Global tectonics and the geoid

A digitised tectonic model, initially built up for regionalization of Rayleigh waves, is applied to the geoid in order to define the mean geoid heights of the following regions: 3 oceanic regions, namely young oceans (0–30 Ma) middle-aged oceans (30–80 Ma) and old oceans (> 80 Ma); trenches and subduction zones; mountains; and shields. The relative importance of the deep sources is damped or enhanced by progressively removing or adding the lower or higher degrees of the geoid. A statistical approach allows us to quantify the success of the correlation between tectonics and these filtered geoids.Significant variations are observed in these correlations for oceanic regions (including subduction zones) with a cut-off between degree-2 and higher degrees. For degrees ? 3, a well-known trend is observed: high values correspond to young oceans (ridges) and low values to old oceans, high values are also obtained for subduction zones. On the contrary, and unexpectedly, for the degree-2 alone a trend reversal is observed: geoid lows are observed over ridges and geoid highs over old oceans; trenches give the same geoid amplitude than old oceans. Clearly this denotes a degree-2 convection pattern connected to plate tectonics. In addition it is shown that the minimum and maximum inertia axes of the surface distribution of young oceans, and independently of old oceans and trenches, coincide with the Earth's equatorial inertia axes (74°E and 164°E), i.e., with the equatorial extremes of the degree-2 geoid.Plate tectonics is uncorrelated with the polar anomaly of the degree-2 geoid, namely the flattening which is not accounted for by Earth rotation. A north-south axisymmetric convection with a degree-2 pattern is proposed to explain this extra flattening; this model is supported by the latitude dependence of the depth of oceanic ridges.     

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.     

Global geoid sections determined by satellite orbit dynamics

Summary This paper ties up with [5, 6] the fundamental notations of which have been adopted. The sets of Stokes' constants (harmonic coefficients) J _n ^(k) , S _n ^(k) were adopted from [4], and the scale factor for lengths, R₀=GM/W₀, from [5]. The equations for global meridional and parallel sections of the geoid surface W=W₀ are formulated. The geoid sections are represented by best fitting ellipses, as regards the meridians always for the arcs between the equator and the pole. Address: Politickych vězňů 12, Praha 1-Nové Město.     

确定(似)大地水准面的方法分析及适用性研究

本文从物理大地测量研究基本原理入手,论述了确定（似）大地水准面的重力/水准法、GPS/水准法及GPS/重力法,对它们的特点、优劣以及适用性等进行分析研究,结合实际应用提出一些改进的方法与建议.     

CFRP对砖墙抗震加固对比试验研究与计算分析

结合一工程实践的需要，通过5片碳纤维布加固的新建墙体在周期反复荷载作用下的试验，研究了碳纤维布加固对砌体结构抗震性能的影响，以及砌砌体在碳纤维布加固后的受力特性，比较了不同加固方案对砖砌体加固效果的影响，在此基础上讨论了对碳纤维布加固砖墙抗剪承载力计算模型，并提出了简化计算公式。     

Gravimetric geoid for Egypt implementing Moho depths and optimal geoid fitting approach

The aim of this paper is to investigate the effect of implementing the experimentally determined GEMMA Moho depths (GOCE Exploitation for Moho Modeling and Applications), which are partly seismically estimated, in gravimetric geoid computation in Egypt. The window remove-restore technique has been proposed to avoid the double consideration of the topographic-isostatic masses in the neighbourhood of the computational point. The plate loading theory has been used to model the seismically determined Moho depths. A constant density contrast between the lower crust and the upper mantle has been postulated. The tailored geopotential model EGTGM2014 has been used for the long wavelength contributions of the Earth’s gravity field. A comparison with a geoid computed using the EGM2008 and Airy floating hypothesis has been made. For all cases, a gravimetric geoid for Egypt has been computed using Stokes’ integral in the frequency domain by 1-D FFT technique. The computed geoids are fitted to the GPS-levelling derived geoid using an optimum geoid fitting technique for Egypt introduced by the author. The results show that using the seismically determined Moho depths within the plate loading theory and the EGTGM2014 tailored geopotential model gives a geoid with external accuracy of about 16 cm.     

临界加速地震矩释放模型的网格计算

根据临界加速地震矩释放模型的基本原理,根据研究目的的不同,采取两种不同的方式进行基于网格的并行处理,即按时间分解和按空间分解.如果要根据历史地震目录资料预测某地区未来的地震活动,可以采用空间分解的方式;如果要根据某地区历史上特定时间段的地震活动情况来检验地震加速破裂模型,则可以采用时间分解的方式.最终,能够在同样计算精...     

基于有限元方法的陆海大地水准面衔接

大陆上用重力数据和GPS水准数据确定(似)大地水准面,海洋上用卫星测高数据确定(似)大地水准面.由于沿海地区和近岸海域往往缺少完好的重力数据,近岸海域卫星测高数据质量相对较差,两类大地水准面在陆海相接区域精度偏低且存在拼合差.纯几何方法拟合陆海局部区域大地水准面,不能顾及大地水准面的物理特性,拟合结果不稳定.顾及到大地水准面的物理特性,依据其在局部所应满足的数学物理方程,拟合陆海局部区域大地水准面问题,转化为Laplace第一边值问题.讨论了有限元法衔接陆海局部区域大地水准面的数学思想,给出了相应的数学模型.     

The geoid and single-cell mantle convection

The geoid shows an antisymmetric departure from the spheroid of best fit. A single zero-elevation contour divides its surface into nearly equal strips in one of which the elevation is everywhere positive and in the other everywhere negative. These two areas are interleaved roughly like the strips covering a tennis ball. This pattern may indicate global single-cell convection in the mantle. It is argued that on this convection hypothesis, the upcurrents underlie the low-geoid strip, although the opposite view could be supported. No simple relation is to be expected between the proposed whole-mantle convection and plate motions, because other constraints act on plates and because the asthenosphere will partially decouple the whole-mantle motions from the lithosphere. However, the proposed whole-mantle convective system is consistent with rapid northwestward motion of the Pacific plate, with fast spreading of the East Pacific Rise and with slow spreading of the North Atlantic Ridge. Seismological velocity anomalies in the mantle, while highly relevant to whole-mantle convection, do not at present decide for or against the hypothesis here advanced.     

IRG2018: A regional geoid model in Iran using Least Squares Collocation

Studia Geophysica et Geodaetica - The aim of this study is to determine an accurate geoid model for Iran based on the Least Squares Collocation method in the framework of the Remove — Compute...     

The modern geoid and ancient plate boundaries

The non-hydrostatic geoid is dominated by three large anomalies: an area of high gravity potential in the equatorial Pacific; another stretching from Greenland through Africa to the southwest Indian Ocean; and a semi-continuous low region passing from Hudson's Bay through Siberia to India and on to Antarctica. None of these three high-amplitude (greater than 60 m) and long-wavelength anomalies corresponds to present-day plate boundaries. However, if the modern geoid is plotted over the positions of continents and plate boundaries at 125 Ma B.P. (reconstructed relative to hotspots) a strong correlation emerges. The modern geoidal low corresponds in position to the areas of subduction surrounding the Pacific 125 Ma ago. The geoidal high now centered on Africa is entirely contained within ancient Pangaea, and the equatorial Pacific high overlies the location of the spreading centers preserved in the magnetic anomalies of the central Pacific. The most plausible cause of the large geoidal undulations is lower mantle convection only weakly coupled to plate motions. The correspondence between modern geoid and ancient plate boundaries implies either that the coupling was much more intimate in the past, or that there is a lag of at least 100 Ma in response of the lower mantle to upper mantle conditions.     

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.     

Surface deformation, gravity and the geoid from a three-dimensional convection model at low Rayleigh numbers

The two-dimensional surface deformation, gravity field and geoid are calculated from the temperature fields of a number of numerical models of constant viscosity three-dimensional convective flows, heated from within and from below, using the appropriate Green's functions. The admittance is positive, with positive gravity anomalies above hot rising regions, except for large aspect ratio circulations with undeformable lower boundaries. The surface deformation and the geoid are insensitive to the short wavelength features of the temperature variation. The gravity field is less smooth, though still does not clearly indicate the narrowness of the upwelling and downwelling regions at large Rayleigh numbers. When the lower boundary of the convecting region is deformable, the gravity field is dominated by lateral temperature variations within the upper thermal boundary layer, even when their contribution to the overall circulation is small. The variation of surface deformation with Rayleigh number agrees well with that expected from simple boundary layer arguments when the circulation is driven by heating from below, but less well when the heating is internal. These results suggest that the convective upwelling beneath regions showing positive geoid and residual depth anomalies is more localized than the horizontal extent of these features would suggest.     

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.     

Global sensitivity analysis of DRAINMOD‐FOREST,an integrated forest ecosystem model

Global sensitivity analysis is a useful tool to understand process‐based ecosystem models by identifying key parameters and processes controlling model predictions. This study reported a comprehensive global sensitivity analysis for DRAINMOD‐FOREST, an integrated model for simulating water, carbon (C), and nitrogen (N) cycles and plant growth in lowland forests. The analysis was carried out for multiple long‐term model predictions of hydrology, biogeochemistry, and plant growth. Results showed that long‐term mean hydrological predictions were highly sensitive to several key plant physiological parameters. Long‐term mean annual soil organic C content and mineralization rate were mainly controlled by temperature‐related parameters for soil organic matter decomposition. Mean annual forest productivity and N uptake were found to be mainly dependent upon plant production‐related parameters, including canopy quantum use efficiency and carbon use efficiency. Mean annual nitrate loss was highly sensitive to parameters controlling both hydrology and plant production, while mean annual dissolved organic nitrogen loss was controlled by parameters associated with its production and physical sorption. Parameters controlling forest production, C allocation, and specific leaf area highly affected long‐term mean annual leaf area. Results of this study could help minimize the efforts needed for calibrating DRAINMOD‐FOREST. Meanwhile, this study demonstrates the critical role of plants in regulating water, C, and N cycles in forest ecosystems and highlights the necessity of incorporating a dynamic plant growth model for comprehensively simulating hydrological and biogeochemical processes. Copyright © 2013 John Wiley & Sons, Ltd.     

Ability of the EGM2008 high degree geopotential model to calculate a local geoid model in Valencia,Eastern Spain

A new generation of global geopotential models (GGM) is being developed. These solutions offer a file with fully-normalized spherical harmonic coefficients of the Earth’s gravitational potential up to a degree greater than 2000 with very low commission errors. This paper analyses the recent Earth Gravitational Model EGM2008, developed up to degree and order 2159 with additional coefficients to degree 2190 and order 2159, which means recovering the gravitational field up to approximately 20 km wavelengths. 223 GPS/levelling points of the new Spanish High Precision Levelling Network in the Valencia region (Eastern Spain) are used as external tool for evaluation in that particular region. The same evaluation has been performed to other different global (EGM96 and EIGENCG03C), continental (EGG97), regional (IGG2005 and IBERGEO2006) and local (GCV07) geoid models for comparison purposes only. These comparisons show that EGM2008 is the geoid model that best fits to the GPS/levelling data in that region.     

Pacific Plate motion and undulations in geoid and bathymetry

Previous studies have shown that the Pacific geoid and gravity fields exhibit lineated anomalies, trending approximately in the direction of absolute plate motion over the underlying mantle. Because the undulations obliquely cross fracture zones they have often been attributed a convective origin. Recently, lithospheric boudinage caused by diffuse extension has been proposed as a possible mechanism. We have examined the undulations in the free-air anomalies, geoid and bathymetry over a portion of the Pacific Plate to determine quantitatively how the undulations are related to plate motion. We compare the observed data to an axisymmetric, sinusoidal undulation defined in an arbitrary frame of reference; in particular, we seek the north pole of this reference frame that maximizes the correlation between data and model. Poles that are close to the Pacific hotspot pole represent copolar undulations possibly related to plate motion. The distance between the best-fitting poles and the hotspot pole is determined as a function of undulation wavelength and reveals several minima (with distance < 10°) for discrete geoid wavebands centered on wavelengths of 160 km, 225 km, 287 km, 400 km, 660 km, 850 km, 1000 km and 1400 km. Bathymetry data have copolar bathymetric expressions as well, giving an implied admittance of 2–3 m/km. The most co-polar geoid/bathymetry undulations (with poles within 2–3° of the average Pacific Euler pole) have wavelengths of 280 km and 1050 km, respectively. The latter could have a convective origin or be related to the spacing of hotspot swells. The former may reflect lithospheric boudinage formed in response to diffuse extension, but could also have a dynamic origin since flexural dampening may only have attenuated the bathymetric amplitude by 50% or less. Radiometric dating of volcanic ridges found in the troughs of prominent gravity lineations gives ages that correlate well with documented changes in Pacific and Indo/Australian Plate motion, suggesting the ridges formed in response to intermittent plate boundary stresses and not as a direct consequence of small-scale convection or diffuse extension.     

SEASAT geoid anomalies and the Macquarie Ridge complex

The seismically active Macquarie Ridge complex forms the Pacific-India plate boundary between New Zealand and the Pacific-Antarctic spreading center. The Late Cenozoic deformation of New Zealand and focal mechanisms of recent large earthquakes in the Macquarie Ridge complex appear consistent with the current plate tectonic models. These models predict a combination of strike-slip and convergent motion in the northern Macquarie Ridge, and strike-slip motion in the southern part. The Hjort trench is the southernmost expression of the Macquarie Ridge complex. Regional considerations of the magnetic lineations imply that some oceanic crust may have been consumed at the Hjort trench. Although this arcuate trench seems inconsistent with the predicted strike-slip setting, a deep trough also occurs in the Romanche fracture zone.Geoid anomalies observed over spreading ridges, subduction zones, and fracture zones are different. Therefore, geoid anomalies may be diagnostic of plate boundary type. We use SEASAT data to examine the Macquarie Ridge complex and find that the geoid anomalies for the northern Hjort trench region are different from the geoid anomalies for the Romanche trough. The Hjort trench region is characterized by an oblique subduction zone geoid anomaly, e.g., the Aleutian-Komandorski region. Also, limited first-motion data for the large 1924 earthquake that occurred in the northern Hjort trench suggest a thrust focal mechanism. We conclude that subduction is occurring at the Hjort trench. The existence of active subduction in this area implies that young oceanic lithosphere can subduct beneath older oceanic lithosphere.     

Subducted lithosphere,hotspots, and the geoid

The earth's largest positive geoid height anomalies are associated with subduction zones and hotspots. Although the correlation with subduction has been noted for many years, the correlation with hotspots is fully evident only when the subduction-related geoid highs are removed from the observed field. Using the assumption that subducted lithospheric slabs are uncompensated and are thermally re-equilibrated with the asthenosphere at the maximum depth of earthquakes, the expected geoid anomaly over subduction zones is calculated. This field provides a satis-factory fit to the observed circum-Pacific high. Subtraction of this predicted anomaly leaves a residual field which is correlated, at greater than the 99% confidence level, with the distribution of hotspots. Broad residual geoid highs occur over the central Pacific and the Africa/eastern Atlantic regions, the same areas where the hotspots are concentrated. The mass anomalies associated with hotspots and subducted slabs apparently control the location of the earth's spin axis.