a t i o s , one f o r each d a t a u n i t . An energy r a t i o o f 1.54 ± 0.09 c o r r e s p o n d s t o a p r e s s u r e r a t i o o f 1.24 ± 0.04. I f - K i s o f t h e same a l g e b r a i c s i g n as - p (case A ) , t h e i n c o m p r e s s i b i l i t y c o n t r a s t i s r e s p o n s i b l e f o r from 100/1.28 t o 100/1.20 p e r c e n t o r f o r 78-83 p e r c e n t o f t h e s c a t t e r e d sound. The d e n s i t y c o n t r a s t i s r e s p o n s i b l e f o r from 20/1.20 t o 28/1.28 89 per cent or for 17-22 per cent of the scattered sound. If the differences are of opposite sign (case B), the incompressibility contrast i s responsible for from 100/3.28 to 100/3.20 per cent or for 30-31 per cent of the scattered sound. The density contrast i s responsible for from 220/3.20 to 228/3.28 or for 69-70 per cent of the scattered sound. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084751/manifest

Comment

Related Items