F. Sacerdote

• University of Florence

Spirit leveling and surface gravity observations can be expressed as orthometric height differences plus corrections which require the knowledge of the Earth crust density. For leveling increments we can write observation equations in a linearized form, according to the standard Molodensky approach, i.e., intrinsic geodesy, depending on normal heig...

Levelling increments must be corrected for gravity in order to get proper dynamic or orthometric heights. In Italy, most of the levelling lines have no associated gravity observations. Thus, only levelling increments are available, and corrections were computed only on a subset of the existing lines. However, gravity is densely observed, and thus,...

The famous work of A. Marussi on the geometry of the Earth’s gravity field is known as intrinsic geodesy. This was aiming at describing all the relevant geodetic quantities in terms of the so called intrinsic coordinates (Λ, Φ, W) and of their reciprocal relation. This has been done in a masterly way including all the interesting variables related...

The famous work of A. Marussi on the geometry of the Earth's gravity field is known as intrinsic geodesy. This was aiming at describing all the relevant geodetic quantities in terms of the so called intrinsic coordinates .ƒ; ˆ; W / and of their reciprocal relation. This has been done in a masterly way including all the interesting variables related...

The Bayesian approach to significance testing, that makes use of prior information, has been studied in the last years, particularly to allow the detection of deformations which are small with respect to measurement errors from repeated surveys. Some investigations showed up to now that, under particular conditions concerning both the parameters of...

The determination of global gravity potential models is a central issue in Geodesy. In principle the existence of solutions, i.e. of harmonic potentials, given certain boundary conditions, depends on the solvability of certain boundary value problems (BVP) for the Laplace equation, an item that has recently received quite an impulse in terms of abs...

The theory of elliptic boundary-value problems in Hilbert spaces has been extensively illustrated some decades ago, e.g., by J.L.Lions and E.Magenes for very general differential operators, with coefficients, right-hand sides of the equations and boundary conditions belonging to irregular function or distribution spaces; consequently solutions too...

It is well known that the classical testing procedures are not able to detect any significant deformation when the estimated displacements stemming from repeated surveys are small with respect to their precisions. This is true even if the displacements show some internal consistency (e.g. all the displacements have a common direction) or agree with...

Riassunto esteso Nel controllo di deformazioni di strutture o di movimenti franosi, spesso le tecniche tradizionali di analisi statistica non sono in grado di evidenziare spostamenti significativi quando la loro entità è relativamente piccola rispetto alla precisione delle misure. Ciò accade anche in quei casi in cui gli spostamenti rilevati mostra...

DEM generation in architecture presents well known problems when the structure is complex and has irregular and discontinue surfaces. Data acquired from laser scanner and photogrammetric systems can be employed to best represent different aspects of the same object: every survey technique is useful to register (and then to show, after data elaborat...

In this paper a multisensor approach (topography, photogrammetry, laser scanning) was exploited to generate a close range model of a cultural heritage object in order to evaluate the accuracy of data in all steps of the model production, from the acquisition to the representation. A programmed data redundancy allowed to verify the accuracy of each...

The analysis of boundary-value problems has always been used in geodesy as a frame to understand the nature of the problem of determining the gravity disturbing potential, with respect to well-posedness (existence, uniqueness, continuous dependence of the solution on boundary data). The first historical problem of this kind is Stokes’s, followed by...

The problem of global geoid determination is usually solved using satellite altimetry data on the oceans, together with an oceanographic model of sea surface topography, and gravity anomaly data on the continents. Such data, however, enable to obtain only potential differences with respect to a reference surface whose absolute potential is unknown....

This paper discusses preliminary results related to the comparison of long baselines obtained from GPS and VLBI data processing in Europe. This comparison was carried out with the aim to check the agreement of the crustal deformation fields derived by the two techniques. An approach based on the theory of stationary and ergodic stochastic processes...

Proceedings of the "Interdisciplinary Inversion Conference 1995", University of Aarhus, Denmark

The recovery of the harmonic coefficients of the anomalous potential from a geodetic quantity sampled over a regular grid is affected by the non-exact discrete orthogonality of spherical harmonics; larger errors occur for block-average quantities owing to the non-simple behaviour of the block-average operator when applied to spherical harmonics. Fo...

Evaluation techniques related to the theory of boundary-value problems with stochastic boundary conditions described by Wiener measures are used to compare the expected accuracies of the geoid obtained from gravity anomalies and from deflections of the vertical, with the current density and precision of individual measurements. Analytical computati...

The calculus of spherical harmonic representation of fields of geodetic interest is often performed by applying integral formulas to block-averaged quantities. Due to the dependence of the block areas on latitude, it is difficult to perform a rigorous computation; in this paper the effects of approximations related to the loss of orthogonality in t...

Presented at Progress Meeting CIGAR, Darmstadt, August 25, 1992

The idea of using a combination of GPS and accelerometric spaceborne observations, to produce a set of estimated vector gravity disturbances along the orbit, has been recently proposed. These data could be block averaged and used as input for an overdetermined BVP to find global gravity models. In this paper the theory is reviewed and relevant simu...

The proposai of combining GPS and accelerometric measurements on a low-orbiting satellite in order to improve thè knowledge of a part of thè harmonic spectrum of thè anomalous gravity potential has been proposed in view of thè ARISTOTELES mission. In thè present paper thè principles of thè computation procedure are illustrated; different error sour...

Presented, on the 70th Anniversary of prof. Mariano Cunietti

It is well-known that the determination of the gravity field requires a complete coverage of the earth’s surface by some kind of boundary data. If the coverage is not complete, it is interesting to study what is the maximum error that can be found degree by degree under suitable statistical constraints. On the other hand, if data are given on surfa...

Two particular cases of the oVerdetermined gravirnetry-gradiometry problem are discussed: a) the case of a latitude-dependent statistical weight for gradiometric data, corresponding to a data distrihution coming from satellite polar orbits, b) the case of a volume distribution, instead of a surface distribution, for satellite gradiometric data. In...

The topographic surface of the sea can be determined by subtracting the geoid from the geometric height of the stationary sea surface. This latter can be obtained from altimetry measurements; the former can be derived from marine gravity measurements, treated in the form of gravity disturbances. When a closed sea is treated, the gravity anomalies o...

Two particular cases of the overdetermined gravimetry-gradiometry problem are discussed: a) the case of a latitude-dependent statistical weight for gradiometric data, corresponding to a data distribution coming from satellite polar orbits, b) the case of a volume distribution, instead of a surface distribution, for satellite gradiometric data. In b...

Observation equations for a gradiometer in inertial flight are described, and the effects of orbit and attitude errors are modelled, showing that, when high precision direction observations are missing, the use of rotation invariant equations is advantageous. The invariant form of the equations is analysed by demonstrating the necessity of using a...

Our specific target is to achieve the best knowledge of a global gravity field model in terms of coefficients of a truncated expansion in spherical harmonics $$\begin{gathered} V(model) = \begin{array}{*{20}{c}} L \\ {{\sum _1}} \\ 0 \end{array}\begin{array}{*{20}{c}} l \\ {{\sum _m}} \\ 0 \end{array}\begin{array}{*{20}{c}} 1 \\ {{\sum _\alpha }} \...

The theory of overdetermined BVP's has been introduced into physical geodesy as a powerful tool to combine different sets of data, when thè measure points are very densely distributed over thè boundary or even at points of thè harmonicity domain. Many times, however, different data sets are referred to different zero-points, scale factors, etc., de...

Presented at XIX General Assembly of IUGG-IAG, August 9-22, 1987

The two Altimetry-Gravimetry linearized boundary value problems, both characterized by gravity anomaly boundary data on the continents, while on the oceans either the gravity potential or its radial derivative is assumed to be known, are investigated in their modified version, in the spherical boundary approximation. A constant unknown bias is adde...

The problem of estimating the gravity potential of the earth is discussed when a large amount of data is available both for gravity anomalies all over the earht's surface (approximated by a sphere) and for the gravity gradient on a spherical surface surrounding the earth and concentric with it. The data are supposed to be affected by white independ...

A new free boundary problem is introduced, that seems to be more consistent with the actually available gravimetric data than the classical problem of Molodensky. Only the gravity modulus, and not its direction, is assumed to be given on the boundary in addition to the value of the potential; on the other hand, only the height of the points of the...

The problem of estimating the gravity potential of the Earth, when more data than those strictly necessary to determine a unique solution are given on its surface, is discussed in a rigorous mathematical frame. The computation procedure is described for a geodetically relevant mixed boundary value problem.-from Authors

The authors stress the interest for many purposes of very accurate links among the different astronomical reference systems, and in particular between the one defined by astrometric star catalogues and that bound to the Earth. They propose to realize such a link by using an astrometric space-borne telescope, similar to that projected for the HIPPAR...

The triple correlation function on a sphere is analyzed using high-frequency approximation for the purpose of applying the function to the earth's gravity field. To test the triple correlation coefficients, a random earth is defined in which harmonic coefficient phases are random and generally no triple correlation exists. It is maintained that pre...

A discussion is given of how satellite-laser-ranging data can be used to determine the geodetic parameters that are relevant for setting up a local network, with consideration given to the most important problems encountered in data analysis for this purpose. Problems examined include: filtering and compressing procedures for raw data, determinatio...

The existence of a unique weak solution continuously depending on the boundary data is proved for the linear problem of Molodenskii in almost spherical approximation, in the case that the boundary surface satisfies a cone condition. A direct constructive approach is used, that generalizes a procedure previously devised for the simple problem of Mol...

The altimetry-gravimetry problem in its modified form, as defined byPellinen (1980) andHolota (1982) (Δg given on land and δg given on sea), is analysed in spherical approximation: broader results concerning existence and uniqueness than those previously known are achieved. A proposal for the numerical solution of the problem is presented. Present...

Presented at XVIII IAG General Assembly, Hamburg 1983

The HIPPARCOS satellite will be launched by ESA in 1985, carrying on board an astrometric telescope of very high accuracy (1). The expected output of the mission is a catalogue of angular positions, proper motions and parallaxes of ~ 105 stars. This will provide a stellar reference system with an internal accuracy of about 0˝.002. Then the necessit...

The accurate tracking of geosynchronous satellites is suggested as an efficient means of improving knowledge of the resonant geopotential coefficients, and therefore of the geoid, as well as of determining with greater precision the radial departure of the sea surface from the geoid, with a view to its seasonal or long period variations. It is show...

Since such polar motions as precession, lunisolar nutation and free nutation introduce small, apparent forces in earth satellite equations of motion in earth-fixed reference frames, attention is given to the possibility of (1) integrating the orbit in such frames when tracking data are used for geophysical applications, and (2) determining a set of...

In an Earth-fixed reference frame, polar motions (precession, lunisolar nutation, free nutation) introduce small apparent forces in the equations of motion of an Earth satellite. We discuss the possibilities (a) of integrating the orbit in an Earth-fixed frame when tracking data are used for geophysical applications, and (b) of determining from orb...

This paper was carried out to promote the valorization of a particular naturalistic sea coast area where complex cultural, archeological, and environmental interactions involve the requirement of an articulate monitoring system. The area of study is part of the coastal macchia mediterranea in Tuscany close to the town of Livorno and presents some m...

In this work we discuss the triple Kaula and expanded at the end of section 1 of pa- correlation function on a sphere, having in view per 1. It becomes therefore essential, before de- its application to the gravity field of the earth. veloping and using more complicated practical col- This is done mainly in the short-wavelength lim- it, which requi...