V Hotine-Marussi Symposium on Mathematical Geodesy: Matera, Italy June 17–21, 2003

355 Pages·2004·14.274 MB·English

by  Battista Benciolini (auth.), Prof. Dr. Fernando Sansò (eds.)

International Association
of Geodesy Symposia
Fernando Sanso, Series Editor
Springer-Verlag Berlin Heidelberg GmbH
International Association
of Geodesy Symposia
Fernando Sanso, Series Editor
Symposium 101: Global and Regional Geodynamics
Symposium 102: Global Positioning System: An Overview
Symposium 103: Gravity, Gradiometry, and Gravimetry
Symposium 104: Sea SurfaceTopography and the Geoid
Symposium 105: Earth Rotation and Coordinate Reference Frames
Symposium 106: Determination of the Geoid: Present and Future
Symposium 107: Kinematic Systems in Geodesy, Surveying, and Remote Sensing
Symposium 108: Application of Geodesy to Engineering
Symposium 109: Permanent Satellite Tracking Networks for Geodesy and Geodynamics
Symposium 110: From Mars to Greenland: Charting Gravity with Space and Airborne Instruments
Symposium 111: Recent Geodetic and Gravimetric Research in Latin America
Symposium 112: Geodesy and Physics of the Earth: Geodetic Contributions to Geodynamics
Symposium 113: Gravity and Geoid
Symposium 114: Geodetic Theory Today
Symposium 115: GPS Trends in Precise Terrestrial, Airborne, and Spaceborne Applications
Symposium 116: Global Gravity Field and Ist Temporal Variations
Symposium 117: Gravity, Geoid and Marine Geodesy
Symposium 118: Advances in Positioning and Reference Frames
Symposium 119: Geodesy on the Move
Symposium 120: Towards an Integrated Global Geodetic Observation System (IGGOS)
Symposium 121: Geodesy Beyond 2000: The Challenges of the First Decade
Symposium 122: IV Hotine-Marussi Symposium on Mathematical Geodesy
Symposium 123: Gravity, Geoid and Geodynamics 2000
Symposium 124: Vertical Reference Systems
Symposium 125: Vistas for Geodesy in the New Millennium
Symposium 126: Satellite Altimetry for Geodesy, Geophysics and Oceanography
Symposium 127: V Hotine Marussi Symposium on Mathematical Geodesy
V Hotine-Marussi
Symposium on
Mathematical Geodesy
Matera, Italy
June 17-21, 2003
Edited by
Fernando Sanso
'Springer
Volume Editor Series Editor
Prof. Dr. Fernando Sanso Prof. Dr. Fernando Sanso
Polytechnic of Milan Polytechnic of Milan
D.I.I.A.R.- Surveying Section D.I.I.A.R.-Surveying Section
Piazza Leonardo da Vinci, 32 Piazza Leonardo da Vinci, 32
20133 Milan 20133 Milan
Italy Italy
ISSN 0939-9585
ISBN 978-3-642-06028-1 ISBN 978-3-662-10735-5 (eBook)
DOI 10.1007/978-3-662-10735-5
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Library of Congress Control Number: 2004104537
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Contents
Foreword .............................................................................................................................. .1
Report on the Symposium
Battista Benciolini ..................................................................................................................... 3
Gaussian Differential Geometry and Differential Geodesy
J.D. Zund ............................................................................................................................... 5
Numerical Techniques for Large Least-Squares Problems with Applications to GOCE
R. Klees, P. Ditmar, J. Kusche ..................................................................................................... .12
The Numerical Treatment of the Downward Continuation Problem for the Gravity Potential
W.-D. Schuh, B. Kargoll ............................................................................................................ 22
Wiener Filters and Collocation in Satellite Gradiometry
A. Albertella, F. Migliaccio, M. Reguzzoni, F. Sanso .......................................................................... 32
How to Handle Colored Noise in Large Least-Squares Problems in the Presence of Data Gaps?
R. Klees, P. Ditmar .................................................................................................................. 39
Statistical Hypothesis Tests in Case oflmprecise Data
H. Kutterer ........................................................................................................................... .49
Multiresolution Data Analysis-Numerical Realization by Use of Domain Decomposition Methods
and Fast Multipole Techniques
W. Freeden, C. Mayer ............................................................................................................... 57
Integer Least-Squares
P.J.G. Teunissen ..................................................................................................................... 69
The Use of Wavelets for the Acceleration oflteration Schemes
W. Keller .............................................................................................................................. 81
Helmert Geometry (abstract only)
T. Krarup, K. Borre .................................................................................................................. 88
Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials
W. Freeden, C. Mayer ............................................................................................................... 90
Fast Spherical Harmonic Synthesis and Co-Synthesis with Applications in Gravity Field Modeling
P. Ditmar, R. Klees, F. Kostenko .................................................................................................. 99
Fixed Effects, Random Effects and the Mixed Model: New Results of Geodetic Estimation
and Prediction Theory (abstract only)
E.W. Grafarend ..................................................................................................................... 10 6
Some Generalized Equivalency Theorems for Least-Squares Adjustment
B. Schaffrin ........................................................................................................................ .1 07
Procrustes Statistics to Test for Significant OLS Similarity Transformation Parameters
A. Beinat, F. Crosilla ............................................................................................................... 113
PDF Evaluation of the Integer Ambiguity Residuals
S. Verhagen, P.J.G. Teunissen ................................................................................................... .120
Multiple Models - Fixed, Switching, Interacting
B. Gundlich, P. Teunissen ......................................................................................................... 129
A Comparison of Data Weighting Methods for the Combination of Satellite and Local Gravity Data
M. Kern .............................................................................................................................. 137
The Rank Deficiency in Estimation Theory and the Definition of Reference Systems
A. Dermanis ........................................................................................................................ 145
ITRF2000: From Theory to Implementation
Z. Altamimi, P. Sillard, C. Boucher ............................................................................................. 157
Problems in the Definition ofVertical Reference Frames
B. Heck .............................................................................................................................. 164
Geodetic Boundary-Value Problems and the Height Datum Problem
F. Sacerdote, F. Sanso ............................................................................................................. 174
GPS Permanent Network Solution: the Impact of Temporal Correlations
R. Barzaghi, A. Borghi, M. Crespi, G. Pietrantonio, F. Riguzzi ............................................................ 179
A Discussion of the Use of Spherical Approximation or no Approximation in Gravity Field Modeling
with Emphasis on Unsolved Problems in Least-Squares Collocation
C.C. Tscheming .................................................................................................................... 184
Some Topics Related to the Solution of Boundary-Value Problems in Geodesy
P. Holota ............................................................................................................................. 189
The Estimation Theory for Random Fields in the Bayesian Context: a Contribution from Geodesy
F. Sanso, G. Venuti ................................................................................................................ 201
Testing Invariance for Random Field Modeling
M. Reguzzoni, G. Venuti ......................................................................................................... 218
A Formal Comparison Between Marych-Moritz's Series, Sanso's Change of Boundary Method
and a Variational Approach for Solving Some Linear Geodetic Boundary Value Problems
J. Otero, A. Auz .................................................................................................................... 226
Potential Coefficients Recovery from the Spectra of the Full Space-Borne Gravity Gradient Tensor
M.S. Petrovskaya, A.N. Vershkov ............................................................................................... 234
Application of Spherical Pseudo-Differential Operators and Spherical Wavelets for Numerical Solutions
of the Fixed Altimetry-Gravimetry Boundary Value Problem
R. Grebenitcharsky, M.G. Sideris ................................................................................................ 242
Ellipsoidal Vertical Deflections: Regional, Continental, Global Maps of the Horizontal Derivative of
the Incremental Gravity Potential
G. Finn, E.W. Grafarend .......................................................................................................... 252
Harmonic Maps (abstract only)
E.W. Grafarend ..................................................................................................................... 260
The Analytical Solutions of the Dirichlet and Neumann Boundary Value Problems with
Ellipsoidal Boundary (abstract only)
J. Yu, L. Lu, C. Jekeli ............................................................................................................. 261
Applications ofNormal Mode Relaxation Theory to Solid Earth Geophysics (abstract only)
R. Sabadini .......................................................................................................................... 262
VI
Geodesy and the Problem oflce Sheets
I. Velicogna, J. Wahr .............................................................................................................. .264
Angular Momentum in the Earth System
R.S. Gross ............................................................................................................................2 74
Gravity Field Variability, the Geoid, and Ocean Dynamics
F. Condi, C. Wunsch ............................................................................................................... 285
Estimating Covariance Parameters in Gravity Downward Continuation
J. Kusche .............................................................................................................................2 93
Relating Gravity, Density, Topography and State of Stress Inside a Planet
B. Valette, F. Chambat ............................................................................................................. 301
The A-Optimal Regularization Parameter in Uniform Tykhonov-Phillips Regularization-a-Weighted BLE
J. Cai, E.W. Grafarend, B. Schaffrin ............................................................................................. 309
Response of the Earth's Crust due to Topographic Loads Derived by Inverse Isostasy
H.A. Abd-Elmotaal ................................................................................................................ 325
SAR Interferometry for Deformation Control
B. Crippa, M. Crosetto, M. Bhizquez, R. Barzaghi ............................................................................ 333
Changes of the Antarctic Ice Sheet Mass and the Instability of the Earth's Rotation over the Last 110 Years
N.S. Sidorenkov .................................................................................................................... 339
Index of Authors ................................................................................................................... 348
List of Participants ................................................................................................................. 349
VII
Foreword
The Hotine-Marussi symposia are, in the life of the International Association of Geodesy, a
moment of pause to stop and think how the geodetic theory, the arsenal of mathematical,
physical and geodetic tools, is finding an assessment, a systematization which all of us could
agree upon and on the same time the craddle of new ideas and new methods boosted by the
fantastic achievements of modem technology, from space geodesy to electronics and informatics,
and brought into the arena oftheoretic debates.
Traditional items in the Hotine-Marussi's are the geometric description of the gravity field, its
mathematical analysis and its approximation methods, the dynamic theory of satellite motion, the
inverse relation between gravity field and mass distributions, the positioning problems,
nowadays inextricably joined to satellite geodesy, the general concept supporting positioning,
namely the definition of reference systems and their practical implementation in frames; across
all these items we find a specific geodetic research on numerical methods for the solution of very
large systems and on statistical methods in handling data.
All these items were touched during the symposium although some of them have got more
relevance in the presentations.
In particular the figure and theoretical achievements of Marussi (the initiatior of the series of
these symposia that now bear his name too) have been discussed in a paper by J. Zund, which is
worth mentioning because it was not presented orally but has been hosted in the proceedings
because of its argument.
As it has been stated, also in a discussion with the reviewers, the paper does not attempt to give a
global judgement on the role of geometric thinking in geodesy, but certainly provides an
interesting view-angle by one of the authors that has traditionally accompanied our reflections in
this area.
Another aspect of this V Hotine-Marussi that I like to underline, is the good interaction that has
been established with scientists from geophysical disciplines naturally interfaced with geodesy,
like geodynamics of the solid earth, related to the geodetic monitoring of deformation, and to the
inverse gravimetric problem, ice and ocean dynamics, so much related to geoid studies, angular
momentum of the earth and global rotational dynamics, so strictly linked to the definition and
maintenance of a global reference system.
During the symposium we also had time to visit the Bepi Colombo Observatory of the Italian
Space Agency (ASI) in Matera, where our classroom was placed, and we would like very much
to thank ASI for the hospitality and the visit.
Also some representatives of firms of geodetic instrumentation, in particular Codevintec,
Geotop, Leica, have shown up in Matera and discussed some technical items with us;
beyond that they have contributed to our budget with funds that have been used for social
activities, during the Symposium period, and we would like to thank them heartly for their
generosity. It has to be mentioned too that, as customary with sponsored Symposia, lAG has also
provided fmancial support, which has been used to fund the participation of young scientists.
A special thank is due to Mrs. Elena Raguzzoni, that took care of the organization of the whole
event, which ran perfectly with no drawbacks.
To conclude, if I look back to the V Hotine-Marussi and to the results presented, I really think it
was worthwhile to have it and hope that such series will last long, to the benefit of the
International Association of Geodesy.
Fernando Sanso
2
Report on the Symposium
The V Hotine-Marussi Symposium on Mathematical Geodesy has been held in Matera from
June 17th to June 218\ 2002.
Geodesists interested in the theoretical and methodological aspects of their discipline discuss
these issues in a symposium that usually takes place every four years and that is hosted in Italy.
Martin Hotine and Antonio Marussi have initiated this tradition in 1959 under the title of
"Symposium on Three Dimensional Geodesy".
More than forty papers have been presented in five sessions dedicated to "New missions", "The
analysis of geodetic data: methods and numerics", "The theory of geodetic reference systems",
"Deterministic and stochastic field theory in geodesy and sister sciences" and "Inverse
problems in geodesy and geodynamics".
Some relevant topics re-appeared in several sessions; this shows not only their special
importance but also the unitary character of the geodetic problems. For example the topic of
boundary value problems has been treated in several sessions under different viewpoints and
with applications to different but related fields. The topic of stochastic models for data analysis
appeared in all the different sessions.
Stochastic methods have been applied to several situations including potential theory, integer
estimation, testing theory for control applications and inverse problems.
Some papers have been dedicated to numerical methods, specially to the method for least
squares estimation applied to the huge amount of data coming from space gravimetric missions,
spherical harmonic analysis and synthesis, multiresolution analysis and integer estimation.
It must be stressed that the problems treated in the symposium have been mainly analyzed from
the theoretical point of view and with a strong attention to methodology, that is the very
purpose of the Hotine-Marussi symposia: nevertheless practical problems of real-life geodesy
have been quite present.
Most of the presented papers are related to problems quite relevant in the applications: in this
respect I want to specially mention the reduction of space-born gravimetry (in a general sense),
the positioning with GNSSs, and the intricate difficulties of establishing a reference system.
Some animated discussions completed the topics presented by the speakers, as it is usual in
these symposia. Some papers and most of the discussions have highlighted not only the new
results obtained but also some important open problems that are relevant both for the
applications and interesting from a general theoretical point of view.
The theory of integer estimation, for example, is now well established, but a satisfactory testing
theory for the estimates still need to be developed. The problem of a "smooth transition"
between real and integer estimations (or float and fixed solution, to stay with the customary
expressions) has been also discussed. The optimal weighting of regularization conditions in