La stima del campo di gravità da dati GOCE: i risultati finali dell’approccio space-wise

In questo lavoro vengono presentati i risultati finali del processamento dati della missione GOCE tramite l’approccio space-wise, da oltre vent’anni studiato ed implementato presso il Politecnico di Milano. In particolare sono stati elaborati i dati di tutta la missione, da novembre 2009 ad ottobre 2013, corrispondente ad oltre cento milioni di epoche. Questo periodo include sia la fase iniziale, durata quasi 3 anni, con il satellite all’altezza nominale di 255 km, sia la fase finale di abbassamento dell’orbita nella quale il satellite è stato lentamente portato fino a 224 km passando attraverso periodi intermedi di misura a quota costante. La fase di preprocessamento dati per la ricerca e la correzione di outlier è stata svolta in modo semi-automatico con una supervisione continua da parte dell’operatore e per questo motivo è stata molto onerosa; tuttavia l’eliminazione degli outlier, presenti in maggior numero nell’ultima fase di abbassamento dell’orbita, è cruciale per il raggiungimento di un risultato soddisfacente, indipendentemente dal metodo di analisi successivamente utilizzato. L’approccio space-wise è sostanzialmente un approccio iterativo di collocazione, che richiede la modellizzazione sia della correlazione temporale dell’errore di misura del gradiometro a bordo del satellite, sia della correlazione spaziale del segnale di gravità che si vuole recuperare. In particolare, l’idea base di questo approccio è quella di ridurre l’enorme mole di dati lungo orbita su una griglia globale all’altezza del satellite applicando la collocazione su aree locali, ciascuna caratterizzata da una covarianza del segnale adattata localmente. In questo modo il livello del filtraggio del dato risulta controllato localmente, diversamente da quanto avviene negli approcci diretto e time-wise dove viene applicata una regolarizzazione globale alla stima ai minimi quadrati dei coefficienti delle armoniche sferiche. Il risultato di questo processamento consiste quindi in griglie globali di derivate seconde del potenziale gravitazionale a una risoluzione spaziale di 0.2°x0.2°. Da queste griglie si deriva un modello globale in armoniche sferiche attraverso integrazione numerica. Sia per le griglie che per i coefficienti armonici viene fornita una stima dell’errore calcolata tramite un’opportuna simulazione Monte Carlo. Il contenuto informativo dei prodotti space-wise è stato valutato confrontandoli con altre griglie e altri modelli globali disponibili. Questo confronto mette in rilievo l’ovvia debolezza della collocazione locale nella stima dei gradi medio-bassi del campo gravitazionale, ma anche la sua miglior capacità di recuperare i più alti degree, ovvero i dettagli del campo. In questo senso l’approccio space-wise può fornire un risultato complementare a quello degli altri due approcci ufficiali all’analisi dati GOCE

Impact of historical tsunamis on a sandy coastal barrier: an example from the northern Gargano coast, southern Italy

International audienceThe Lesina coastal barrier is characterized by the presence of three wide washover fans. They were formed by three distinct tsunamis which struck the northern coast of the Gargano Promontory (Apulia, Italy) during historical times. A model for their formation is presented. It takes into account the geomorphological data collected and some reports about the effect of recent tsunamis on coastal barriers and beaches. Washover fans were produced by tsunami waves which ran through coseismic cracks developed on dune ridges shaping a narrow, straight and relatively deep trench which constitutes the fan throat. Moreover, each tsunami event most likely caused severe erosion of the coastal barrier, shaping erosive grooves across the dune ridges, causing beach cliffs and causing the nourishment of submarine offshore bars. After the tsunami, a phase of coastal barrier recovery began, forming new dune ridges and closing washover fan throats. Morphological, archeological and radiometric data indicate a pre-Roman age for the oldest event, which was dated at 2430 years BP. The second tsunami struck the Lesina coastal barrier with similar magnitude 1550 years BP; it was caused by the strong earthquake that occurred at Gargano Promontory in the year 493 AD as reported by a medieval sacred legend. The smallest and more recent fan formed following the tsunami that hit the northern coast of Gargano on 30 July 1627

GTE. A new software for gravitational terrain effect computation: theory and performances

The computation of the vertical attraction due to the topographic masses, the so-called Terrain Correction, is a fundamental step in geodetic and geophysical applications: it is required in high-precision geoid estimation by means of the remove–restore technique and it is used to isolate the gravitational effect of anomalous masses in geophysical exploration. The increasing resolution of recently developed digital terrain models, the increasing number of observation points due to extensive use of airborne gravimetry in geophysical exploration and the increasing accuracy of gravity data represents nowadays major issues for the terrain correction computation. Classical methods such as prism or point masses approximations are indeed too slow while Fourier based techniques are usually too approximate for the required accuracy. In this work a new software, called Gravity Terrain Effects (GTE), developed to guarantee high accuracy and fast computation of terrain corrections is presented. GTE has been thought expressly for geophysical applications allowing the computation not only of the effect of topographic and bathymetric masses but also those due to sedimentary layers or to the Earth crust-mantle discontinuity (the so-called Moho). In the present contribution, after recalling the main classical algorithms for the computation of the terrain correction we summarize the basic theory of the software and its practical implementation. Some tests to prove its performances are also described showing GTE capability to compute high accurate terrain corrections in a very short time: results obtained for a real airborne survey with GTE ranges between few hours and few minutes, according to the GTE profile used, with differences with respect to both planar and spherical computations (performed by prism and tesseroid respectively) of the order of 0.02 mGal even when using fastest profiles

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage fordealing with non-stationarity in geodetic data. We then compared stationary and non-stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC

Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity

Closed-Form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates(Φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution.These will be useful for those dealing with ellipsoidal representations of the Earth's gravityfield or other oblate ellipsoidal figures. The numerical stability of the transformations for nearpolarand near-equatorial regions is also considered