The relationship between gravity and bathymetry in the Pacific Ocean

Summary. Surface-ship and satellite derived data have been compiled in new free-air gravity anomaly, bathymetry and geoid anomaly maps of the Pacific Ocean basin and its margin. The maps are based on smoothed values of the gravity anomaly, bathymetry and geoid interpolated on to a 90 × 90 km grid. Each smoothed value was obtained by Gaussian filtering measurements along individual ship and subsatellite tracks. The resulting maps resolve features in the gravity, bathymetry and geoid with wavelengths that range from a few hundred to a few thousand kilometres. The smoothed values of bathymetry and geoid anomaly have been corrected for age. The resulting maps show the Pacific ocean basin is associated with a number of ENE–WSW-trending geoid anomaly highs with amplitudes of about ± 5 m and wavelengths of about 3000 km. The most prominent of these highs correlate with the Magellan seamounts–Marshall Gilbert Islands–Magellan rise and the Hess rise–Hawaiian ridge regions. The correlation between geoid anomaly and bathymetry cannot be explained by models of static compensation, but is consistent with a model in which the geoid anomaly and bathymetry are supported by some form of dynamic compensation. We suggest that the dynamic compensation, which characterizes oceanic lithosphere older than 80 Myr, is the result of mantle convection on scales that are smaller than the lithospheric plates themselves.     

Detailed 1×1° gravimetric Indian Ocean geoid and comparison with GEOS-3 radar altimeter geoid profiles

Summary. A new set of 1×1° mean free-air anomalies in the Indian Ocean is determined on the basis of previously published free-air anomaly maps (Talwani & Kahle) and the most recent Lamont surface ship gravity measurements. The data are then used to compute a (total) 1×1° gravimetric Indian Ocean geoid. The computation is carried out by combining the Goddard Space Flight Center (GSFC) GEM-6 geoid and a difference geoid that corresponds to the differences between the set of 1×1° surface gravity values and the GEM-6 gravity anomalies. The difference geoid is highest over the Madagascar Ridge (+ 20 m) and lowest over the Timor Trough (-30 m). The total geoid is compared with GEOS-3 radar altimeter derived geoid profiles and geophysical implications are discussed.     

The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data

Observations of gravity can be aliased by virtue of the logistics involved in collecting these data in the field. For instance, gravity measurements are often made in more accessible lowland areas where there are roads and tracks, thus omitting areas of higher relief in between. The gravimetric determination of the geoid requires mean terrain-corrected free-air anomalies; however, anomalies based only on the observations in lowland regions are not necessarily representative of the true mean value over the topography. A five-stage approach is taken that uses a digital elevation model, which provides a more accurate representation of the topography than the gravity observation elevations, to reduce the unrepresentative sampling in the gravity observations. When using this approach with the Australian digital elevation model, the terrain-corrected free-air anomalies generated from the Australian gravity data base change by between 77.075 and −84.335 mgal (−0.193 mgal mean and 2.687 mgal standard deviation). Subsequent gravimetric geoid computations are used to illustrate the effect of aliasing in the Australian gravity data upon the geoid. The difference between 'aliased' and 'non-aliased' gravimetric geoid solutions varies by between 0.732 and −1.816 m (−0.058 m mean and 0.122 m standard deviation). Based on these conceptual arguments and numerical results, it is recommended that supplementary digital elevation information be included during the estimation of mean gravity anomalies prior to the computation of a gravimetric geoid model.     

Validation and fusion of different databases in preparation of high-resolution geoid determination

An up to date determination of a high-resolution geoid requires the use of best available databases concerning digital terrain model (DTM), bathymetry, global geopotential model and gravity field. The occasion to revisit methods to validate and merge different data sets has been created by a new project for the determination of a new European Geoid.
Since the computation of the latest European geoid and quasi-geoid model (EGG97), significant new or improved data sets have become available, such as new global geopotential models from CHAMP and GRACE missions, new national and global DTMs and new or upgraded gravity data sets.
In the context of the new European Gravity and Geoid Project (EGGP), within the IAG Commission 2, some data validation tests have been performed in the Italian zone.
In the area 19°× 17° wide, covering Italy, three kinds of tests have been performed: comparison among different DTMs in order to choose the best one to be used; comparisons in terms of geoid computation in some coastal areas, to evaluate bathymetry effects, and the validation of the EIGEN-CG01C and EIGEN-CG03C new global models up to degree and order 360.
These preliminary tests lead to the choice of SRTM DTM (integrated in no-data holes), with an added bathymetry derived by the Italian 1:25 000 official cartography near the coasts and the NOAA bathymetry in high seas. The validation of the new global models and the comparison with EGM96 model show that, in terms of geoid computation, the EGM96 yields better results. Moreover, the validation of new available land gravity data and the cross-validation of two sets of gravity data on sea have been completed.     

Structural effects of the crust on the geoid modelled using deep seismic sounding interpretations

According to the theory of isostasy, the Earth has a tendency to deform its surface in order to reach an equilibrium state. The land-uplift phenomenon in the area of the Fennoscandian Shield is thought to be a process of this kind. The geoid, as an equipotential surface of the Earth's gravity field, contains information on how much the Earth's surface departs from the equilibrium state. In order to study the isostatic process through geoidal undulations, the structural effects of the crust on the geoid have to be investigated.
  The structure of the crust of the Fennoscandian Shield has been extensively explored by means of deep seismic sounding (DSS). The data obtained from DSS are used to construct a 3-D seismic-velocity structure model of the area's crust. The velocity model is converted to a 3-D density model using the empirical relationship that holds between seismic velocities and crustal mass densities. Structural effects are then estimated from the 3-D density model.
  The structural effects computed from the crustal model show that the mass deficiency of the crust in Fennoscandia has caused a geoidal depression twice as deep as that observed from the gravimetric geoid. It proves again that the crust has been isostatically compensated by the upper mantle. In other words, an anomalously high-density upper mantle must exist beneath Fennoscandia.     

A technique for computing geoid height anomalies over two-dimensional earth models

Summary A technique is presented for calculating geoid height anomalies over two-dimensional models of Earth structure. The method consists of convolving gravity anomalies over the structure with filters which take into account the finite size of the structure in the third dimension and the curvature of the Earth. Similar filters are also developed for a flat earth case. The method is applied to a sea-surface gravity profile crossing the Tonga-Kermadec trench and is found to give good agreement with a Geos-3 radar altimetry profile in the same region. The example demonstrates that introducing arbitrary offsets in computing gravity anomalies can result in spurious long-wavelength effects in the computed geoid. Comparison of the results obtained using flat earth and spherical earth filters suggests that the effects of the curvature of the Earth only become significant for wavelengths in the gravity field greater than about 1000 km.     

论青藏高原范围与面积

长期以来 ,种种因素导致学者们对青藏高原确切范围的认识和理解存在差异。根据青藏高原相关领域研究的新成果和多年野外实践 ,从地理学角度 ,充分讨论了确定青藏高原范围和界线的原则与涉及的问题 ,结合信息技术方法对青藏高原范围与界线位置进行了精确的定位和定量分析。得出 :青藏高原在中国境内部分西起帕米尔高原 ,东至横断山脉 ,横跨 31个经度 ,东西长约 2 94 5km ;南自喜马拉雅山脉南缘 ,北迄昆仑山 -祁连山北侧 ,纵贯约 13个纬度 ,南北宽达 15 32km ;范围为 2 6°0 0′12″N～ 39°4 6′5 0″N ,73°18′5 2″E～ 10 4°4 6′5 9″E ,面积为 2 5 72 4× 10 3km2 ,占我国陆地总面积的 2 6 8%。     

High-resolution mean sea surface computed with altimeter data of Ers-1 (geodetic mission) and topex-poseidon

The remote-sensing satellite ERS-1, launched in 1991 to study the Earth's environment, was placed on a geodetic (168-day repeat) orbit between 1994 April and 1995 March to map, through altimetric measurements, the gravity field over the whole oceanic domain with a resolution of 8 km at the equator in both along-track and cross-track directions. We have analysed the precise altimeter data of the geodetic mission, and, by also using one year of Topex-Poseidon altimeter data, we have computed a global high-resolution mean sea surface. The various steps involved in pre-processing the ERS-1 data consisted of correcting the data for environmental factors, editing, and reducing, through crossover analyses, the radial orbit error, which directly affects sea-surface height measurements. For this purpose, we adjusted sinusoids at 1 and 2 cycle rev⁻¹ along the ERS-1 profiles in order to minimize crossover differences between ERS-1 and yearly averaged Topex-Poseidon profiles. In effect, the orbit of Topex-Poseidon is very accurately determined (within 2–3 cm for the radial component), so Topex-Poseidon altimeter profiles can serve as a reference to reduce the ERS-1 radial orbit error. The ERS-1 residual orbit error was further reduced through a second crossover analysis between all ascending and descending profiles of the geodetic mission. The along-track ERS-1 and Topex-Poseidon data were then interpolated over the whole oceanic domain on a regular grid of 1/16°× 1/16° size. The mapping of the gridded sea-surface heights reveals the very fine structure of the marine geoid, up until now unknown at a global scale. This new data set will be most useful for marine geophysical and tectonic investigations.     

A Maastrichtian palaeomagnetic pole for the Pacific plate from a skewness analysis of marine magnetic anomaly 32

The asymmetry (skewness) of marine magnetic anomaly 32 (72.1–73.3  Ma) on the Pacific plate has been analysed in order to estimate a new palaeomagnetic pole. Apparent effective remanent inclinations of the seafloor magnetization were calculated from skewness estimates of 108 crossings of anomaly 32 distributed over the entire Pacific plate and spanning a great-circle distance of ~12  000  km. The data were inverted to obtain a palaeomagnetic pole at 72.1°N, 26.8°E with a 95 per cent confidence ellipse having a 4.0° major semi-axis oriented 98° clockwise of north and a 1.8° minor semi-axis; the anomalous skewness is 14.2° ± 3.7°. The possible dependence of anomalous skewness on spreading rate was investigated with two empirical models and found to have a negligible effect on our palaeopole analysis over the range of relevant spreading half-rates, ~25 to ~90  mm  yr⁻¹ . The new pole is consistent with the northward motion for the Pacific plate indicated by coeval palaeocolatitude and palaeoequatorial data, but differs significantly from, and lies to the northeast of, coeval seamount poles. We attribute the difference to unmodelled errors in the seamount poles, mainly in the declinations. Comparison with the northward motion inferred from dated volcanoes along the Hawaiian–Emperor seamount chain indicates 13° of southward motion of the Hawaiian hotspot since 73  Ma. When the pole is reconstructed with the Pacific plate relative to the Pacific hotspots, it differs by 14°–18° from the position of the pole relative to the Indo–Atlantic hotspots. This has several possible explanations including bias in one or more of the palaeomagnetic poles, motion between the Pacific and Indo–Atlantic hotspots, and errors in plate reconstructions relative to the hotspots.     

Small-scale instabilities below the cooling oceanic lithosphere

Interpretation of satellite altimetry data as well as ship bathymetry data revealed strongly elongated anomalies roughly perpendicular to the mid-ocean ridges in the Indian and east Pacific oceans. A spectral analysis of gravity altimetry data along profiles parallel to the East Pacific Rise indicated wavelengths of about 150–180  km close to the ridge and about 250  km further away. A simple model of Rayleigh–Taylor instabilities developing at the base of the cooling lithosphere is discussed and applied to the data. By considering thermal diffusion and comparing Rayleigh–Taylor growth rates to the velocity of the thermal front in the cooling lithosphere, we are able to explain the observed anomalies by instabilities developing below the lithosphere in a layer with a viscosity of about 10¹⁹  Pa  s above an asthenospheric layer with a viscosity reduction of 2–3 orders of magnitude.     

Free-surface formulation of mantle convection—II. Implication for subduction-zone observables

Viscous and viscoelastic models for a subduction zone with a faulted lithosphere and internal buoyancy can self-consistently and simultaneously predict long-wavelength geoid highs over slabs, short-wavelength gravity lows over trenches, trench-forebulge morphology, and explain the high apparent strength of oceanic lithosphere in trench environments. The models use two different free-surface formulations of buoyancy-driven flows (see, for example, Part I): Lagrangian viscoelastic and pseudo-free-surface viscous formulations. The lower mantle must be stronger than the upper in order to obtain geoid highs at long wavelengths. Trenches are a simple consequence of the negative buoyancy of slabs and a large thrust fault, decoupling the overriding from underthrusting plates. The lower oceanic lithosphere must have a viscosity of less than to²⁴ Pa s in order to be consistent with the flexural wavelength of forebulges. Forebulges are dynamically maintained by viscous flow in the lower lithosphere and mantle, and give rise to apparently stiffer oceanic lithosphere at trenches. With purely viscous models using a pseudo-free-surface formulation, we find that viscous relaxation of oceanic lithosphere, in the presence of rapid trench rollback, leads to wider and shallower back-arc basins when compared to cases without viscous relaxation. Moreover, in agreement with earlier studies, the stresses necessary to generate forebulges are small (∼ 100 bars) compared to the unrealistically high stresses needed in classic thin elastic plate models.     

Mantle convection under simulated plates: effects of heating modes and ridge and trench migration, and implications for the core—mantle boundary, bathymetry, the geoid and Benioff zones

Summary. Numerical convection models are presented in which plates are simulated by imposing piecewise constant horizontal velocities on the upper boundary. A 4 × 1 box of constant viscosity fluid and two-dimensional (2-D) flow is assumed. Four heating modes are compared: the four combinations of internal or bottom heating and prescribed bottom temperature or heat flux. The case with internal heating and an isothermal base is relevant to lower mantle or whole mantle convection, and it yields a lower thermal boundary layer which is laterally variable and can be locally reversed, corresponding to heat flowing back into the core locally. When scaled to the whole mantle, the surface deflections and gravity and geoid perturbations calculated from the models are comparable to those observed at the Earth's surface. For models with migrating ridges and trenches, the flow structure lags well behind the changing surface 'plate'configurations. This may help to explain the poor correlation between the main geoid features and plate boundaries. Trench migration substantially affects the dip of the cool descending fluid because of induced horizontal shear in the vicinity of the trench. Such shear is small for whole mantle convection, but is large for upper mantle convection, and would probably result in the Tonga Benioff zone dipping to the SE, opposite to the observed dip, for the case of upper mantle convection.     

A proposed granite batholith along the western flank of the North Sea Viking Graben

Summary. A pronounced positive magnetic anomaly of approximately 300 gamma occurs over the eastern edge of the East Shetland Platform at approximately 60°N, 1°E. After the removal of the regional gravity variation and the gravity effect of the known geological structure, it is found that this magnetic high correlates with a negative gravity residual anomaly of approximately 30 mGal. Seismic data indicate that these anomalies occur in an area of relatively shallow basement on the upthrown side of the main Viking Graben margin fault. The presence of a buried granite batholith of approximately 40 × 40km may explain the gravity, magnetic and seismic observations. The observed deviation of the fault defining the edge of the Viking Graben in the proximity of the proposed granite may be explained in terms of the tectonic influence of the buoyant granite block during the taphrogenic development of the graben.     

Inference of mantle viscosity from GRACE and relative sea level data

Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr⁻¹ slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between  1.4 × 10²¹  and  2.3 × 10²¹  Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of  5.3 × 10²⁰  and  2.3 × 10²¹  Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.     

Thermal origin of mid-plate hot-spot swells

Summary. Additional evidence supports the idea that the shallow rises surrounding mid-plate, hot-spot volcanoes are caused by a broad-scale reheating of the lithosphere above hot-spots. Firstly, as required by the reheating concept, the rises appear to be supported by a density deficiency within the normal thickness of the lithosphere. The gravity anomalies over the Bermuda, Cape Verde, Hawaii and Cook-Austral swells indicate that the compensation of these swells is only 40 to 100 km deep. The geoid anomaly over the Hawaiian swell is consistent with these depths. Secondly, as also required by the reheating concept; swells and the volcanoes formed on swells subside at the same rate as younger, hotter lithosphere which is at the same ocean depth. Almost all mid-plate swells rise to an ocean depth of 4250 m, the depth of normal 25 Myr-old lithosphere. The Hawaiian Swell, Emperor Guyots, Cook-Austral Swell and Bikini and Enewetok Atolls all subside as 25 Myr-old lithosphere subsides.     

利用FG5绝对重力仪进行南极长城站绝对重力测定

在南极地区进行重力测量是建立高程基准的基础,2005年,在南极长城站进行了绝对重力测量,观测仪器采用FG5绝对重力仪,经固体潮改正、海潮改正、极移改正及气压改正等,精度达±3×10-8m s-2,并同时利用2台LCR相对重力仪进行了重力垂直梯度测量和水平梯度测量。长城站绝对重力测量的实施,对于新一代卫星重力计划如CHAMP、GRACE和GOCE的地面校准及建立南极地区的高精度、高分辨率的大地水准面模型提供了基础数据。     

Improved ocean-geoid resolution from retracked ERS-1 satellite altimeter waveforms

The ocean geoid can be inferred from the topography of the mean sea surface. Satellite altimeters transmit radar pulses and determine the return traveltime to measure sea-surface height. The ERS-1 altimeter stacks 51 consecutive radar reflections on board the satellite to a single waveform. Tracking the time shift of the waveform gives an estimate of the distance to the sea surface. We retrack the ERS-1 radar traveltimes using a model that is focused on the leading edge of the waveforms. While earlier methods regarded adjacent waveforms as independent statistical events, we invert a whole sequence of waveforms simultaneously for a spline geoid solution. Smoothness is controlled by spectral constraints on the spline coefficients. Our geoid solutions have an average spectral density equal to the expected power spectrum of the true geoid. The coherence of repeat track solutions indicates a spatial resolution of 31  km, as compared to 41  km resolution for the ERS-1 Ocean Product. While the resolution of the latter deteriorates to 47  km for wave heights above 2  m, our geoid solution maintains its resolution of 31  km for rough sea. Retracking altimeter waveform data and constraining the solution by a spectral model leads to a realistic geoid solution with significantly improved along-track resolution.     

Odd zonal harmonics in the geopotential, from analysis of 28 satellite orbits

Summary. The geopotential is usually expressed as an infinite series of spherical harmonics, and the odd zonal harmonics are the terms independent of longitude and antisymmetric about the equator: they define the 'pear-shape' effect. The coefficients J ₃, J ₅, J ₇, … of these harmonics have been evaluated by analysing the variations in eccentricity of 28 satellite orbits from near-equatorial to polar. Most of the orbits from our previous determination in 1974 are used again, but three new orbits are added, including two at inclinations between 62° and 63°, which have been specially observed for more than five years by the Hewitt cameras. With the help of the new orbits and revised theory, we have obtained sets of J -coefficients with standard deviations about 40 per cent lower than before. A 9-coefficient set is chosen as representative, and is as follows (all × 10⁹): J ₃=– 2530 ± 4, J ₅=–245 ± 5, J ₇=–336 ± 6, J ₉=–90 ± 7, J ₁₁= 159 ± 9, J ₁₃=–158 ± 15, J ₁₅=– 20 ± 15, J ₁₇=– 236 ± 14, J ₁₉=– 27 ± 19. With this set of values, the pear-shape asymmetry of the geoid (north polar minus south polar radius) amounts to 45.1 m instead of the previous 44.7 m. The accuracy of the longitude-averaged geoid profile is estimated as 50 cm, except at latitudes above 86°. The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those from other sources.     

Combination of TOPEX/POSEIDON data with a hydrographic inversion for determination of the oceanic general circulation and its relation to geoid accuracy

A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceano-graphic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations, Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.     

Coseismic slip model of the 2007 August Pisco earthquake (Peru) as constrained by Wide Swath radar observations

The Pisco earthquake ( M _w 8.0; 2007 August 15) occurred offshore of Peru's southern coast at the subduction interface between the Nazca and South American plates. It ruptured a previously identified seismic gap along the Peruvian margin. We use Wide Swath InSAR observations acquired by the Envisat satellite in descending and ascending orbits to constrain coseismic slip distribution of this subduction earthquake. The data show movement of the coastal regions by as much as 85 cm in the line-of-sight of the satellite. Distributed-slip model indicates that the coseismic slip reaches values of about 5.5 m at a depth of ∼18–20 km. The slip is confined to less than 40 km depth, with most of the moment release located on the shallow parts of the interface above 30 km depth. The region with maximum coseismic slip in the InSAR model is located offshore, close to the seismic moment centroid location. The geodetic estimate of seismic moment is 1.23 × 10²¹ Nm ( M _w 8.06), consistent with seismic estimates. The slip model inferred from the InSAR observations suggests that the Pisco earthquake ruptured only a portion of the seismic gap zone in Peru between 13.5° S and 14.5° S, hence there is still a significant seismic gap to the south of the 2007 event that has not experienced a large earthquake since at least 1687.