Oceanography

Marie-Hélène Rio

Interaction between Geodesy and Oceanography: results and open problems

In the era of space oceanography and in particular altimetry, Geodesy and Oceanography have been walking hand in hand. Indeed, what an altimeter measures from space with very high accuracy is the distance between the satellite orbit and the surface of the ocean. By subtracting the known distance between the satellite orbit and the reference ellipsoid, very accurate information on the distance between the sea level and the reference ellipsoid can be retrieved. However, for an oceanographer, the signal of interest is the sea level above the geoid, the so-called dynamic topography, from which the ocean surface currents can be inferred using the geostrophic approximation. At the time first altimeter missions were launched, the geoid was not known with sufficient precision to be directly removed from the altimeter sea level measurements. Instead, repetitive altimeter missions were planned in order to calculate a temporal sea level mean and remove it from each along-track measurement. However, by doing so, not only the unknown geoid information is removed but also the stationary component of the dynamic topography, i.e. the Mean Dynamic Topography (MDT). This mean component therefore needs to be retrieved from other sources and added back to the altimeter Sea Level Anomalies. In the last 25 years, with the advent of space-borne gravity missions as GRACE and GOCE, huge improvements have been made in the knowledge of the marine geoid and the Mean Dynamic Topography, with a direct consequence on the retrieval of ocean surface currents.

In addition, the GRACE mission has allowed for the first time ever to measure, at large spatial scales, the temporal variations of the gravity field. Over the oceans this is directly linked to ocean mass variations and therefore represents another very significant contribution for ocean dynamics analysis.

In this talk, we will review the state-of-the-art in those domains and discuss the main open issues and perspectives for the future.

Glaciology

F. Olivier, T. Van Dam

Absolute Gravity and Surface Displacements in Greenland

Measurements of vertical crustal uplift from bedrock sites around the edge of the Greenland ice sheet (GrIS) can be used to constrain present day mass loss. Interpreting any observed crustal displacement around the GrIS in terms of present day changes in ice is complicated, however, by the glacial isostatic adjustment (GIA) signal. With GPS observations alone, it is impossible to separate the uplift driven by present day mass changes from that due to ice mass changes in the past. Wahr et al. (1995)demonstrated that viscoelastic surface displacements were related to the viscoelastic gravity changes through a proportionality constant that is nearly independent of the choice of Earth viscosity or ice history model. Thus, by making measurements of both gravity and surface motion at a bedrock site, the viscoelastic effects could be removed from the observations and we would be able to constrain present day ice mass changes. Alternatively, we could use the same observations of surface displacements and gravity to determine the GIA signal. In this paper, we extend the theory of Wahr et al. (1995) by introducing a constant, Z, that represents the ratio between the elastic changes in gravity and elastic uplift at a particular site due to present day mass changes. Further, we combine 20yrs of GPS observations of uplift with eight absolute gravity observations over the same period to determine the GIA signal near Kulusuk, a site on the southeastern side of the GrIS, to experimentally demonstrate the theory. We estimate that the GIA signal in the region is 4.49 ±1.44 mm/yr and is inconsistent with most previously reported model predictions that demonstrate that the GIA signal here is negative. However, as there is very little in situ data to constrain the GIA rate in this part of Greenland, the Earth model or the ice history reconstructions could be inaccurate (Khan et al., 2016). Improving the estimate of GIA in this region of Greenland will allow us to better determine the present-day changes in ice mass in the region, e.g. from GRACE.

Atmosphere

R. Pacione and J. Dousa

Geodesy and Atmospheric Science: a collaboration mutually beneficial

Geodesy, the science of the Earth’s shape, gravity and rotation, contributes to Atmospheric Science by providing some of the Essential Climate Variables of the Global Climate Observing System (GCOS) such as: see level from radar altimetry, ice mass loss and terrestrial water storage from satellite- gravimetric mission, atmospheric water vapor from ground-based and space-based GNSS as well as from VLBI radio telescopes and DORIS. This presentation will be focused on water vapor, the most abundant greenhouse gas of the atmosphere, sensed by space geodetic techniques with a particular attention to the so called GNSS-Meteorology technique. Water vapor is under-sampled in the current meteorological and climate observing systems, therefore obtaining and exploiting more high-quality humidity observations is essential to weather forecasting and climate monitoring. The production, exploitation and evaluation of operational GNSS-Meteorology for weather forecasting is well established in Europe thanks to about two decades of outstanding cooperation between the atmospheric and geodetic communities. In contrast, the use of ground-based GNSS long-term data for climate research is still an emerging field and is now possible because of the availability of long- term homogeneously reprocessed time series on global and regional scale. The present state-of- the-art of GNSS-Meteorology would have been impossible without the products provided by the Global Geodetic Observing System (GGOS, http://www.ggos.org). GGOS products are provided by the services of the International Association of Geodesy (IAG, http://www.iag-aig.org). Of primary importance is the International GNSS Service (IGS, http: //www.igs.org) that provides a wide range of satellite precise orbit and clock products fundamental for GNSS-Meteorology. On the other hand, improved modelling of the atmospheric influence can contribute to the fast convergence and higher accuracy of GNSS positioning and navigation services, making the collaboration between the geodetic and atmospheric communities mutually beneficial.

Mathematics

W. Freeden, F. Sansò

Geodesy and Mathematics: acquisitions and open problems

The presentation highlights arguments that, coming from Mathematics, have fostered the advancement of Geodesy, as well as those that, generated by geodetic problems, have contributed to the enhancement of different branches in Mathematics.

Furthermore not only examples of success are examined, but also open questions that can constitute stimulating challenges for geodesists and mathematicians.

In the first part of the paper we perform a general overview, without any pretense of completeness, of areas like geometry of the Gravity Field ( GF ), boundary value problems ( BVP ) for the Laplace operator, probability theory ( in particular Generalized Random Fields ) and statistics ( in particular integer parameters estimation and rank deficient problems ), improperly posed and inverse problems for the GF.

In the second part of the paper, we focus on the ill­posed inverse gravimetric problem, namely deriving from gravimetric information on geological characteristics of the density contrast function. Different methodologies and their numerical implementations are examined. Singular integral theory based inversion of the Newtonian integral equation, such as a Haar­type solution, is handled in a multiscale framework to decorrelate specific geological signal signatures with respect to inherently given features.

Reproducing kernel Hilbert space regularization techniques are studied to provide geological contrast density distributions by “downward continuation” from terrestrial and/or space borne data.

Solid Earth system structure from space

R. Haagmans

Solid Earth-System structure from satellites

Various satellite missions provide information on the surface or surface changes of the Earth, the gravity field, the magnetic field and even other variables than can be related to processes at the surface of the Earth or in its interior. The presentation aims to provide a quick overview by means of examples followed by a more in depth look at ESA’s gravity field mission GOCE and magnetic field mission Swarm.

ESA has launched two Earth Explorer satellite missions since 2009 that focus on Earth gravity and magnetic field. The first one GOCE focussed on providing the best measurements of gravity gradients from a satellite to a detail in space of about 80km along the tracks. These gravity gradients, together with gravity and the geoid provide a new source of information for the geophysical and geological community. The gradients at satellite height have the potential to provide directional information on subsurface structures that is complementary to gravity near the surface and this can be used to improve regional modelling of the subsurface to a depth of about 150km or even deeper depending on the tectonic setting. The larger scale gravity and geoid signals more dominantly display the effects of deeper structures and dynamic processes in the Earth interior.

In November 2013, a constellation of three satellites was launched to map the magnetic field of Earth and to investigate its interaction with the solar wind. One of the goals of the mission is to improve the crustal field to a resolution that aeromagnetic/marine surveys and global models from satellites complement each other’s scales, which is not the case today.

Recent ESA studies focus on combining satellite data, seismological and geological based to arrive at a consistent picture of Earth’s interior up to the core-mantle boundary. Sensitivity analysis of data and models and understanding of models from neighbouring communities is essential to progress in this field. The most recent results reveal interesting challenges, which will also be presented.

Seismology

A. Peresan, M. Crespi, G. F. Panza, A. Mazzoni

Geodesy and Seismology: a key synergy for the understanding and forecasting of earthquakes

A novel scheme, able to fully exploit the information content of the available data, is proposed for the synergic use of seismological and geodetic information, in order to delineate, as precisely as possible, the regions where to concentrate prevention actions and seismic risk mitigation planning. From the seismological point of view, long-lasting practice and results obtained for the Italian territory in two decades of rigorous prospective testing of fully formalized algorithms (e.g. CN), prove the feasibility of earthquake forecasting based on the analysis of seismicity patterns at the intermediate-term (i.e. several months) middle-range scale (i.e. few hundred kilometers).

These algorithms deal with multiple sets of seismic transients and allow for the identification of the region and time interval where a strong event (above a given magnitude threshold) is likely to occur. This information, as a rule not aiming at red alert, may allow prevention actions to be properly focalized. An improved but not ultimate precision can be achieved reducing as much as possible the space-time volume of the alarms, by jointly considering seismological and geodetic information.

A pioneering step was made in the framework of the project SISMA funded by Italian Space Agency about ten years ago. Now, differently from the standard approach, the geodetic information coming from GNSS and SAR are not used to estimate the standard 2D velocity and strain field in the area, but to reconstruct the velocity and strain pattern along transects oriented according to the a priori known tectonic setting, in total respect of the real information content of available data. Considering properly defined transects within the region(s) alarmed by CN algorithm, the velocity variation and the related strain accumulation are highlighted, with due consideration of the errors involved in GNSS data.

A retrospective analysis (including stability tests) was carried out on GPS data preceding the 2012 Emilia earthquake and the Central Italy seismic crisis (started on 24 August 2016 with the Amatrice earthquake). Tools have been developed to allow for a systematic analysis of the velocity variations together with their accuracy along a number of transects, properly located, along strike and across strike, according to the tectonic and seismological information. The aim is to identify reliable anomalies in the strain rate distribution in space; in fact no time dependence has been detected in the more than 10 years preceding the occurrence of the studied events. Some counter examples, considering both along strike and across strike transects, traversing CN alarmed and not-alarmed areas, do not show any spatial acceleration localized trend, comparable to the one well defined along the Amatrice (across strike) and Emilia (Apennines crest and Brisighella along strike) transects.

The results obtained so far show that the combined analysis of the results (time dependent within decadal interval) of intermediate-term middle-range earthquake prediction algorithms, like CN, with those from the processing of adequately dense and permanent GNSS network data (time independent wthin the same decadal interval), possibly complemented by a continuous InSAR tracking, may allow the routine localized highlight in advance of the strain accumulation. Therefore the extent of the alarmed areas, identified based on seismicity patterns at the intermediate scale (i.e. few hundred kilometers), can be significantly reduced.