Erwin Groten

Vertical Land Motion in the Mediterranean Sea from Altimetry and Tide Gauge Stations

We have computed estimates of the rate of vertical land motion in the Mediterranean Sea from differences of sea level heights measured by the TOPEX/Poseidon radar altimeter and by a set of tide gauge stations. The comparison of data at 16 tide gauges, using both hourly data from local datasets and monthly data from the PSMSL dataset, shows a general agreement, significant differences are found at only one location. Differences of near-simultaneous, monthly and deseasoned monthly sea level height time-series have been considered in order to reduce the error in the estimated linear-term. In a subset of 23 tide gauge stations the mean accuracy of the estimated vertical rates is 2.3 ± 0.8 mm/yr. Results for various stations are in agreement with estimates of vertical land motion from geodetic methods. A comparison with vertical motion estimated by GPS at four locations shows a mean difference of −0.04 ± 1.8 mm/yr, however the length of the GPS time-series and the number of locations are too small to draw general conclusions.

Geodetic techniques applied to the detection and monitoring of recent crustal movements

Abstract Geoditic space techniques became a very precise tool in detecting and monitoring recent crustal movements: in a well defined and exactly implemented frame of reference, mainly determined by very long baseline interferometry and absolute gravity a global system is established with centimeter accuracy within which repeated regional measurements of recent crustal movement can take place even over long intervals of time with high accuracy. Global Positioning system (GPS) meanwhile found its place, together with relative gravimetry, as an additional component which is directly related to the International Earth Rotation Service global system of reference. Repeated observations were carried out in various parts of the world which clearly demonstrate the high flexibility, impressive accuracy and extreme usefulness of GPS together with precise gravimetry. Detailed network design, accuracies and rates of repeated measurements, numerical results and analysis of data for short or large distances are considered. Moreover, the use of local geodetic techniques, based on tiltmeters, etc., and their combination with space methods is discussed. Specific problems associated with applications in Africa are pointed out.

On the Upper Bound of the Liquid Core Viscosity

By using Molodensky and Sasao (1995a) and Molodensky and Groten (1998) an approach of expansion in powers of the small parameter κ=(σ+ω)/ω (where σ+ω and ω are the frequencies of nutational motion in space and in a mantle-fixed reference frame, respectively, σ is tidal frequency) a theory of diurnal Earth tides and nutation for a realistic model of the Earth with an inhomogeneous, viscous liquid core and an anelastic mantle is constructed. It is shown that our approach is self-consistent for semi-annual, annual, and principal nutational components (when |κ|≤1/180). By comparing the results of modern VLBI-nutational data and the results of our calculations, we have found the region of possible values of the parameters which describe the anelastic properties of the Earths lower mantle and the viscosity of the liquid core. It is shown that modern VLBI-data are about six orders of magnitude more sensitive to the liquid core viscosity than modern seismic data or Earth free oscillations data.

Methods and experiences of high precision gravimetry as a tool for crustal movement detection

Abstract Whenever vertical dislocation is of primary interest, purely geometric surveying techniques, such as GPS, VLBI etc, are deficient in detecting and interpreting geodynamic phenomena such as subsidence and uplift. Absolute gravimetry meanwhile became so accurate that it can successfully be applied under usual conditions. However, for dense field observations in regional and/or local studies relative gravimetry still cannot yet be fully replaced by absolute gravimetry. The basic advantage of gravimetry, in combination with satellite or traditional surveying techniques, lies in its “integrating effect”, which means that height and gravity changes together enable, at least in principle, the solution of a four-dimensional boundary value problem, so that a clearer interpretation of uplift and subsidence becomes available. Two examples are outlined where gravity networks are intended to resolve vertical displacement or changes in potential in relation to earthquake events. A local network in the Friuli seismic risk zone, where highest accuracy of about 5 microgal † is obtained, is compared to a large scale gravity net in South America, where 10–20 μgal accuracy is demonstrated for gravity variations between consecutive epochs. However, in both cases deficiencies still exist which make it necessary to carry out additional observations before unique results can be expected. In case of South America extreme environmental conditions prevented the accuracy usually achieved with 3 or 4 repeated campaigns to be obtained. In case of Friuli the second measurement clearly reveals still unexplained phenomena when compared with the first campaign. Thus possibilities as well as limitations are pointed out.

Combined Sea Surface Determination Based on Various Geometric and Dynamic Techniques

Abstract The combined use of Global Positioning System (GPS) differential positioning as well as ERS‐1 altimeter data is considered in implementing geodetic vertical datums and their unification. The article describes concepts, techniques, practical realization, and associated questions and problems. Particular aspects in view of small sea surface perturbations in offshore areas in determining sea surface components (variable and steady state) are discussed. The combinations of tide gauge data with altimetry and (mainly) GPS positioning for geodetic purposes are discussed in detail. Special attention is devoted to the associated reference systems as well as to the combination of dynamic (level and nonlevel surfaces) with geometric quantities. The discussion is based on a specific ERS‐1 project supported by the National Science Foundation. Implications and practical impact of the project are outlined.

Global tidal parameters

SummaryGlobal tidal parameters are shown to have recently increased in accuracy, after more than twenty years of LLR and a decade of superconducting gravimetry, whereas the numerical values for the Earth have not changed substantially. Numerical values of Love numbers for terrestrial planets and the moon are also given for degrees higher than four as load numbers are basically linear combinations of Love numbers, at least for spherical non-rotation approximations. Numerical values for planetary moons, as far as they are known, have also been included in the paper. The static and dynamic behaviour of long-period and pole tide is discussed. Inner solid and outer fluid core effects are critically reviewed, also in view of a century of terrestrial tide observations of the classical type. The separation of long-period tides from secular effects (on a rotating Earth) such as Jn (n<5), is considered.

A Discussion of Fundamental Constants in View of Geodetic Reference Systems

Besides global terrestrial reference systems, such as ITRF (S) WGS 84, as updated in 1997, there exist a variety of continental or regional reference systems basically related to ITRF. With ongoing applications of global vertical positioning a global vertical datum becomes feasible. As systems, such as EUREF etc., are basically three-dimensional, the combination and unification of continental and regional vertical datums can now be implemented. First approaches of that kind, using tide-gauges in combination with repeat GPS-positioning as well as levelling together with satellite altimetry of different kind (TP, ERS-1/2 etc.) are affected by the temporal changes of global heights which are basically different from temporal changes in horizontal systems which are dominated by global plate tectonics in such a way that, at least, large scale behavior can be modelled by NUVEL-1A and similar systems. Moreover, in vertical systems the global geoid in terms of the geopotential W has to be incorporated. Thus an additional parameter which is not very well known globally, even though regional differences were meanwhile quite well explored, plays a significant role. Together with the geoid a Somigliana type normal field is appropriately introduced. In view of ecological and climatological aspects the mass exchange of ocean and atmosphere, its temporal variations in terms of El Nino and climatology, and a variety of dynamic aspects related to oceanic effects become relevant. In SC-3 of IAG all these aspects are presently discussed. New results have been investigated and compared with each other. In that connection the geopotential at the geoid W° plays a significant role and the accuracy of its present determination, problems associated with it, its interrelation with other global parameters and its use as a primary constant were considered. Results are presented in this paper.

On the Dynamical Effects of the Mantle in the Theory of Nutations

The influence of inerial forces in the mantle on its tidal deformations is considered. It is shown that the main role is played the corrections, described by spheroidal deformations, which result in corrections of nutational amplitudes of about −0.076 mas for the prograde semi-annual component, −0.056 mas for the retrograde annual component, 0.099 mas for the retrograde 19-year component, and −0.024 mas for the prograde 14-day component. These values exceed the errors of modem VLBI-measurements significantly (being of the order of 0.02-0.03 mas with the exception of the main nutational component); the effect of toroidal deformations is negligibly smalt in comparison with the accuracy of the VLBI-measurements, and for any practical purposes need not be considered.

Geopotential Reconstruction, Decomposition, Fast Computation, and Noise Cancellation by Harmonic Wavelets

Harmonic wavelets are introduced within the framework of the Sobolev-like Hilbert space H of potentials with “square-integrable restrictions” to the Earths (mean) sphere ΩR. Basic tool is the construction of H-product kernels in terms of an (outer harmonics) orthonormal basis in H. Scaling function and wavelet are defined by means of so-called H-product kernels. Harmonic wavelets are shown to be “building blocks” that decorrelate geopotential data. A pyramid scheme enables fast computations. Multiscale signal-to-noise thresholding provides suitable denoising. Multiscale modelling of the Earths anomalous potential from EGM96-model data is illustrated by use of bandlimited harmonic wavelets, i.e. Shannon and CP-wavelets.

On the Models of the Lower Mantle Viscosity Consistent with the Modern Data of Core-Mantle Boundary Flattening

In Forte and Claire Perry (2000) models of mantle viscosity (by using the data on tectonic plate velocities, of global free-air gravity anomalies, of surface topography corrected for crustal isostasy, and the excess of dynamic ellipticity of the core-mantle boundary in accordance with Herring et al., 1986 and Mathews et al., 1999) have been constructed. In the following investigation we reconsider the results which are obtained from the presently available data on core-mantle boundary flattening (abbreviated by CMBF). In contrast with the aforementioned work, we use below the value of CMBF (Molodensky and Groten, 1998) which is based on a new approach to the theory of diurnal Earth tides and nutation which takes into account the second-order terms of expansions of a small parameter κ (for a detailed discussion of this subject see (Molodensky and Groten, 1998)). Below we find the area of admissible values of mantle viscosity which does not contradict the following data sets: (a) the numerical value on CMBF; (b) the value of the whole Earths dynamical flattening, and (c) the data on the secular deceleration of the Earths rotation. Our estimations show, that the maximal viscosity at depth 2000 km may be of the order of 1027 Poise. This value is consistent with the distribution obtained by Trubitsin (2000) who adopted the viscosity dependence on temperature and pressure by an exponential function with olivine parameters under the assumption that the activation energy varies only weakly with pressure, and the activation volume varies in inverse proportion to temperature. Under these assumptions, his solution of convection equations gave the depth dependence of temperature and thereby the viscosity distribution.