Improved Constraints on Models of Glacial Isostatic Adjustment: A Review of the Contribution of Ground-Based Geodetic Observations

The provision of accurate models of Glacial Isostatic Adjustment (GIA) is presently a priority need in climate studies, largely due to the potential of the Gravity Recovery and Climate Experiment (GRACE) data to be used to determine accurate and continent-wide assessments of ice mass change and hydrology. However, modelled GIA is uncertain due to insufficient constraints on our knowledge of past glacial changes and to large simplifications in the underlying Earth models. Consequently, we show differences between models that exceed several mm/year in terms of surface displacement for the two major ice sheets: Greenland and Antarctica. Geodetic measurements of surface displacement offer the potential for new constraints to be made on GIA models, especially when they are used to improve structural features of the Earth’s interior as to allow for a more realistic reconstruction of the glaciation history. We present the distribution of presently available campaign and continuous geodetic measurements in Greenland and Antarctica and summarise surface velocities published to date, showing substantial disagreement between techniques and GIA models alike. We review the current state-of-the-art in ground-based geodesy (GPS, VLBI, DORIS, SLR) in determining accurate and precise surface velocities. In particular, we focus on known areas of need in GPS observation level models and the terrestrial reference frame in order to advance geodetic observation precision/accuracy toward 0.1 mm/year and therefore further constrain models of GIA and subsequent present-day ice mass change estimates.     

Density Structure,Isostatic Balance and Tectonic Models of the Central Tien Shan

A new combined satellite-terrestrial model of the gravity field is used together with seismic data for construction of a density model of the lithosphere of the Central Tien Shan and for estimation of its isostatic balance. The Tien Shan is one of the most active intraplate orogens in the world, located about 1,500 km north of the convergence between Indian and Eurasian plate, and surrounded by stable Kazakh platform to the north and the Tarim block to the south. Although this area was extensively studied during recent decades, several principal problems, related to its structure and tectonics, remain unsolved up to now: (1) various geodynamic scenarios have been discussed so far to explain tectonic evolution, such as direct “crustal shortening,” intracontinental subduction and some others, but no definite evidence for any of them has been found. (2) Still, it is not clear why Tien Shan grows so far from the plate boundary at the Himalayan collision zone. Gravity modeling can provide valuable constraints to resolve these questions. The results of this study show that: (1) there exists a very strong deflection of the Tien Shan lithosphere from isostatic equilibrium. At the same time, the patterns of the isostatic anomalies are very different in the Western and Central Tien Shan. The latter one is characterized by much stronger variations. The best fit of the modeling results is found for the model according to which the Tarim plate partially underthrusts the Central Tien Shan; (2) negative density anomalies in the upper mantle under the central block possibly relate to magmatic underplating during the initial stage of the tectonic evolution. Therefore, the weak lithosphere could be the factor that initiates mountain building far away from the collision zone. Alternatively, this might be a gap after detachment of the eclogised lower crust and lithospheric lid, which is filled with the hot asthenospheric material.     

Radiative Feedbacks and Monsoon Circulations: A View from Simplified Models

The modulation of radiative processes by changes in water vapor and cloudiness is at the origin of important feedbacks which control climate variability as well as climate changes. These feedbacks are especially active in the intertropical area, where it is possible to diagnose a combination of partially compensating positive and negative feedbacks. The characteristics and the strength of those feedbacks is closely associated with the dynamical regimes in which they develop. Reverse changes in dynamical patterns may cause a modulation of the radiative processes. A first approach to these problems is to distinguish between two ascending and subsiding circulation patterns. This bimodality of the circulation is well established in the tropical area, and favors the use of simplified models as an appropriate tool to carry out a first-order quantification of these processes. In particular, this combination of radiative and dynamical feedbacks characterizes the development of the monsoons and their variability. Simple conceptual models can thus serve to characterize some of the factors which will affect the intraseasonal variations of the monsoon.     

Integration of space geodesy: A US National Geodetic Observatory

In the interest of improving the performance and efficiency of space geodesy a diverse group in the US, in collaboration with IGGOS, has begun to establish a unified National Geodetic Observatory (NGO). To launch this effort an international team will conduct a multi-year program of research into the technical issues of integrating SLR, VLBI, and GPS geodesy to produce a unified set of global geodetic products. The goal is to improve measurement accuracy by up to an order of magnitude while lowering the cost to current sponsors. A secondary goal is to expand and diversify international sponsorship of space geodesy. Principal benefits will be to open new vistas of research in geodynamics and surface change while freeing scarce NASA funds for scientific studies. NGO will proceed in partnership with, and under the auspices of, the International Association of Geodesy (IAG) as an element of the Integrated Global Geodetic Observation System project. The collaboration will be conducted within, and will make full use of, the IAG's existing international services: the IGS, IVS, ILRS, and IERS. Seed funding for organizational activities and technical analysis will come from NASA's Solid Earth and Natural Hazards Program. Additional funds to develop an integrated geodetic data system known as Inter-service Data Integration for Geodetic Operations (INDIGO), will come from a separate NASA program in Earth science information technology. INDIGO will offer ready access to the full variety of NASA's space geodetic data and will extend the GPS Seamless Archive (GSAC) philosophy to all space geodetic data types.     

Isostatic Consequences of Giant Landslides on the Hawaiian Ridge

—Giant landslides, like melting glaciers, lead to a redistribution of mass which will have isostatic consequences. Three-dimensional numerical modeling experiments were devised to examine how this mass redistribution affects the isostatic flexural curve. A debris avalanche of 10–40% of pre-slide Oahu is required to account for the 1200–5000 km³ Nuuanu deposit, while only ～ 1% of pre-slide Hawaii Island is necessary to generate the 200–800 km³ Alika I and II avalanche deposits. Trials were run using 25, 30, and 40 km elastic plate thicknesses (T _e ). The island uplift resulting from the Nuuanu slide was calculated to be 23 m and 109 m for 10% and 40% volume slides, respectively, both using T _e = 25 km. A rebound of 10 m and 49 m was calculated for the same volumes, respectively, using T _e = 40 km. A greater amount of uplift is expressed direct lyover the failed flank, causing the edifice to tilt away from the calved-off portion. The landslide deposit depresses the plate several meters beneath the debris field itself. Smaller slides (e.g., Alika I and II) do not produce as much flexural response, with 17 m and 7 m uplift for T _e = 25 and 40 km, respectively. The effects of slow moving, intact slumps where the failed blocks remain relatively close to the island pedestal were examined for the case of the Hilina slump, making up approximately 10% of the Hawaii Island edifice. Perhaps more significant than the uplift for the Hilina slump, comparable to that for the 10% Nuuanu debris avalanche, is the 114 m and 56 m of downwarp beneath its massive slumped foot (T _e = 25 and 40 km, respectively). The landslide rebound process, in the case of a relatively large landslide, should be considered as an added component to the evolutionary course of oceanic islands.     

Geodetic calculus with block-averages observations on the sphere

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 the discretization and averaging procedures are numerically studied; a simple numerical approach to improve the efficiency of the estimates is presented.     

Constraints on Glacial Isostatic Adjustment from GOCE and Sea Level Data

Current constraints on the glacial isostatic adjustment (GIA) process are mainly provided by relative sea-level data and GPS measurements. Due to a lack of resolving power in the shallow earth (down to about 200 km), these data sets only provide weak constraints on the shallow viscosity structure and the thickness of the lithosphere. Future high-resolution gravity data, as expected from ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) launched on March 17, 2009, are predicted to provide additional information on the shallow earth, more specifically the viscosity structure. Here we present an overview of recent developments in extracting information on rheology and stratification of the shallow earth from high-resolution quasi-steady gravity and geoid data to be obtained from GOCE.     

唐山及大同－阳高地震大地形变与重力前兆综合研究

本大概还了近年来利用大地形变及重力复测资料研究唐山及大同－阳高地震的丰富成果，对这２次地震震前大地形变及重力前兆综合研究认为：震中区震前呈现闭锁状态；断层蠕滑及深部物质的运移，是震前的显著标志；地震成因的组合模式可以较好地解释唐山及大同一阳高地震的机制；跟踪监测形变场、重力场及断层活动时空演化特性，是利用大地形变及重力测量手段进行地震预测的基本出发点。     

Isostatic status in North China (1)

Following Airy and Pratt principles, five kinds of local-compensation models are analysed and a rapid 3-D gravity formula is utilized to calculate isostatic anomalies for 66 models with different parameters. It is noted that isostatic gravity maps appear nearly identical in their main patterns and features. The optimum compensation model in North China is one of modified Airy models in which the different density distribution in the surface, upper crust and lower crust is taken into account and the standard crustal thickness is about 50km. The position of the complete compensation interface is located in the upper mantle. The North China platform as a whole is under sub-isostatic equilibrium status with an isostatic anomaly of about 18·10^?5 m/s² on an average. The distribution of isostatic gravity anomaly shows an obvious blockwise pattern. Most positive anomaly areas occur over the eastern part, the Jiao-Liao Block, Mt. Yan block and northern margin of the Hebei-Shandong block, whereas a negative area occurs in the Shanxi graben. The comparison of models indicates that the Moho discontinuity is not suitable to be taken as a compensation interface, and the compensation effects in Airy model are better than that in Pratt model, which is consistent with the feature of dominant layered structure and less lateral inhomogeneity in crust. Some results about composite compensation, the basic characteristics of isostatic anomaly and deep stucture will be published later in the second part of this paper.     

地震研究中的大地测量

本文简要回顾了我国大地测量工作者将大地测量技术应用于地震监测和预测的历程。介绍了过去几十年在地震监测和预测中大地测量工作取得的主要进展和成绩,讨论了存在的不足和改进的地方。并且结合近二十年来以3S(GPS、RS、GIS)为代表的高新技术的引入给对地观测技术带来的革命性变化,使得观测结果的精度和时空域中密度大为改观这一事实,对地震研究中的大地测量的发展方向提出了一些看法和建议。     

Geodetic data shed light on ongoing caldera subsidence at Askja, Iceland

Subsidence within the main caldera of Askja volcano in the North of Iceland has been in progress since 1983. Here, we present new ground- and satellite-based deformation data, which we interpret together with new and existing micro-gravity data, to help understand which processes may be responsible for the unrest. From 2003 to 2007, we observe a net micro-gravity decrease combined with subsidence and from 2007 to 2009 we observe a net micro-gravity increase while the subsidence continues. We infer subsidence is caused by a combination of a cooling and contracting magma chamber at a divergent plate boundary. Mass movements at active volcanoes can be caused by several processes, including water table/lake level movements, hydrothermal activity and magma movements. We suggest that, here, magma movement and/or a steam cap in the geothermal system of Askja at depth are responsible for the observed micro-gravity variations. In this respect, we rule out the possibility of a shallow intrusion as an explanation for the observed micro-gravity increase but suggest magma may have flowed into the residing shallow magma chamber at Askja despite continued subsidence. In particular, variable compressibility of magma residing in the magma chamber as well as compressibility of the surrounding rock may be the reason why this additional magma did not create any detectable surface deformation.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Recent Geodetic Results in the Azores Triple Junction Region

—GPS (Global Positioning System) observations started to be carried out in the Azores region under the scope of the TANGO (TransAtlantic Network for Geodesy and Oceanography) project in 1988. The measurements carried out between 1993 and 2000 (five campaigns) on nine GPS sites (one per island) were reprocessed using two state–of–the-art software packages. Different methodologies were applied to compute each campaign solution and the derived velocity field. The velocity fields, including the motions of two permanent stations, recently installed in the Azores, were computed within the most recent geodetic reference frame, ITRF2000 (International Terrestrial Reference Frame, solution 2000). They are compared with the motions of the stable rigid tectonic plates using as reference DEOS2k, a global tectonic model developed using geodetic data. The relative motions between the Western and Central groups of islands yield to evaluate the opening rate of the Mid-Atlantic Ridge (boundary between the North American plate and the Eurasian and African plates). Concerning the boundary between the Eurasian and African plates, the motion of the TANGO sites in the Central and Eastern groups clearly identifies the transition pattern between those two plates. Two of the sites are considered to be located in the stable part of these plates, whereas the remaining five are within the deformation region of the Eurasia-Africa boundary. The conclusions are analyzed in view of the different deformation models, derived from geodynamic or geophysical data that have been proposed for the region.     

Detecting Regional Events via Statistical Analysis of Geodetic Networks

We present an application of hidden Markov models (HMMs) to analysis of geodetic time series in Southern California. Our model-fitting method uses a regularized version of the deterministic annealing expectation-maximization algorithm to ensure that model solutions are both robust and of high quality. Using the fitted models, we segment the daily displacement time series collected by 127 stations of the Southern California Integrated Geodetic Network (SCIGN) over a two-year period. Segmentations of the series are based on statistical changes as identified by the trained HMMs. We look for correlations in state changes across multiple stations that indicate region-wide activity. We find that although in one case a strong seismic event was associated with a spike in station correlations, in all other cases in the study, time period strong correlations were not associated with any seismic event. This indicates that the method was able to identify more subtle signals associated with aseismic events or long-range interactions between smaller events.     

Glacial Isostatic Adjustment and Contemporary Sea Level Rise: An Overview

Glacial isostatic adjustment (GIA) encompasses a suite of geophysical phenomena accompanying the waxing and waning of continental-scale ice sheets. These involve the solid Earth, the oceans and the cryosphere both on short (decade to century) and on long (millennia) timescales. In the framework of contemporary sea-level change, the role of GIA is particular. In fact, among the processes significantly contributing to contemporary sea-level change, GIA is the only one for which deformational, gravitational and rotational effects are simultaneously operating, and for which the rheology of the solid Earth is essential. Here, I review the basic elements of the GIA theory, emphasizing the connections with current sea-level changes observed by tide gauges and altimetry. This purpose is met discussing the nature of the “sea-level equation” (SLE), which represents the basis for modeling the sea-level variations of glacial isostatic origin, also giving access to a full set of geodetic variations associated with GIA. Here, the SLE is employed to characterize the remarkable geographical variability of the GIA-induced sea-level variations, which are often expressed in terms of “fingerprints”. Using harmonic analysis, the spatial variability of the GIA fingerprints is compared to that of other components of contemporary sea-level change. In closing, some attention is devoted to the importance of the “GIA corrections” in the context of modern sea-level observations, based on tide gauges or satellite altimeters.     

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.     

Geodetic measurements on the Asal Rift (Djibouti): Twelve years of observations

The resurvey of both a geodetic network and a levelling net was carried out in June 1981, 8 months after the M_s = 7.3 El Asnam earthquake of 10 October 1980. Previous seismological and neotectonic studies indicate that this event results from a north-east-trending overthrust complex fault of about 40-km length, which shows at least three principal segments with slightly different directions.Vertical movements, evaluated by means of a trigonometric levelling method show an uplift of the thrust fault of about 5 m and a depression of the southeastern edge of about 1 m. These movements are progressively attenuated away from the fault trace (see fig. 1). Horizontal movements have been evaluated by a classical first-order triangulation method. (see fig. 2 and table 1).The resulting mean strain tensors, calculated for different triangles of the geodetic network, indicate a shortening of about 2.50 m which is consistent with the SE-NW direction of compression determined from neotectonic evaluations and focal mechanisms (see fig. 3). Dislocation models are used to explain and discuss the observed deformations in the light of the seismological data and the observed ground breakages. Five segments are required to explain both horizontal and vertical deformations. The magnitude of vertical displacement (about 6 m) at the junction between the southwest and the central segments of the fault argues for the breaking of this area during the main shock and for a slip vector of about 8 m, at least in the central segment.In such circumstances where the first field observations show that a strong coseismic movement has taken place, the best methodology to be used seems to be:

• - to resurvey as quickly as possible the widest acceptable zone of the old existing geodetic network, without special attention paid to the precision of these measurements.

• - to set up as soon as possible a small aperture geodetic network of high accuracy in order to monitor the possible postseismic readjustments.

For vertical movements, trigonometric leveling using reciprocal zenith measurements with two high-precision theodolites and EDM appears to be far the best solution. It is much quicker than classical leveling and it can afford the same precision if necessary. In our case, the precision was not critical, so that long ranges (up to 1500 m) between stations were used when necessary.