Global Crust-Mantle Density Contrast Estimated from EGM2008, DTM2008, CRUST2.0, and ICE-5G

We compute globally the consolidated crust-stripped gravity disturbances/anomalies. These refined gravity field quantities are obtained from the EGM2008 gravity data after applying the topographic and crust density contrasts stripping corrections computed using the global topography/bathymetry model DTM2006.0, the global continental ice-thickness data ICE-5G, and the global crustal model CRUST2.0. All crust components density contrasts are defined relative to the reference crustal density of 2,670 kg/m³. We demonstrate that the consolidated crust-stripped gravity data have the strongest correlation with the crustal thickness. Therefore, they are the most suitable gravity data type for the recovery of the Moho density interface by means of the gravimetric modelling or inversion. The consolidated crust-stripped gravity data and the CRUST2.0 crust-thickness data are used to estimate the global average value of the crust-mantle density contrast. This is done by minimising the correlation between these refined gravity and crust-thickness data by adding the crust-mantle density contrast to the original reference crustal density of 2,670?kg/m³. The estimated values of 485 kg/m³ (for the refined gravity disturbances) and 481?kg/m³ (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480?kg/m³, which is adopted in the definition of the Preliminary Reference Earth Model (PREM). This agreement is more likely due to the fact that our results of the gravimetric forward modelling are significantly constrained by the CRUST2.0 model density structure and crust-thickness data derived purely based on methods of seismic refraction.     

基于地形精化的金星重力场模型VGM2013

高精度金星重力场的获取,是金星探测的重要内容.本文利用最新的金星地形和重力模型,通过高通滤波后的残差地形（RTM）并在考虑均衡改正的情况下改进了重力的短波成分,最终提出了一个新的金星重力模型VGM2013,该模型赤道分辨率达10 km量级,大大高于现有的金星重力场模型,最终结果是金星表面重力加速度和重力扰动.研究中同时发现金星在Airy-Heiskanen均衡模型下的全球最优补偿深度为30 km,金星地壳的密度可能小于当前认为的2700~2900 kg·m^-3.VGM2013模型的结果可为将来的金星探测器定轨和着陆导航提供参考,作为重力计算的先验模型.但由于该模型没有包含短波重力观测信息,不建议直接用于更小尺度的地质和地球物理解释.     

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

Gravity-based heights require gravity values at levelled benchmarks (BMs), which sometimes have to be predicted from surrounding observations. We use the Earth Gravitational Model 2008 (EGM2008) and the Australian National Gravity Database (ANGD) as examples of model and terrestrial observed data respectively to predict gravity at Australian National Levelling Network (ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BM gravity values and then into gravimetric height corrections (HCs). Our results indicate that an approximate ±1 arc-min horizontal position error of the BMs causes maximum errors in EGM2008 BM gravity of ~22 mGal (~55 mm in the HC at ~2200 m elevation) and ~18 mGal for ANGD BM gravity because the values are not computed at the true location of the BM. We use RTM (residual terrain modelling) techniques to show that ~50% of EGM2008 BM gravity error in a moderately mountainous region can be accounted for by signal omission. Non-representative sampling of ANGD gravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmert orthometric correction at ~2200 m elevation). For modelled gravity at BMs to be viable, levelling networks need horizontal BM positions accurate to a few metres, while RTM techniques can be used to reduce signal omission error. Unrepresentative gravity sampling in mountains can be remedied by denser and more representative re-surveys, and/or gravity can be forward modelled into regions of sparser gravity.     

Residual Terrain Modelling: The Harmonic Correction for Geoid Heights

Surveys in Geophysics - The harmonic correction (HC) is one of the key quantities when using residual terrain modelling (RTM) for high-frequency gravity field modelling. In the RTM technique,...     

RTM-based omission error corrections for global geopotential models: Case study in Central Europe

The aim of this paper is to evaluate the effects of residual terrain model (RTM) on potential and on gravity and to point out how significant can the omission error of global geopotential models (GGMs) be and how it can influence their testing. The RTM for Central Europe is computed in the spherical approximation. The topography is modelled by spherical tesseroids and the gravitational effect of the topography is obtained as a sum of their partial gravitational effects. A detailed picture of RTM in Slovakia is shown. The testing of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) global geopotential models in Central Europe published earlier is re-evaluated with the more rigorous omission error estimation. Experimental results show significantly better agreement between the gravity anomalies computed from global geopotential models with the omission-error estimation and gravity anomalies obtained from the direct measurements. On the other hand, for height anomalies such an improvement is not observed. The results are discussed in context of the other previously published studies.     

The role of regional-scale faults in controlling a trapdoor caldera,Coromandel Peninsula,New Zealand

Regional gravity data from an eroded Miocene to Pliocene volcanic arc exposed in the Coromandel Peninsula, New Zealand, delineate a circular − 26-mGal, 15-km-diameter gravity anomaly. This anomaly, which has steep gradients on its northern and western margins but shallow gradients elsewhere, correlates with relatively young volcanic and volcaniclastic rocks within a broad topographic depression. Gravity modelling, using an exponentially decreasing density contrast with depth profile, requires very low-density rocks (ca. 2280 kg m^− 3) in the near-surface to account for the observed anomaly, giving a total depth of ca. 2.8 km for these rocks. The northern and western margins of this body dip steeply inward at 70°, whereas the southern and eastern margins have shallow inward dips (20–30°). The western margin coincides with the regional-scale Mangakino Fault, but the northern margin, recognizable only in the geophysical data (and named here the Ohinemuri Fault), is partially buried under younger volcanic rocks. We interpret these deep and steeply bounded, low-density volcanics in terms of a trapdoor caldera, faulted on its northern and western margins, with its hinge on the southern and eastern margins. Epithermal deposits are spatially associated with the Mangakino and Ohinemuri Faults, suggesting that both structures may have influenced hydrothermal fluid flow. These deposits pre-date caldera fill, indicating that caldera development followed pre-existing regional faults. These results delineate the subsurface geometry of a trapdoor caldera and highlight the role of pre-existing, regional-scale faults in controlling such caldera location and collapse.     

基于泊松小波径向基函数融合多源数据的局部重力场建模

融合多源数据的高精度、高分辨率的局部重力场建模是物理大地测量学的前沿和热点问题.本文研究了基于径向基函数融合多源数据的局部重力场建模方法,利用Monte-Carlo方差分量估计实现了不同类型的观测数据的合理定权,引入了最小标准差法确定基函数的适宜网络,分析了地形因素对于基函数网络确定及局部重力场建模精度的影响.以泊松小波基函数为构造基函数,结合残差地形模型,融合实测的陆地重力异常、船载重力异常及航空重力扰动数据构建了局部区域陆海统一的似大地水准面模型.研究结果表明:引入残差地形模型平滑了地形质量引入的高频扰动信号,简化了基函数的网络设计;并提高了重力似大地水准面的精度,平原地区其精度提高了4mm,地形起伏较大的山区其精度提高了约5cm.总体而言,基于"三步法"构建的局部重力似大地水准面在荷兰、比利时及德国相关区域,其精度分别达到1.12cm、2.80cm以及2.92cm.     

An alternative method for density variation modeling of the crust based on 3-D gravity inversion

In this paper we are proposing an alternative method for determination of density variations of the crust from constrained inversion of the terrestrial gravity data. The main features of the method can be summarized as follows: (i) Constructing a band-pass filter to remove the long and short wavelength signals from the terrestrial gravity data. (ii) Using an iterative method for stabilization and solution of the inverse problem. The mentioned regularization method is first validated by simulated gravity data and next the methodology is used for development of a new regional density variation model of the crust in three layers based on real gravity data in geographical area of Iran. Application of the band-pass filter to the latter data resulted the residual gravitation variations in the range of − 300 to 50 (mGal) which next based on the iterative method resulted following ranges for residual densities: −120 to 40 (kg/m³) in first layer, −40 to 40 (kg/m³) in second layer, and − 40 to 40 (kg/m³) in third layer.     

A fluid dynamics approach to modelling the 18th March 2007 lahar at Mt. Ruapehu,New Zealand

Lahars are water-sediment mass flows from a volcanic source. They can be triggered by a variety of mechanisms and span a continuum of flow rheology and hydraulic properties, even within the same event. Lahars are extremely powerful landscaping agents and represent a considerable hazard potential. However, this highly dynamic character and a lack of direct measurements has made modelling lahars difficult. This study therefore applies a fluid dynamics model; Delft3D, to analyse the 18th March 2007 dam break lahar at Mount Ruapehu, New Zealand. The modelled lahar routed through the Whangaehu gorge in ~30 min, crossed the Whangaehu fan in ~60 min, and then over a further 3 h travelled an additional ~22 km distance along the Whangaehu River to the Tangiwai bridge. The modelled mean frontal velocity was 6.5 m s⁻¹ along the gorge although peak velocity reached up to 19.6 m s⁻¹. The modelled lahar flow front progressively slowed across the fan but along the River it accelerated from 2.1–3.3 m s⁻¹. Calculated peak velocity along the River was <4.5 m s⁻¹. These results generally compare well with gauged records, with historical records, and with other modelling approaches. However, discrepancies in frontal velocity and time to peak stage arise due to (1) specifying roughness, which arises from slope variations between adjacent computational nodes, and which is stage-dependant, and (2) due to rapid topographic changes that produce frequent hydraulic jumps, which are inadequately accommodated in the numerical scheme. The overall pattern of discharge attenuation, and of relationships between topographic and hydraulic variables, is similar to that calculated for lahars on other volcanoes. This modelling method could be applied at other similar sites where a likely source hydrograph and high-resolution topographic data are available. These results have important implications for hazard management at Ruapehu and for examining geomorphic and sedimentary impacts of this lahar.     

Layer-Based Modelling of the Earth’s Gravitational Potential up to 10-km Scale in Spherical Harmonics in Spherical and Ellipsoidal Approximation

Global forward modelling of the Earth’s gravitational potential, a classical problem in geophysics and geodesy, is relevant for a range of applications such as gravity interpretation, isostatic hypothesis testing or combined gravity field modelling with high and ultra-high resolution. This study presents spectral forward modelling with volumetric mass layers to degree 2190 for the first time based on two different levels of approximation. In spherical approximation, the mass layers are referred to a sphere, yielding the spherical topographic potential. In ellipsoidal approximation where an ellipsoid of revolution provides the reference, the ellipsoidal topographic potential (ETP) is obtained. For both types of approximation, we derive a mass layer concept and study it with layered data from the Earth2014 topography model at 5-arc-min resolution. We show that the layer concept can be applied with either actual layer density or density contrasts w.r.t. a reference density, without discernible differences in the computed gravity functionals. To avoid aliasing and truncation errors, we carefully account for increased sampling requirements due to the exponentiation of the boundary functions and consider all numerically relevant terms of the involved binominal series expansions. The main outcome of our work is a set of new spectral models of the Earth’s topographic potential relying on mass layer modelling in spherical and in ellipsoidal approximation. We compare both levels of approximations geometrically, spectrally and numerically and quantify the benefits over the frequently used rock-equivalent topography (RET) method. We show that by using the ETP it is possible to avoid any displacement of masses and quantify also the benefit of mapping-free modelling. The layer-based forward modelling is corroborated by GOCE satellite gradiometry, by in-situ gravity observations from recently released Antarctic gravity anomaly grids and degree correlations with spectral models of the Earth’s observed geopotential. As the main conclusion of this work, the mass layer approach allows more accurate modelling of the topographic potential because it avoids 10–20-mGal approximation errors associated with RET techniques. The spherical approximation is suited for a range of geophysical applications, while the ellipsoidal approximation is preferable for applications requiring high accuracy or high resolution.     

The evolution of andesite volcano structures: new evidence from gravity studies in Costa Rica

Published gravity data on active volcanoes generally reflecteither the low density scoriaceous/pumiceous deposits that are localized within ring-fracture collapse depressions, such as the calderas of mature silicic volcanoes,or the high density frozen magma conduits that occur beneath basaltic shields and cones. The intensive gravity surveys reported here over three complex andesite volcanoes reveal features of both types. Their multi-component gravity fields have crater-centred positive anomalies (1–2 km diameter) surrounded by broader zones of negative gravity with similar amplitudes but greater width (5–10 km). The former are thought to reflect sub-crater magma pipes ofnormal density (ca. 2.5–2.6 Mg m⁻³) surrounded by pyroclastic scoria, ashes and occasional lava flows of muchlower net density (1.8–2.4 Mg m⁻³) which, in turn, account for the negative anomalous zones because the deeper, more consolidated and older parts of these andesite volcano edifices have more normal densities (2.3–2.6 Mg m⁻³).The low density materials are particularly interesting because they appear to have filled topographic depressions to depths of several hundred metres, especially where old caldera-like structures have been postulated from the steep gravity gradients over perimeter ring faults. A model is developed whereby short periods of caldera collapse, associated with intermittent, large high level magma bodies, are interspersed by normal crater-like activity with narrow sub-surface magma pipes. Dominantly pyroclastic activity from summit craters generates the materials that gradually fill earlier-formed topographic depressions. This study demonstrates the unique value of detailed gravity surveys, combined with surface geological information, for modelling and understanding the evolution of active volcano summit regions.     

On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution

In geophysical studies investigating the lithosphere structure, the gravitational field generated by the ocean density contrast (i.e., bathymetry-generated gravitational field) represents a significant amount of the signal to be modelled and subsequently removed from the Earth’s gravity field. The ocean density contrast is typically calculated as the difference between the mean density values of the Earth’s crust and seawater. The approximation of the actual seawater density distribution by its mean value yields relative errors up to about 2% in computed quantities of the gravitational field. To reduce these errors, a more realistic model of the seawater density distribution is utilized based on the analysis of existing oceanographic data of salinity, temperature, and pressure (depth). We study the accuracy of the bathymetry-generated gravitational field quantities formulated for a depth-dependent model of the seawater density distribution. This density distribution approximates the seawater density variations due to an increasing pressure with depth, whereas smaller lateral density variations caused by salinity, temperature, and other oceanographic factors are not taken into consideration. The error analysis reveals that the approximation of the seawater density by the depth-dependent density model reduces the maximum errors to less than 0.6%. The corresponding depth-averaged errors are below 0.1%. The depth-dependent seawater density model is further facilitated in expressions for computing the bathymetry-generated gravitational field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The numerical realization reveals large differences in the results obtained with and without consideration of the depth-dependent seawater density distribution. The maxima of absolute differences reach 201 m²/s² and 16.5 mGal in computed values of the potential and attraction, respectively. The application of the depth-dependent seawater density model thus significantly improves the accuracy in the forward modelling of the bathymetric gravitational field quantities.     

Regional gravimetric quasi-geoid model and transformation surface to national height system for Turkey (THG-09)

Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric models for Turkish territory were computed depending on OSU91 (TG-91) and EGM96 (TG-03) earth gravitational models. The release of the Earth Gravitational Model 2008 (EGM08), the collection of new surface gravity observations, the advanced satellite altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain Model (RTM) reduction of the surface gravity data. Fast Fourier Transformation (FFT) was then used to obtain the residual quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height (TQG-09). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model (TQG-09) was then converted to the geoid model (TG-09) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09) (or a transformation surface) to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be ± 0.95 cm, which represents the internal precision of the final combination. And finally, we tested the hybrid geoid model with GPS/leveling data, which were not used in the combination, to assess the external accuracy. Results show that the external accuracy of the THG-09 model is ± 8.4 cm, a precision previously not achieved in Turkey until this study.     

Structure and State of Stress of the Chilean Subduction Zone from Terrestrial and Satellite-Derived Gravity and Gravity Gradient Data

It is well known that the quality of gravity modelling of the Earth’s lithosphere is heavily dependent on the limited number of available terrestrial gravity data. More recently, however, interest has grown within the geoscientific community to utilise the homogeneously measured satellite gravity and gravity gradient data for lithospheric scale modelling. Here, we present an interdisciplinary approach to determine the state of stress and rate of deformation in the Central Andean subduction system. We employed gravity data from terrestrial, satellite-based and combined sources using multiple methods to constrain stress, strain and gravitational potential energy (GPE). Well-constrained 3D density models, which were partly optimised using the combined regional gravity model IMOSAGA01C (Hosse et al. in Surv Geophys, 2014, this issue), were used as bases for the computation of stress anomalies on the top of the subducting oceanic Nazca plate and GPE relative to the base of the lithosphere. The geometries and physical parameters of the 3D density models were used for the computation of stresses and uplift rates in the dynamic modelling. The stress distributions, as derived from the static and dynamic modelling, reveal distinct positive anomalies of up to 80 MPa along the coastal Jurassic batholith belt. The anomalies correlate well with major seismicity in the shallow parts of the subduction system. Moreover, the pattern of stress distributions in the Andean convergent zone varies both along the north–south and west–east directions, suggesting that the continental fore-arc is highly segmented. Estimates of GPE show that the high Central Andes might be in a state of horizontal deviatoric tension. Models of gravity gradients from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission were used to compute Bouguer-like gradient anomalies at 8 km above sea level. The analysis suggests that data from GOCE add significant value to the interpretation of lithospheric structures, given that the appropriate topographic correction is applied.     

A geophysical approach to the granite batholith under the eastern Southern Uplands,Scotland

From our interpretation of the Bouguer gravity and aeromagnetic anomalies in south-east Scotland, we conclude that a massive granite batholith underlies the greater part of the eastern Southern Uplands. The granite model which we computed earlier from gravity anomalies in the Tweeddale area fits the observed magnetic anomalies closely, if a normal magnetization of 0.095 A m^–1 is assigned, similar to values found for exposed local granites. Further gravity modelling shows that, apart from the Tweeddale boss, the granite shallows to less than 1 km near Lammer Law in East Lothian and extends north of the Lammermuir Fault. A model for the East Lothian volcanics was computed from their aeromagnetic anomalies, then their gravitational effect was combined with that estimated for the Devonian and Carboniferous sediments and the result stripped off the observed gravity field. The residual gravity anomalies were used to generate a two-dimensional model for the granite north of the Lammermuir Fault. The expected tectonic consequences of a massive granite batholith in the eastern Southern Uplands are compared with the known development of faults and sedimentary basins around its margins.     

The Rock–Water–Ice Topographic Gravity Field Model RWI_TOPO_2015 and Its Comparison to a Conventional Rock-Equivalent Version

RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the \(5'\times 5'\) global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the \(1'\times 1'\) Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model.     

Hyperscale terrain modelling of braided rivers: fusing mobile terrestrial laser scanning and optical bathymetric mapping

Quantifying the morphology of braided rivers is a key task for understanding braided river behaviour. In the last decade, developments in geomatics technologies and associated data processing methods have transformed the production of precise, reach‐scale topographic datasets. Nevertheless, generating accurate Digital Elevation Models (DEMs) remains a demanding task, particularly in fluvial systems. This paper identifies a threefold set of challenges associated with surveying these dynamic landforms: complex relief, inundated shallow channels and high rates of sediment transport, and terms these challenges the ‘morphological’, ‘wetted channel’ and ‘mobility’ problems, respectively. In an attempt to confront these issues directly, this paper presents a novel survey methodology that combines mobile terrestrial laser scanning and non‐metric aerial photography with data reduction and surface modelling techniques to render DEMs from the resulting very high resolution datasets. The approach is used to generate and model a precise, dense topographic dataset for a 2.5 km reach of the braided Rees River, New Zealand. Data were acquired rapidly between high flow events and incorporate over 5 x 10⁹ raw survey observations with point densities of 1600 pts m^‐2 on exposed bar and channel surfaces. A detailed error analysis of the resulting sub‐metre resolution is described to quantify DEM quality across the entire surface model. This reveals unparalleled low vertical errors for such a large and complex surface model; between 0.03 and 0.12 m in exposed and inundated areas of the model, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

Spectral expressions for modelling the gravitational field of the Earth’s crust density structure

We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm⁻³. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure.     

Gravity evidence for an extinct magma chamber beneath Syrtis Major, Mars: a look at the magmatic plumbing system

Syrtis Major is an ancient basaltic shield volcano on Mars with a basal diameter of 1100 km. The free-air gravity anomaly is 126 mGal at spherical harmonic degree 50 and reaches its maximum amplitude over the 2 km deep topographic caldera. The observed gravity anomaly cannot be explained by flexurally supported surface topography and requires the presence of a buried, high-density load. The geologically most reasonable interpretation of this high-density load is that it represents the magma chamber of Syrtis Major, now solidified and filled at least in part by dense igneous cumulates. Pyroxene is likely to be the dominant cumulate mineral in this system, although olivine may also be present. Gravity models presented here define the structure of the buried load and in essence provide a look at the magmatic plumbing system of this volcano. The preferred model involves a buried load that is approximately 300×600 km across, roughly twice as large as the topographic caldera. Both the buried load and the caldera are elongated in the north-south direction. In the center of the buried load, the minimum thickness is 2.8 km for an olivine-dominated cumulate system or 3.9 km for a pyroxene-dominated system. The best terrestrial analog for this structure is the Bushveld Complex, an igneous cumulate body that is similar in size and thickness to the Syrtis Major structure. Assuming that the mean crustal density is 2600 kg m⁻³ due to impact brecciation, the elastic lithosphere at Syrtis Major was 10-15 km thick at the time when the topographic load was emplaced. This corresponds to a lithospheric thermal gradient of 28-52 K/km and a surface heat flux of 70-130 mW m⁻². Higher resolution gravity data, such as that which is planned for the 2005 Mars Reconnaissance Orbiter, will permit further refinement of the dimensions of this structure.     

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.