(NASA-TP-7958:! VFRY LCYG 9ASYL1Wf N78-; 1C30 IYTFFFEROMPTFY :PPLIED TO PCLhR ROTTCN, RELATIVITY .?YP GP03PSY Ph.9, Thesis - 'laryland Unjv. A)397 p HC ;17/,*1F .:01 Unclas CSCL OeF G3/46 257d' Technical Memorardum 79582 Very Long Baseline Interferometry Applied to Polar Motion, Relativity and Geodesy MAY 1978 National Aeronautics and Space Administration Goddard Space Right Center Greenbelt, Maryland 20771 APPROVAL SHEET Title of Thesis: Very Long Baseline Interferometry applied to Polar Motion, Relativity, and Geodesy Name of Candidate: Chopo Ma ktor of Philosophy, 1978 Thesis and Abstract approved: Jean-Paul Richard Associate Professor Department of Physics and Astronomy Date Approved : VITA Name: Chopo Ha Permanent Address: 90 La Salle Street New York, New York 10027 Degree and date to be conferred: Ph. D. Hay, 1978 Date of bi-tk: Place of birth: Secondary education: Bronx High School of Science, New York, New York Collegiate institutions: Harvard College 1969-1 967 A. 8. June 1967 University of Maryland 1967-1 968 University of kryland 1970- 1378 Ph. D. May 1978 Major: Physics Publications : T. A. Clark, I. K. Hutton, C. Ha, I. I. Shapiro, J. J. Wittels, 3. S. Robertson, H. F. Hinteregger, C. A. Knight, A. E. E. Rogers, A. R. Uhitney, A. E. Niell, C. M. Resch, Y. J. Webster. "An Unusually Strong Radio Outburst in Algol: VLBI Observatiocsw Ap. J. 206, L:07, 1976 D. M. Gibson, M. Viner, S. Peterson, T. Clark, L. Hutton, C. Ma, Y. Vebster, H. Hineregger, A. Rogers, I. Shapiro, A. Vhitney, J. Uittels, A. Niell, C. Resch. "An Extraordinary Radio Outburst in Algol: Flux and Structure Observationsw 8. A. A. S. 7, 498, 1975 J. V. Ryan, T. A. Clark, R. Coates. C. Ma, D. S. Robertson, B. E. Corey, C. C. Counselman, I. I. Shapiro, J. J. Uittels, H. F. Hinterreger, C. A. Knight, A. E. E. Rogers, A. R. Uhitney, J. M. Moran. wPrecision Surveying Using Very Long Baseline InterfermetryW CSFC X-922-77-242, 1977 J. J. Wittels, I. I. Shapiro, H. F. Hinterreger, C. A. Knight, A. E. E. Rogers, A. R. Whitney, T. A. Clark, C. Ha, L. K. Hutton, D. S. Robertson, B. 0. Ronnang, 0. E. H. Rydbeck, A. E. Niell, C. M. Resch. "A High Declination Search at 8 GHz for Compact Radio SourcesN submitted to The Astronomical Journal Positions held: Teaching assistant - University of Maryland, 1967-1966, 1971 Research assistant - University of Maryland, 1971-1978 ABSTRACT Title of thesis: Very long baseline interferometry applied to polar motion, relativity, and geodesy chop0 Ha, ~octorof Philosophy, 1978 Thesis directed by: Associate Professor Jean-Paul Richard The causes and effects of diurnal polar motion are described. An algorittm is developed for modeling the effects on very long baseline interferometry observables. Five years of radio-freauency very long baseline interferometry data from stations in Plassachusetts, California, and Sweden are analyzed for diurnal polar motion. It is found that the effect is larger than predicted by NcClure. Corrections to the standard nutation series caused by the defomability of the earth have a significant effect on the estimated diurnal polar motion scaling factor and the post-fit residual scatter. Simulation3 of high precision very long baseline interferometry expertments taking into account both measurement uncertainty and modeled errors are described. It is found that the Wide-Band Optical Very Long Baseline Interferometer may bc useful in studying gravitational deflection near Jupiter. A selection is made between two three-station netvorks for monitoring plar motion. The effects of schedul ir~and the number of scurces observed on est imated baseline errors are discussed. It is found that a moderate number of sources. should yield the best results. A comparison of actual and simulated experiments indicates that the present variability of real data is not well predicted. VERY LONG BASELINE INTERPERWETRY APPLIED TO POLAR HOTION, RELATIVITY, AND GEODESY by Chopo Ma Dissertation submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1978 I would like to thank the large cast of characters that made this production possible. First, Prof. 3. P. Richard for his patience, Dr. T. A. Clark for taking re in out of the cold, and &. J. V. Ryan for his unfailing good humor. Hy advisors, Prof. Richard and Dr. Clark, and the mabers of my committee, Profs. C. C. Counselman, I). G. Currie and 51. C. Erickson, for keeping my nose to the grindstone and making this a different piece of work than it might have been. George Kaplan for invaluable discussions of the physical and political complexities of nutation and polar motion. The past and present members, willing and unwilling, of the VLBI groups at Haryland, Goddard, Haystack, HIT, JPL, Onsala, and NRAO, too numerous to list but not forgotten, and the supporting staff of the participating observatories, particularly the Haystack computer operators, without whom no data would have been available. Dr. D. S. Robertson for editing most of the data into a useful form and developing the VLBI3 program. Hay it now fade away. Dr. A. R. Uhitney for the care and feeding of the HP 21HX and discussions of the Mark 111 that is to be. The swing and grave shifts of the Uoddard 360/91 for allowing me a private queue and pushing through my altogether too numerous computer runs. J. Hodge for the drawings, E. Fisher for typing the equations, and Y. noran for providing an alternate printer in time of need. Hy roommates, Gerry Ilarandino, Bob Braunstein, and Bob McCann, for their support over the seaingly interminable years. Part of this research at the University of Uaryland was supported by the National Aeronautics and Space Administration under grant MSG 5035 and by the Computer Science Center. The experiments described - were supported in part by the National Science Foundation under grant EbR76-22615, the Advanced Research Frojects Agency under contract 23601-71-0092 mod 2, the U. ". Geological Survey under contract 14-08-001-14148, and the National Aeronautics and Space Administration - --..- under contracts WAS 7-100 and NAS5-22843 and grant NGR22-009-839. Habstack Observatory is partially supported by the National Science Foundation under grant GP-25865. The VLBI program at the Onsala Space Observatory is supported in part by the Swedish National Science Research Council and the Swedish Board for Technical Developmeat. The Owens Valley Radio Observatory is operated by the California Institute of Technology. TABLE OF CONTENTS Chapter Page DEDICATION . if ACKNOVLEDGEHENTS . iii LISTOFTABLES .......................... X LIST OF FIGURES . xiii IWTRODUCTlON . * . I CHAPTER I. PRINCIPLES OF VERY LONG BASELINE INTERFEROMETRY . 4 A. The VLBI observables . 0. Basic geometry and apparatus of VLBI . 4 C. Dependence of VLBI observables on geometry . 10 D. Dependence of VLBI observables on the propagation medim . 18 E. Dependence of VLBI observables on instrumentation . 21 F. %asurement uncertainties of the VLBI observables . - 23 C. VLBI instrumentati~nsystems . 25 CHAPTER 11. PHYSICAL MODELS USED IN HIGH PRECISION INTERFEROMETRY . 27 A. The VL0I reference frames . 28 8. Description of various time and time-like quantities . 32 C. Expressions for theoretical valaes of the VLBI observabies . 35 D. Models which determine the baseline orientation . 38 1. Precession ....................... 39 2. Nutation.. 42 3. Diurnal rotation . .............. 44 4. Diurnal polarmotion. 46 5. Polar motion . 50 6. Time derivatives of the coordinate transformations . 51 E . Perturbations of the observation gmetry 1 . Solid earth tides .......... 2 . Antenna structure .......... 3 . Relativistic gravitational deflection 9 . Ocean loading ............ F . Propagation IBedi~models ........ 1 . Atmosphere .............. 2 . Ionosphere .............. 3 . Corona ..............*. C . Basic geometrical derivatives ...... 1 . Site coordinate derivatives ..... 2 . Source position derivatives ............... CHAPTER I11 . HEASURWNT OF DIURNAL POLAR MOTION ......... A . Nomenclature of polar motion ................. B . Causes and effects of diurnal polar motion .......... C . Implementation of diurnal polar motion ............ D . Effect of diurnal polar motion on VLBI delay observable ... E . Observations and data preparation ........ F . Estimation of diurnal polar motion ........ 1 . Clock parameterization ............ 2 . Residual behavior .......... .... 3 . Effect of phase variation .......... 4 . Significance test .......... .... G . Comparison with literature ............ .... H . Interpretation of the diurrtal polar motion scaling factor 1 . Solid earth tides .............. 2 . Nutation ................... 3 . Core-mantle interactions .................159 4 . Other effects ...................... 161 5 . Conclusions .......................162 CHAPTER IV. SIMULATION OF HIGH PRECISION IHTSRFEROHETRIC EXPERIMENTS ...................... 163 A . Statistical theory ......................163 1 . Least squares covariance analysis ............1.b4 2 . Enlarged parameter set ..................168 3 . Errorsanderrormodels .................169 4 . The effect of model errors on unadjusted parameters ...172 B . neasurement of the relativistic light bending parameter ...175 1 . Occultations by Jupiter ................. 176 2 . Algorithms for modeling the light deflectioc parameter . 177 3 . Observations at Jupiter's stationary point ........ 182 4 . Observations at Jupiter's maximum velocity point .....192 5 . Observations at intermediate