Regional compensation of subducted lithosphere: effects on geoid,gravity and topography from a preliminary model

It is proposed that the anomalous mass of subducted lithospheric slabs is partially compensated by two mechanisms: (a) by stresses transmitted up the slab to the surface lithosphere, causing the trench, and (b) by stresses transmitted through the mantle wedge overlying the slab, which cause a broad shallow depression. Results calculated from a preliminary two-dimensional model show that it can give a first-order account of observed topography, gravity and geoid anomalies. In particular, the model can reconcile the large mass anomaly predicted for the slab by thermal conduction theory with the smaller than expected gravity and geoid anomalies. Preliminary results indicate substantial compensation by mechanism (a), implying rather large stresses at the top of the slab: these could be important for theories of earthquake mechanisms and plate driving mechanisms. Roughly 50% of the possible compensation by mechanism (b) is indicated: the resulting depression, the order of 500 m deep and over 500 km wide, could explain anomalously deep marginal basins and some marine transgressions of continents.     

High-harmonic geoid signatures related to glacial isostatic adjustment and their detectability by GOCE

The Earth’s asthenosphere and lower continental crust can regionally have viscosities that are one to several orders of magnitude smaller than typical mantle viscosities. As a consequence, such shallow low-viscosity layers could induce high-harmonic (spherical harmonics 50–200) gravity and geoid anomalies due to remaining isostasy deviations following Late-Pleistocene glacial isostatic adjustment (GIA). Such high-harmonic geoid and gravity signatures would depend also on the detailed ice and meltwater loading distribution and history.ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, planned for launch in Summer 2008, is designed to map the quasi-static geoid with centimeter accuracy and gravity anomalies with milligal accuracy at a resolution of 100 km or better. This might offer the possibility of detecting gravity and geoid effects of low-viscosity shallow earth layers and differences of the effects of various Pleistocene ice decay scenarios. For example, our predictions show that for a typical low-viscosity crustal zone GOCE should be able to discern differences between ice-load histories down to length scales of about 150 km.One of the major challenges in interpreting such high-harmonic, regional-scale, geoid signatures in GOCE solutions will be to discriminate GIA-signatures from various other solid-earth contributions. It might be of help here that the high-harmonic geoid and gravity signatures form quite characteristic 2D patterns, depending on both ice load and low-viscosity zone model parameters.     

High-harmonic geoid signatures related to glacial isostatic adjustment and their detectability by GOCE

The Earth’s asthenosphere and lower continental crust can regionally have viscosities that are one to several orders of magnitude smaller than typical mantle viscosities. As a consequence, such shallow low-viscosity layers could induce high-harmonic (spherical harmonics 50–200) gravity and geoid anomalies due to remaining isostasy deviations following Late-Pleistocene glacial isostatic adjustment (GIA). Such high-harmonic geoid and gravity signatures would depend also on the detailed ice and meltwater loading distribution and history.ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, planned for launch in Summer 2008, is designed to map the quasi-static geoid with centimeter accuracy and gravity anomalies with milligal accuracy at a resolution of 100 km or better. This might offer the possibility of detecting gravity and geoid effects of low-viscosity shallow earth layers and differences of the effects of various Pleistocene ice decay scenarios. For example, our predictions show that for a typical low-viscosity crustal zone GOCE should be able to discern differences between ice-load histories down to length scales of about 150 km.One of the major challenges in interpreting such high-harmonic, regional-scale, geoid signatures in GOCE solutions will be to discriminate GIA-signatures from various other solid-earth contributions. It might be of help here that the high-harmonic geoid and gravity signatures form quite characteristic 2D patterns, depending on both ice load and low-viscosity zone model parameters.     

The geoid: From geodesy to geophysics and from geophysics to geodesy

The word geoid appeared for the first time in 1873 in a work by Listing, at a time when an increasing number of measurements of meridian arcs were made, in order to determine the figure of the Earth.From that time, the mathematical methods (least squares, inverse methods ...) and the observation and modelling methods (collecting data, precision ...) have made concurrently great progress. Owing to these advances, the geometric method first, and the dynamic method next were developed by geodesy for the computation of the geoid. In particular, the increasing of data brought by satellites since the 60's led to a detailed knowledge of the geoid.The determination of the geoid is, for geodesy, a goal in itself. The geophysical viewpoint is to study the inner structure and the internal dynamics of the Earth, by the interpretation of the shape of the geoid and its anomalies. The two approaches are complementary to one another and react one on the other: from geodesy to geophysics and from geophysics to geodesy. The geoid has three advantages that can be stated in a few words each, although the third advantage brings in a complex subject. They are: first, the advantage of thinking in terms of small numbers; second, the fact that we know or can know directly the form of the geoid as a physical reality over much of the earth's surface; third, the geophysical implications of a knowledge of the geoid. Walter D. Lambert, 1961     

Combining T/P altimetric data with hydrographic data to estimate the mean dynamic topography of the North Atlantic and improve the geoid

The mean dynamic topography of the surface of the North Atlantic is estimated using an inverse model of the ocean circulation constrained by hydro-graphic and altimetric observations. In the North Atlantic, altimetric observations have no significant impact on the topography estimate because of the limited precision of available geoid height models. They have a significant impact, however, when uncertainties in the density field are increased to simulate interpolation errors in regions where hydrographic data are scarce. This result, which moderates the conclusion drawn by Ganachaud and co-workers of no significant contribution of altimetric observations to the determination of the large-scale steady circulation, reflects the simple idea that altimetric data are most useful near the surface of the ocean and in areas where the hydrography is poorly determined. One application of the present inverse estimate of the mean dynamic topography is to compute a geoid height correction over the North Atlantic which reduces the uncertainty in the geoid height expanded to spherical harmonic 40 down to a level of about 5 cm.     

A contemporary winter ground thermal profile in the Lesotho highlands and implications for active and relict soil frost phenomena

A 2 m deep ground thermal pro?le is constructed from temperature data collected over the winter and spring of 2000 at 3220 m a.s.l. near the Thabana Ntlenyana summit (3482 m) in Lesotho, southern Africa. The zero isotherm is found to have penetrated to 0·16 m soil depth. Ground remained frozen at 0·05 m for a total of 79 days and for shorter periods at 0·02 m and 0·10 m. Diurnal freezing and thawing is restricted to the upper 0·10 m and conforms to the observed depth of active micro‐patterned ground found in the region. Holocene temperature depressions projected along the thermal pro?le can account for freezing down to 0·45 to 0·65 m. Deeper sorting to 1 m, evident from relict patterned ground near the logger site, corresponds to at least a 2·5 °C temperature depression and such landforms are evidently pre‐Holocene. Projections indicate a seasonal freezing depth exceeding 2 m during the Pleistocene Last Glacial Maximum although the existence of permafrost appears unlikely. Copyright © 2003 John Wiley & Sons, Ltd.     

The gravity and isostatic Moho in North China Craton and their implications to seismicity

The Bouguer gravity is the combination of field sources in different depths. Based on the multi-scale analysis of the Bouguer gravity, we can get the gravity anomaly caused by the Moho undulation. This study presents the various orders of approximation of gravity anomaly in North China Craton (NCC), the possible source depths with radial logarithmic power spectrum, and the relationship between the deep structure and gravity anomaly. Furthermore, we discuss the isostatic compensation about the Moho depth from gravity and deep seismic sounding profiles (DSS). The results show that: (1) the fourth approximation could have resulted from the Moho undulation, (2) in contrast to the isostatic Moho, the inverted gravity Moho and the DSS Moho show that most of NCC has been isostatically compensated, and (3) the isostatic compensation rate has some close relation to the seismicity.     

Aspects of Caledonian palaeomagnetism and their tectonic implications

Palaeomagnetic results from the Lower Palaeozoic inliers of northern England cover the upper part of the (Middle Ordovician) Borrowdale Volcanic Series (palaeomagnetic pole 208°E, 18°S, A₉₅ = 9.4°), minor extrusive units relating to the Caradoc and Ashgill stages of Ordovician times, intrusive episodes of Middle Ordovician and Middle Silurian to Late Devonian age, and the Shap Granite of Devonian (393 m.y.) age (palaeomagnetic pole 313°E, 33°S, A₉₅ = 5.6°).A complete assessment of Ordovician to Devonian palaeomagnetic data for the British region shows that the pole was nearly static relative to this region for long intervals which were separated by shifts occupying no more than a few millions of years. The mean palaeomagnetic poles are: Ordovician (6°E, 16°S), Lower Silurian (58°E, 16°N), Middle Silurian/Lower Devonian (318°E, 6°N) and Middle/Upper Devonian (338°E, 26°S); the first two shifts separating these mean poles can be explained predominantly in terms of rotational movements of the crustal plate but the last involved appreciable movement in palaeolatitude.Comparison of Lower Palaeozoic palaeomagnetic data from the British region with contemporaneous data from continental Europe/North America on the Pangaean reconstruction reveals a systematic discrepancy in palaeolatitude between the two regions prior to Middle Devonian times. This discrepancy was eliminated during a few millions of years of Lower/Middle Devonian times (ca. 395 m.y.) and can be explained in terms of ca. 3500 km of sinistral strike-slip movement close to the line of the orthotectonic Caledonides. This motion is linked both in time and place to the impingement of the Gondwanaland and Laurentian supercontinents during the Acadian orogeny; this appears to have displaced the British sub-plate until it became effectively locked between the Baltic and Laurentian regions. Although movement of the dipole field relative to the British region in Lower Palaeozoic times is now well defined, nearly one fifth of the total data show that the geomagnetic field was more complex than dipolar during this interval. Until the significance of these anomalies is fully resolved, the tectonic model derived from the palaeomagnetic data cannot be regarded as unambiguous.     

中国华南地区地壳厚度与波速比分布特征及其地质意义

本研究利用中国国家地震台网336个固定地震台站记录的远震波形资料,通过P波接收函数H-κ分析估算了中国华南地区的地壳厚度和地壳平均波速比.研究结果显示,地壳厚度约为25~46 km,整体表现西深东浅的变化特点.研究区地壳厚度变化分别与布格重力异常和地形呈现负相关和正相关.扬子块体东部显示较低地壳波速比（< 1.7）可能与地表沉积岩的存在相关.四川盆地内部的平均地壳波速比（约1.71~1.8）与全球大陆地盾/克拉通地区相当.但其周围地区地壳平均波速比明显增高（1.81~1.95）,推测可能是克拉通形成过程中岩浆的底侵引起下地壳组分以铁镁质麻粒岩为主.华夏块体西部表现为薄的地壳厚度和低的地壳平均波速比（1.65~1.75）,暗示该区基性下地壳物质的缺失可能与增厚的地壳发生拆沉有关.华夏块体东南段呈现出较高的地壳平均波速比（约1.77~1.86）,地壳组成以中基性铁镁质为主,推断可能与晚中生代铁镁质岩浆底侵作用密切相关.

     

Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro,Brazil: A case study with Voronoi/Delaunay discretisations

The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes, target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones, as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m, respectively, for Voronoi, Delaunay, Voronoi/Delaunay with gridded-data alone and EGM08, computed between 32 GPS/leveling points.     

Modelling the fine-structure of the geoid: Methods,data requirements and some results

The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas. In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km.     

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.     

Response of large-scale coastal basins to wind forcing: influence of topography

Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.     

Correction to: Experimental investigation of internal tides generated by finite-height topography

Ocean Dynamics - The original version of this article unfortunately contained mistakes. An incorrect name was used in the funding information and two references were missed, Munk and Wunsch 1998...     

Deep underwater seismic explosion experiments and their possible ecological impact - The case of Lake Arenguade - Central Ethiopian highlands

The study was conducted in Lake Arenguade (Lake Haro Hadho) from 2008 to 2009 and results were compared with previous studies conducted by different authors since the 1960s. The study included the chemistry and chlorophyll-a biomass in micrograms per liter (μg L⁻¹). Results showed that chlorophyll-a biomass dramatically decreased since the 1960s. Previous studies indicated that the phytoplankton community of Lake Arenguade was dominated by a single cyanobacterium species, Arthrospira fusiformis (Voronichin) Komárek et Lund (syn. Spirulina fusiformis Voronichin) while the present study showed co-dominance of the lake's phytoplankton by another cyanobacterium species, Anabaenopsis elenkinii Miller. The trend shows that A. fusiformis is on the verge of disappearance from Lake Arenguade. While other factors can be responsible for such a change, the contribution of underwater seismological detonation experiments carried out repeatedly cannot be ruled out. Based on the results, recommendations were forwarded for possible full-fledged environmental impact assessment of explosion experiments in Lake Arenguade; and other lakes in which similar explosion experiments were carried out.     

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

Magnetic measurements over the Hawaiian ridge and their vulcanological implications

The results of an aeromagnetic survey of the Hawaiian Islands are studied in terms of the local magnetic anomalies defined and their relation to known centers of vulcanism. A quantitative analysis as to the depth of origin of the anomalies indicates that in nearly all cases they can be attributed to sub-surface intrusive rock masses at depths of the order of 2 to 6 kilometers. That the intrusive rocks defined are probably related to intrusions of magma derived from the underlying mantle is indicated by both quantitative studies of associated gravity anomalies and seismic refraction crustal measurements. On the basis of these integrated geophysical studies, it appears that there has been extensive intrusion of mantle-derived magma into the crust along the East-West trending submarine Molokai Fracture Zone and that where this fracture system intersected a Northwest-Southeast zone of tectonic weakness or fracture there was vulcanism that led to the formation of the Hawaiian Islands. Although magnetic data are lacking as yet over the entire Hawaiian Ridge from Hawaii to Midway Island, it is not an unreasonable hypothesis that the Ridge as a whole developed in a similar manner over its entire length as a progressive feature with time, in response to a secular shift in crustal stress pattern at the intersection of two major translational fault systems.