Assimilation of geodetic dynamic ocean topography using ensemble based Kalman filter

Estimation of ocean circulation is investigated via assimilation of satellite measurements of the dynamic ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of a geodetic approach from carefully cross-calibrated multi-mission altimeter data and GRACE gravity fields. The spectral consistency was achieved by consistently filtering both, the sea surface and the geoid. The filter length is determined by the spatial resolution of the gravity field and corresponds to approximately 241 km half width for the GRACE-based gravity field model ITG-Grace03s.The assimilation of the geodetic DOT was performed by employing a local singular evolutive interpolated Kalman (SEIK) filter in combination with the method of weighting of observations. It is shown that this approach leads to a successful assimilation technique that reduced the RMS difference between the model and the data from 16 cm to 5 cm during one year of assimilation. The ocean model returns an optimized mean dynamic ocean topography. The effects of assimilation on transport estimates across several hydrographic World Ocean Circulation Experiment (WOCE) sections show improvements compared to the FEOM run without data assimilation. As a result of the assimilation, DOT estimates are available in the polar or coastal regions where the geodetic estimates from satellite data alone are not adequate. Furthermore, more realistic features of the ocean can be seen in these areas compared to those obtained using the filtered data fields.     

The seismically active Andean and Central American margins: Can satellite gravity map lithospheric structures?

The spatial resolution and quality of geopotential models (EGM2008, EIGEN-5C, ITG-GRACE03s, and GOCO-01s) have been assessed as applied to lithospheric structure of the Andean and Central American subduction zones. For the validation, we compared the geopotential models with existing terrestrial gravity data and density models as constrained by seismic and geological data. The quality and resolution of the downward continued geopotential models in the Andes and Central America decrease with increasing topography and depend on the availability of terrestrial gravity data. High resolution of downward continued gravity data has been obtained over the Southern Andes where elevations are lower than 3000 m and sufficient terrestrial gravity data are available. The resolution decreases with an increase in elevation over the north Chilean Andes and Central America. The low resolution in Central America is mainly attributed to limited surface gravity data coverage of the region.To determine the minimum spatial dimension of a causative body that could be resolved using gravity gradient data, a synthetic gravity gradient response of a spherical anomalous mass has been computed at GOCE orbit height (254.9 km). It is shown that the minimum diameter of such a structure with density contrast of 240 kg m⁻³ should be at least ∼45 km to generate signal detectable at orbit height. The batholithic structure in Northern Chile, which is assumed to be associated with plate coupling and asperity generation, is about 60–120 km wide and could be traceable in GOCE data. Short wavelength anomalous structures are more pronounced in the components of the gravity gradient tensor and invariants than in the gravity field.As the ultimate objective of this study is to understand the state of stress along plate interface, the geometry of the density model, as constrained by combined gravity models and seismic data, has been used to develop dynamic model of the Andean margin. The results show that the stress regime in the fore-arc (high and low) tends to follow the trend of the earthquake distributions.     

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.     

Regional geoid modeling in the area of subglacial Lake Vostok,Antarctica

We present a geoid model for the area of Lake Vostok, Antarctica, from a combination of local airborne gravity, ice-surface and ice-thickness data and a lake bathymetry model. The topography data are used for residual terrain modeling (RTM) in a remove–restore approach together with GOCE satellite data. The quasigeoid is predicted by least-squares collocation (LSC) and subsequently converted to geoid heights. Special aspects of that method in presence of an ice sheet are discussed.It is well known that a body freely floating in water is in a state of hydrostatic equilibrium (HE). This usually applies, e.g., to ice shelves or sea ice. However, it has been shown that this is valid also for the ice sheet covering the subglacial Lake Vostok. Thus, we demonstrate the use of such a refined regional geoid model for glaciological and geophysical applications by means of the HE surface of that lake. The mean quadratic residual geoid signal (0.56 m) w.r.t. the GOCE background model exceeds the residual variations of the estimated apparent lake level (ALL) (0.26 m) within the central part of the lake. An approach considering the actual geopotential at the ALL has been derived and subsequently applied. In this context, downward continuation of the potential field within the ice sheet as well as the latitudinal tilt of off-geoid equipotential surfaces are discussed. In view of the accuracy of the ice-thickness measurements that dominate the total error budget of the estimated ALL these effects are negligible. Thus, the HE surface of subglacial lakes may safely be described by a constant height bias in small-scale regional applications. However, field continuation is significant with respect to the formal uncertainty of the quasigeoid, which is at the level of 5 cm given that accurate airborne gravity data (±2 mGal) are available.     

Improving airborne strapdown vector gravimetry using stabilized horizontal components

Integrating the deflections of the vertical along the flight line can yield geoid profiles which are valuable in the study of geodesy and geophysics, fortunately, the deflections can be measured directly by vector gravimetry. Airborne vector gravimetry using a Strapdown Inertial Navigation System and the Global Navigation Satellite System (SINS/GNSS) has shown promising results in previous studies. However, the quality of the SINS and GNSS is a major limitation; in particular, the attitude errors induced by the gyros will result in large measurement errors to the horizontal components of the gravity disturbance, and these measurement errors represent the behavior of low-frequency trend. An airborne vector gravimetry method used to remove the bias and low-frequency trends in the gravity disturbance estimated for each survey line has been developed. This method uses the horizontal components of the gravity disturbance computed from EGM2008 (Earth Gravitational Model 2008) as a reference. Firstly, the horizontal measurement results obtained from the gravimeter are divided into high- and low-frequency components according to the resolution of the EGM2008, and then, the bias and low-frequency trends of the low-frequency components are corrected using a linear fit to the EGM2008 reference data. Finally, the ultimate results can be acquired after combining the high-frequency components and the corrected low-frequency components. The data used was obtained from the SGA-WZ, which is the first strapdown airborne gravimeter developed in China. The results of this method are promising. The internal accuracy of the gravity disturbance's horizontal components for repeated survey lines exceeds 3.5 mGal, and the corresponding resolution is approximately 4.8 km based on 160-s data smoothing and an airplane averaging speed of approximately 216 km/h. After applying the WCF (Wavenumber Correlation Filter), the internal accuracy of the horizontal components exceeds 2 mGal. This can satisfy the requirement of the application in geodesy and solid earth geophysics.     

The new quasi-geoid model IRQG09 for Iran

Iran is a mountainous country with large lateral density variations of its crust. Constant density value is commonly used to determine the geoid models as well as topographic corrections. The effect of lateral density variation in the geoid can reach up to 14 cm in Iran which is not negligible in a precise geoid modelling. Also, the current height datum of Iran is based on the orthometric system but the effect of gravity variation was not applied in height parameter. Furthermore, the height systems of most neighbouring countries are defined as normal height. Connection of networks can be useful for the unification of height datum, geodynamics researches and optimal adjustment of levelling network. The new quasi-geoid model based on a recent EGM2008 global geo-potential model was created to solve the mentioned problem. The main purpose of the present study is to discuss the results of a research project in which a gravimetric quasi-geoid model for Iran was computed based on the least-squares modification of Stokes' formula. The evaluation is made using 475 GPS/levelling height anomalies covering the major parts of the country except the mountainous areas to the North and West. After a 7-parameter fit, the most promising attempt achieved a RMS value of 19 cm for the residuals based on the GPS/levelling data.     

Combined Regional Gravity Model of the Andean Convergent Subduction Zone and Its Application to Crustal Density Modelling in Active Plate Margins

The Central Andean subduction system is one of the most active geological structures on Earth. Although there have been a few previous studies, the structure and dynamics of the system are still not well understood. In the present study, we determine a combined regional gravity model of the Andean convergent subduction region for constraining lithospheric models. After a thorough validation and cleaning of the terrestrial gravity and height databases, the method of Least Squares Collocation was applied to consistently combine terrestrial and satellite gravity data, putting much emphasis on the stochastic modelling of the individual data components. As a result, we computed the first high-resolution regional gravity model of the study region that includes GOCE satellite gravity information. The inclusion of GOCE is an essential distinction from the independent global gravity model EGM2008. Validation against EGM2008 reveals that our regional solution is very consistent in regions where terrestrial gravity data are available, but shows systematic differences in areas with terrestrial data gaps. Artefacts in the EGM2008 of up to 150 mGal could be identified. The new combined regional model benefits from the very homogeneous error characteristics and accuracy of GOCE gravity data in the long-to-medium wavelengths down to 80–100 km. Reliable density modelling became possible also in the region of Central Andes, which lacks terrestrial gravity data. Finally, density models were adapted to fit the new regional gravity field solution. The results clearly demonstrate the capabilities of GOCE to better constrain lithospheric models.     

Preliminary analysis of the connection between ocean dynamics and the noise of gravity tide observed at the Sopronbánfalva Geodynamical Observatory,Hungary

An experimental development of a computer controlled photoelectric ocular system applied for the LaCoste and Romberg G949 gravimeter made the continuous observation of time variation of gravity possible. The system was operated for half a year in the Sopronbánfalva Geodynamical Observatory to test its capabilities. The primary aim of this development was to provide an alternative and self-manageable solution instead of the standard electronic (Capacitive Position Indicator) reading of this type of gravimeter and use it for the monitoring of Earth tide. It, however, turned out that this system is sensitive enough to observe the effect of variable seismic noise (microseisms) due to the changes of ocean weather in the North Atlantic and North Sea regions at microGal level (1 μGal = 10⁻⁸ m/s²). Up to now not much attention was paid to its influence on the quality and accuracy of gravity observations because of the large distance (>1000 km) between the observation place (generally the Carpathian–Pannonian basin) and the locations (centres of storm zones of the northern hydrosphere) of triggering events. Based on an elementary harmonic surface deformation model the noise level of gravity observations was compared to the spectral characteristics of seismic time series recorded at the same time in the observatory. Although the sampling rate of gravity records was 120 s the daily variation of gravity noise level showed significant correlation with the variation of spectral amplitude distribution of the analysed high pass filtered (cut-off frequency = 0.005 Hz) seismograms up to 10 Hz. Also available daily maps of ocean weather parameters were used to support both the correlation analysis and the parameterization of the triggering events of microseisms for further statistical investigations. These maps, which were processed by standard image processing algorithms, provide numerical data about geometrical (distance and azimuth of the storm centres relative to the observation point) and physical (mass of swelling water) quantities. The information can be applied for characterizing the state of ocean weather at a given day which may help the prediction of its influence on gravity measurements in the future. Probably it is the first attempt to analyse quantitatively the effect of ocean weather on gravity observations in this specific area of the Carpathian–Pannonian region.     

A study of regional gravity field recovery from GOCE vertical gravity gradient data in the Auvergne test area using collocation

Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the first satellite mission that observes gravity gradients from the space, to be primarily used for the determination of high precision global gravity field models. However, the GOCE gradients, having a dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model (EGM). This is investigated in Auvergne test area using Least Squares Collocation (LSC) with GOCE vertical gravity gradient anomalies (T_zz), removing the long wavelength part from EGM2008 and the short wavelength part by residual terrain modelling (RTM). The results show that terrain effects on the vertical gravity gradient are significant at satellite altitude, reaching a level of 0.11 E?tv?s unit (E.U.) in the mountainous areas. Removing the RTM effects from GOCE T_zz leads to significant improvements on the LSC predictions of surface gravity anomalies and quasigeoid heights. Comparison with ground truth data shows that using LSC surface free air gravity anomalies and quasi-geoid heights are recovered from GOCE T_zz with standard deviations of 11 mGal and 18 cm, which is better than those obtained by using GOCE EGMs, demonstrating that information beyond the maximal degree of the GOCE EGMs is present. Investigation of using covariance functions created separately from GOCE T_zz and terrestrial free air gravity anomalies, suggests that both covariance functions give almost identical predictions. However, using covariance function obtained from GOCE T_zz has the effect that the predicted formal average error estimates are considerably larger than the standard deviations of predicted minus observed gravity anomalies. Therefore, GOCE T_zz should be used with caution to determine the covariance functions in areas where surface gravity anomalies are not available, if error estimates are needed.     

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.     

Local geoid determination based on airborne gravity data

A mathematical model used for determination of a local geoid model by combining airborne gravity disturbances and the Earth Gravitational Model 2008 (EGM08) is shortly reviewed. The precision of the estimated local geoid model of Taiwan is tested by its comparison with the “real” geoid at Global Satellite Navigation Systems (GNSS)/levelling points. The same comparison at GNSS/levelling points is done for the geoid evaluated only by using EGM08. Conclusions concerning a rate of improvement of the “global” geoid from EGM08 using the “local” geoid from airborne gravity data are presented.     

GRACE/GOCE扩展重力场模型确定我国1985高程基准重力位的精度分析

高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47m~2·s~(-2)和62636853.49m~2·s~(-2),精度均为1.51m~2·s~(-2);发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9cm,南北向倾斜约为1.4cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16m~2·s~(-2).     

One technique for refining the global Earth gravity models

The results of the theoretical and experimental research on the technique for refining the global Earth geopotential models such as EGM2008 in the continental regions are presented. The discussed technique is based on the high-resolution satellite data for the Earth’s surface topography which enables the allowance for the fine structure of the Earth’s gravitational field without the additional gravimetry data. The experimental studies are conducted by the example of the new GGMplus global gravity model of the Earth with a resolution about 0.5 km, which is obtained by expanding the EGM2008 model to degree 2190 with the corrections for the topograohy calculated from the SRTM data. The GGMplus and EGM2008 models are compared with the regional geoid models in 21 regions of North America, Australia, Africa, and Europe. The obtained estimates largely support the possibility of refining the global geopotential models such as EGM2008 by the procedure implemented in GGMplus, particularly in the regions with relatively high elevation difference.     

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.     

Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology

Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology (n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A ∼ 10⁻³⁵ Pa⁻³ s⁻¹ for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.     

On the comparison of tidal gravity parameters with tidal models in central Europe

Two accurately calibrated superconducting gravimeters (SGs) provide high quality tidal gravity records in three central European stations: C025 in Vienna and at Conrad observatory (A) and OSG050 in Pecný (CZ). To correct the tidal gravity factors from ocean loading effects we compared the load vectors from different ocean tides models (OTMs) computed with different software: OLFG/OLMP by the Free Ocean Tides Loading Provider (FLP), ICET and NLOADF. Even with the recent OTMs the mass conservation is critical but the methods used to correct the mass imbalance agree within 0.1 nm/s². Although the different software agrees, FLP probably provides more accurate computations as this software has been optimised. For our final computation we used the mean load vector computed by FLP for 8 OTMs (CSR4, NAO99, GOT00, TPX07, FES04, DTU10, EOT11a and HAMTIDE). The corrected tidal factors of the 3 stations agree better than 0.04% in amplitude and 0.02° in phase. Considering the weighted mean of the three stations we get for O1 δ_c = 1.1535 ± 0.0001, for K1 δ_c = 1.1352 ± 0.0003 and for M2 δ_c = 1.1621 ± 0.0003. These values confirm previous ones obtained with 16 European stations. The theoretical body tides model DDW99/NH provides the best agreement for M2 (1.1620) and MATH01/NH for O1 (1.1540) and K1 (1.1350). The largest discrepancy is for O1 (0.05%). The corrected phase α_c does not differ significantly from zero except for K1 and S2. The calibrations of the two SG's are consistent within 0.025% and agree with Strasbourg results within 0.05%.     

GOCO05c: A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting

GOCO05c is a gravity field model computed as a combined solution of a satellite-only model and a global data set of gravity anomalies. It is resolved up to degree and order 720. It is the first model applying regionally varying weighting. Since this causes strong correlations among all gravity field parameters, the resulting full normal equation system with a size of 2 TB had to be solved rigorously by applying high-performance computing. GOCO05c is the first combined gravity field model independent of EGM2008 that contains GOCE data of the whole mission period. The performance of GOCO05c is externally validated by GNSS–levelling comparisons, orbit tests, and computation of the mean dynamic topography, achieving at least the quality of existing high-resolution models. Results show that the additional GOCE information is highly beneficial in insufficiently observed areas, and that due to the weighting scheme of individual data the spectral and spatial consistency of the model is significantly improved. Due to usage of fill-in data in specific regions, the model cannot be used for physical interpretations in these regions.     

Quantities,composition, and sources of beach debris in Korea from the results of nationwide monitoring

This study assessed the levels of marine debris pollution and identified its main sources in Korea. The surveys were bimonthly conducted by NGO leaders and volunteers on 20 beaches from March 2008 to November 2009. The quantities of marine debris were estimated at 480.9 (±267.7) count ⋅ 100 m⁻¹ for number, 86.5 (±78.6) kg ⋅ 100 m⁻¹ for weight, and 0.48 (±0.38) m³ ⋅ 100 m⁻¹ for volume. The level of marine debris pollution on the Korean beaches was comparable to that in the coastal areas of the North Atlantic ocean and South Africa. Plastics and styrofoam occupied the majority of debris composition in terms of number (66.7%) and volume (62.3%). The main sources of debris were fishing activities including commercial fisheries and marine aquaculture (51.3%). Especially styrofoam buoy from aquaculture was the biggest contributor to marine debris pollution on these beaches.     

地形/均衡重力场模型构制及其拟稳分析

重力空白区数据填补的一个主要方法是基于地壳均衡理论进行的,该方法亦用于EGM系列模型的构建中.本文研究了地形数据在构制地形/均衡重力场模型中的应用,分析了补偿深度对Airy位模型和面凝聚位模型的影响,给出二者的最佳补偿深度分别为50 km和40 km.以纯卫星重力模型为参考,后者在前120阶的精度要高于前者,但在121~250阶的精度较低,组合模型精度高于单一模型精度.对地形/均衡地球重力场模型进行了EGM2008拟稳分析,研究了不同分辨率基准的拟稳效果,分析表明：30'分辨率的拟稳基准所得拟稳模型对应的阶方差与参考阶方差曲线直到360阶都有较好的一致性,以EGM2008为基准,其相对累计大地水准面高误差在140阶时为6.83cm,相对累计重力异常误差在220阶时为1.10 mGal.