CONTENTS 



INTRODUCTION . . . page 3 

 GENERAL SOLUTION ... 4 

 DETERMINANT ... 8 



FINDING EIGENVALUES ... 10 



Control cards ... 1 

 Iteration termination ... 1 1 



SOUND SPEED PROFILE ... 1 1 



NUMERICAL BREAKDOWN ... 1 5 



Program modifications ... 1 8 



Preventing zeroes in the determinant ... 1 9 



REFLECTION COEFFICIENTS AND OTHER AUXILIARY OUTPUTS ... 20 



COMPUTATION OF THE MODIFIED HANKEL FUNCTIONS ... 22 



Power series expansion ... 23 



Asymptotic series expansion using continued fractions ... 25 



Comparative accuracy ... 34 



MODE FOLLOWER PROGRAM ... 36 



Implementation of the mode follower ... 38 

 Input and output ... 40 



CONCLUSIONS ... 41 



RECOMMENDATIONS ... 41 



REFERENCES ... 41 



APPENDIX A: NORMAL MODE PROGRAM IN FORTRAN ... 43 



APPENDIX B: SAMPLE RUN ... 74 



APPENDIX C: HANKEL FUNCTION PARAMETERS ... 89 



APPENDIX D: MODE FOLLOWER PROGRAM IN FORTRAN ... 93 



