GOCE
BRIEF DESCRIPTION OF THE PROJECT
The calibrated GOCE gravity gradient observables (Gravity field and Steady-state Ocean Circulation Explorer) can be used to determine the static field of the Earth with excellent precision and resolution (see www.earth.esa.int/workshops/goce06). Many specialists in Europe and in the whole world will utilize the GOCE data. Our small group from the Czech Republic around the Astronomical Institute of the Czech Academy of Sciences wants to focus on the following 5 topics, with possible extension due to course:
1. Orbit choice and tunning for GOCE measuring phases
2. Novel geodetic computational methodologies.
3. Comparison of detailed satellite and terrestrial data
4. Detection of hidden impact (meteoritic) structures on the Earth surface
5. Others
Item 1. Orbit choice and tunning for GOCE measuring phases.
(responsible persons Jaroslav Klokočník and Jan Kostelecký)
The diminished resolution of solutions for variations of the gravity field from the Gravity Recovery And Climate Experiment (GRACE) around September 2004 was related to the short orbit repeat cycle of R/D = 61/4 for the GRACE A/B satellites (R = 61 satellite’s nodal revolutions per D = 4 synodic days). Similar situations were encountered in GRACE’s past orbit and may be encountered in its future free fall. We use recent models of atmospheric density to estimate minimum and maximum drag and the orbit decrease of GRACE, providing a warning of possible future degradation. The densities of the ground tracks of CHAMP, GRACE or GOCE are investigated to get a better insight into how these patterns and accuracy of the solved-for gravity field parameters are related. The density depends strongly not only on a “distance” from a low order R/D repeat (i.e., on time), but also on geographic latitude. Implications for GOCE are also discussed, with some suggestions for the orbit choice or tuning for the measuring phases of this mission.
We would like to continue in this analysis. From summary of orbit resonances which would be encountered in theoretical case of free-falling GOCE, we can choose those orbits for measuring phases MP1 and 2 (duration 6 months each), with constant altitude that will be far enough from stronger repeat orbits and their degradating influences. The most important is the 16/1 resonance with particularly poor track density. The orbit of GOCE should be as far as possible from the 16/1 repeat, preferably below it, for the benefit of the gradiometer measurements.
In a repeat orbit (compared to a "non-repeat" regime), one may have the same number and quality of observations for gravity parameter recovery, but the space distribution of the data due to the repeat condition is inevitably sparser. Over a long mission, encompassing many such repeat orbits, the density variations may be large both in time, and are large also in geographic latitude. This space density consideration was not so critical for pre-CHAMP models based on a variety of higher repeat and non-repeat satellite orbits as well as on terrestrial data. The consequence for the recent single satellite missions of geopotential recovery is clear: to achieve the maximum accuracy and resolution in recovery the orbit design must avoid short repeat cycles as much as possible either by (1) station keeping in an orbit with suitably dense tracks or (2) by maneouvering to avoid undesirable orbits (in an otherwise 'free fall').
Item 2. Novel geodetic computational methodologies
Goce gravity field modeling with full variance-covariance information
(responsible person: Christian Gruber)
The team is in the position to estimate and evaluate global gravity field parameters derived from satellite missions from gradiometry as well as orbitography and their combination/stabilization with selected ground based gravity data by different approaches including direct inversion with full var/cov information. The team has experiences in gravity field estimation of CHAMP & GRACE data as well as with its evaluation. The calibrated GOCE gravity gradient observables can be used to determine the static field of the Earth gravity potential. Due to the huge amount of observational data on one hand and the complexity of the geopotential model on the other hand a solution for the parameters remains a highly demanding computational task. An alternative method has been developed to minimize the necessary workload concerning parameter estimation. While a full matrix inversion for parameter estimation is nowadays feasible up to degree/order 210 on a single personal computer (8GB storage) the assembling of the corresponding observational data by standard processing methods into the normal equation system is by far too time consuming to be processed on a single processor system. By evaluating the empirical product-sums of the involved base-functions a new, redundancy-free procedure to assemble the required normal equation system has been developed and can be used for the rigorous in-situ global spherical harmonic analysis with full var-covariance information up to degree/order 200. The data integration reduces substantially compared to the conventional approach (outer product of the observation equations) and can be therefore conveniently handled on a desktop PC. A speed up by L/6, where L is the maximum degree of the model can be expected for the single observation component. Moreover, since the diagonal tensor observations refer to the same locations, the integration of all tree observables can be handled in a single step by superposing the respective eigenvalues of the observational equations leading to a total speedup by L/2.
A comprehensive software package is under development at the Astronomical Institute in Ondrejov for the frequency-wise as well as the rigorous approach and is undergoing tests with simulated GOCE as well as real CHAMP & GRACE data and their combination. The successful integration of real GOCE data would be a desirable next step.
During first half of 2008 the software interfaces will be adopted to meet the GOCE data formats. Theoretical issues and simulation studies will be finalized. Numerical results might be expected later.
Item 3. Comparison of detailed satellite and terrestrial data
Using GOCE data for estimation of the height transformation
surface over the territory of the Czech Republic
(responsible person: Pavel Novák)
Despite the current large progress in global gravity field modeling, high accuracy and resolution local/regional models of the geoid/quasi-geoid to be used for geodetic height transformations must still rely on combination of global (spaceborne) and local (ground and/or airborne) gravity data. This situation will not change even after the GOCE data will be released. Most of the current techniques for regional gravity field modeling is based on a weighted combination of harmonic geopotential coefficients and observed local gravity data (ground anomalies, airborne disturbances). In an alternative approach, ground, airborne and spaceborne observables could be combined directly in derivation of a unique and frequency-seamless model of the geopotential, thus also of the gravimetric geoid/quasi-geoid. The GOCE data represented by selected components of the gradiometric tensor will offer a completely new spaceborne data type with
unprecedented properties, both in terms of their spatial distribution and namely spectral content. It will be very interesting to include this data type to other gravity field observables available over the territory of Central Europe in an attempt of derivation of the most accurate regional gravity field model to-date. Besides the main aim of this project represented by a surface for height transformation, the combination of the GOCE data with other available gravity information will be used for testing the quality of the solution, thus also of the GOCE-based component, with a help of high-precision and resolution GPS/leveling data in the region. For this purpose, a regional database of gravity, elevation, density and GPS/leveling data has been compiled. Relevant experiences for the project of a similar kind were obtained while using currently available CHAMP and GRACE observables and their corresponding observations for regional gravity field modeling.
Item 4. Detection of hidden impact (meteoritic) structures on the Earth surface
Crater Chicxulub as seen by GOCE gradiometer data and possible discoveries
of further hidden impacts on the Earth
(responsible person: Jaroslav Klokocnik)
Can the second gravity derivatives, namely Vzz, derived from GOCE gradiometer measure-ments, be used to identify impact craters on the Earth still hidden under rain forests, deserts seas and similar places? About 150 large impacts is already known for sure. In accordance with opinion of various astronomers and geologists, there are many impact structures still hidden and waiting to be revealed. Sufficiently accurate and dense GOCE data may lead to a great progress in this direction, with fast and non in situ-measurements, without additional costs to the GOCE project. In the first phase, we should test GOCE data on existing known impact craters, in the second phase we could try to discover craters not yet known.
The concept is based on a simple mascon approach (but may be improved, and we are working on it). A crater is a mascon, generating a signal which might be measurable by GOCE. For the first rough informative estimate, we consider only the component Vzz,= 2 GM/r3, where M is the mass of the impact crater, r its distance from the measuring instrument (i.e. height of flight of GOCE), and G is the universal gravitational constant.
We assume GOCE at height 250 km (on circular orbit) flying directly overhead (realistic cases of the ground track densities and signal attenuation during overflights need to be investigated). The measuring precision of GOCE gradiometer is about 3 miliEötvös (0.003 E) for frequency range 5-100 mHz. To be conservative, we take σ = 0.010 E as a typical measuring accuracy of the second derivatives from GOCE gradiometer. Rate of gradiometer measurements is 1Hz, but 10 Hz data might be also available (Floberghagen, priv. commun. during the GOCE workshop in Frascati, 2006). The orientation of the s/c body can be determined with arc of second accuracy so even those components of the gravity tensor which are dependent on rotation should not be affected more than in miliEotvos level.
Chicxulub crater in north-west Yucatan is a good test sample of well known and analysed crater on the Earth. It is a result of 65 milion year old impact. It has no significant topographic expression of the crater but is buried under karst and sediment layers. Two craters inner and outer separated by a rim have together diameter about 180 km and a depth of material with changed density may be 5 km. The crater was discovered by petroleum companies (later airborne measurements done by GFZ) from measurements of magnetic and gravity anomalies, which ranges between -15m Gals and +54 mGals. Negative gravity anomalies could indicate fracturing and other structural disturbances that increase the volume of normal rocks or could be due to infilling by low-density carbonate sediments. Positive anomalies indicate dense rocks such as the low-porosity impact melt sheet or up-thrust deep structural rocks.
To estimate the signal Vzz,= 2 GM/r3 due to Chicxulub burried crater, we approximate the crater by cylinder with diameter d =180 km and thickness v = 1 km (minimal estimate). Its volume is then V=πd2v/4. The density contrast is difficult to estimate, but we infer from measured gravity anomalies that it may be more than ρ= 1.0 g/cm3. The mass is then M = 1016 kg. For r = 250 km, using G = 6,7 x 10-11 m3/kg/s2, we get Vzz,= 0,2 E. We see the signal to noise ratio Vzz/σ ≈ 20, so even much smaller impacts than Chixculub might be identified from GOCE.
Item 5. Others
Low-order harmonics of Earth's potential field should also be studied in view of their possible impact on the rotation of the Earth. Namely, the influence of both zonal and sectorial harmonics and their temporal variations on precession-nutation will be addressed.
Milestones and schedule:
(i) launch of GOCE – spring 2008 (simulation software must be ready)
(ii) begining of data delivery by ESA – autumn 2008
(iii) processing, analyses, consultations, expert exchange .... 2007-2011
(iv) presentations/publications, conferences like EGU, special GOCE workshops
2008-2011
Principal Investigator : Jaroslav Klokočník
Address : Astronomical Institute,
251 65 Ondřejov,Czech Republic
jklokocn@asu.cas.cz
