Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^ˆ ≤ ϕ ≤ 35^ˆ and 15^ˆ ≤ λ ≤ 25^ˆ. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8-20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).     

High resolution gravimetric geoid heights and gravimetric vertical deflections of Europe including marine areas

Gravimetric geoid heights and gravimetric vertical deflections have been detemined for Europe including the Mediterranean Sea, North Sea, Norwegian Sea, Baltic Sea and parts of the North Atlantic Ocean in a 12′×20′ grid. The computation has been carried out by least squares spectral combination using closed integral formulas, combining 104 000 mean free air gravity anomalies in 6′×10′ blocks, 12 000 mean free air gravity anomalies in 1⁰×1⁰ blocks and the sherical harmonic model GEM9. The precision of the computed geoid heights has been estimated to ±1 m, the precision of the computed vertical deflections has been estimated to ±2″. Comparisons of the gravimetric geoid heights and vertical deflections with a number of other solutions have been carried out, confirming the precision estimation.     

Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.     

Bathymetry enhancement by altimetry-derived gravity anomalies in the East Sea (Sea of Japan)

The gravity-geologic method (GGM) was used to enhance the bathymetry of the East Sea (Sea of Japan) with satellite altimetry-derived free-air gravity anomalies and shipborne depth measurements. By comparison with the bathymetry model of Smith and Sandwell’s (SAS) approach (1994), GGM was found to have an advantage with short wavelength (≤12 km) components, while SAS better predicts longer wavelength (≥25 km) components, despite its dependency on density contrast. To mitigate this limitation, a tuning density contrast of 10.25 g/cm³ between seawater and the seafloor was primarily estimated by the downward continuation method and then validated by the check points method with GGM. Similarly, SAS is limited by the “A” value in low-pass part of the Wiener filter, which defines the effective range of the wavelength components on bathymetry. As a final result, we present an enhanced GGM bathymetry model by integrating all available data.     

Combined satellite altimetry and shipborne gravimetry data processing

The recovery of quantities related to the gravity field (i.e., geoid heights and gravity anomalies) is carried out in a test area of the central Mediterranean Sea using 5' × 5' marine gravity data and satellite altimeter data from the Geodetic Mission (GM) of ERS‐J. The optimal combination of the two heterogeneous data sources is performed using (1) the space‐domain least‐squares collocation (LSC) method, and (2) the frequency‐domain input‐output system theory (IOST). The results derived by these methods agree at the level of 2 cm in terms of standard deviation in the case of the geoid height prediction. The gravity anomaly prediction results by the same methods vary between 2.18 and 2.54 mGal in terms of standard deviation. In all cases, the spectral techniques have a much higher computational efficiency than the collocation procedure. In order to investigate the importance of satellite altimetry for gravity field modeling, a pure gravimetric geoid solution, carried out in a previous study for our lest area by the fast collocation approach (FCOL), is used in comparison with the combined geoid models. The combined solutions give more accurate results, at the level of about 15 cm in terms of standard deviation, than the gravimetric geoid solution, when the geoid heights derived by each method are compared with TOPEX altimeter sea surface heights (SSHs). Moreover, nonisotropic power spectral density functions (PSDs) can be easily used by IOST, while LSC requires isotropic covariance functions. The results show that higher prediction accuracies are always obtained when using a priori nonisotropic information instead of isotropic information.     

RTM Gravity Forward-Modeling Using Topography/Bathymetry Data to Improve High-Degree Global Geopotential Models in the Coastal Zone

We apply the residual terrain modeling (RTM) technique for gravity forward-modeling to successfully improve high-resolution global gravity fields at short spatial scales in coastal zones. The RTM scheme is combined with the concept of rock-equivalent topography, allowing to use a single uniform constant mass-density in the RTM forward-modeling, both at land and sea. SRTM30_PLUS bathymetry is merged with higher-resolution SRTM V4.1 land topography, and expanded into spherical harmonics to degree 2160, yielding a new and consistent high-degree RTM reference surface. The forward-modeling performance is demonstrated in coastal zones of Greece and Canada using ground-truth vertical deflections, gravity from land and shipborne gravimetry, and geoid heights from GPS/leveling, with improvements originating from bathymetry clearly identified. We demonstrate that the SRTM30_PLUS bathymetry carries information on gravity field structures at spatial scales less than 5 arc minutes, which can be used to augment EGM2008 in (rugged) coastal zones, both over land and marine areas. This may be of value (i) to partially reduce the signal omission error in EGM2008/GOCE-based height transfer in areas devoid of dense gravity data, (ii) to fill the gap between land gravity and shipborne gravity along rugged coastlines, and (iii) for the development of next-generation altimetric gravity fields.     

Bathymetry Inversion with the Gravity-Geologic Method: A Study of Long-Wavelength Gravity Modeling Based on Adaptive Mesh

Modeling of long-wavelength gravity anomaly is crucial for bathymetry inversion with a gravity-geologic method. We propose a new method, named as iGGM, to approximate the long-wavelength gravity anomalies by using a finite element method based on an adaptive triangular mesh which is constructed by uneven control points. The mesh size is suitably controlled to ensure that there are several control points in each grid. By using iGGM, the bathymetry in the South China Sea (Test Area #1: 112°E–119°E, 12°N–20°N) and East China Sea (Test Area #2: 125°E–130°E, 25°N–30°N) is estimated. The performance of the method was evaluated by comparing the predictions with Earth topographical database 1 (ETOPO1) model and shipborne depths in the test points. Results show that the depths derived by iGGM have a strong correlation with the shipborne depths. In the test points, the mean values of their differences are smaller than 10 m. The standard deviations of their differences are smaller than 120 m and their correlation is stronger than 0.98. Meanwhile, the results provided by the iGGM model are comparable with that obtained by the ETOPO1 model, e.g., the differences between iGGM and ETOPO1 models in test points for Test Areas 1 and 2 are 116 and 70 m in standard deviation, respectively.     

A Bathymetric Model for the South China Sea from Satellite Altimetry and Depth Data

A bathymetric model for the South China Sea is computed from altimeter-derived gravity anomalies, shipborne depths, ETOPO5, and the GMT shorelines using a procedure that includes downward continuation, linear regression, and data merging. The model best fits the GMT shorelines and is a compromise between smoothness, degree of agreement with ship data, and the seafloor features we wish to retain. The model is proven useful in studying the tectonics and modeling the ocean tide of the South China Sea.     

Predicting Bathymetry from the Earth's Gravity Gradient Anomalies

Historically, prediction of ocean floor depth, or bathymetry, has been based on the isostatic modeling and linearized relationships between gravity anomalies and bathymetry. The need for isostatic modeling limits the application of the resulting bathymetry predictions as constraints in geophysical models. An alternative technique making use of the Earth's vertical gravity gradient for predicting bathymetry is explored in this paper. This technique is based on the fact that the observed gravity gradient anomalies result primarily from local mass concentrations on the ocean floor, and that mass compensation by the oceanic crust has an insignificant effect on the gravity gradients, and can be neglected. The resulting bathymetry prediction therefore is independent of isostatic modeling assumptions, allowing it to be used as a constraint on models of lithospheric compensation and for other geodetic and geophysical applications.     

Geophysical interpretation of features in the marine geoid of fennoscandia

An interpretation of the geoid in and around Scandinavia in terms of crustal depth structure has been made. Correlations as high as 0.92 were found between current models of crustal depth and the geoid for marine areas of Scandinavia. The Fennoscandian land uplift together with its corresponding resultant change of geoid were also found to be highly correlated with crustal depth structure. Results of these correlations compare favorably with theoretical models based upon large scale isostatic behavior of the lithosphere. These models indicate that the crustal thickness variations of Scandinavia are compensated generally at depths greater than 100 km. The results indicate that previous attempts to correlate the geoid with the causes of present land uplift have overestimated the remaining isostatic geoid anomaly in Fennoscandia. The application of these results would reduce the isostatic geoid anomaly by as much as 80% for marine areas of Fennoscandia. This may be interpreted as placing the estimated upper mantle viscosities for Fennoscandia closer to 10²¹ Pa s.     

Evolution of errors in the altimetric bathymetry model used by Google Earth and GEBCO

We analyze errors in the global bathymetry models of Smith and Sandwell that combine satellite altimetry with acoustic soundings and shorelines to estimate depths. Versions of these models have been incorporated into Google Earth and the General Bathymetric Chart of the Oceans (GEBCO). We use Japan Agency for Marine-Earth Science and Technology (JAMSTEC) multibeam surveys not previously incorporated into the models as “ground truth” to compare against model versions 7.2 through 12.1, defining vertical differences as “errors.” Overall error statistics improve over time: 50th percentile errors declined from 57 to 55 to 49 m, and 90th percentile errors declined from 257 to 235 to 219 m, in versions 8.2, 11.1 and 12.1. This improvement is partly due to an increasing number of soundings incorporated into successive models, and partly to improvements in the satellite gravity model. Inspection of specific sites reveals that changes in the algorithms used to interpolate across survey gaps with altimetry have affected some errors. Versions 9.1 through 11.1 show a bias in the scaling from gravity in milliGals to topography in meters that affected the 15–160 km wavelength band. Regionally averaged (>160 km wavelength) depths have accumulated error over successive versions 9 through 11. These problems have been mitigated in version 12.1, which shows no systematic variation of errors with depth. Even so, version 12.1 is in some respects not as good as version 8.2, which employed a different algorithm.     

Calculation of geoid undulations and gravity anomalies in the Northwest Pacific by using the Topex/Poseidon and Geosat altimeter data

INTRODUCTIONThegeoidistheiargeopotentials~econfidingmostlywiththemeanseasurfaceandisdenotedastheheightrelativetotheidealelliPSes~eoftheearth.Thegeoidundulationsinglobalaceareupto100m.TheunevenstructureOftheearthgivesrisetotheunevenfeatureofthecitysot...     

Thermal structure of the crust in the Black Sea: comparative analysis of magnetic and heat flow data

This paper presents the first study of mapping of the Curie point depth (CPD) from magnetic data for the Black Sea and a comparison with a classical thermal modeling from heat flow data. The provided relationship between radially averaged power spectrum of the magnetic anomalies and the depths to the magnetic sources of the Black Sea vary from 22 to 36 km. Deepening of CPDs observed in the western and eastern Black Sea basins correspond with the thickest sediment areas, whereas the shallow CPDs are related to the Mid-Black Sea Ridge and thin sediment areas at the costal side of the Black Sea. For comparison, the temperature field was also modeled from heat flow data from the Black Sea along three approximately north–south directed profiles corresponding to known DSS soundings. The Curie isotherm along the profiles occurs at depths of 22–35 km. A comparison of the results of the two independent methods reveals only 8–10 % discrepancy. This discrepancy is equal to an accuracy of temperature determination from heat flow data.     

Predicting Bathymetry from the Earth's Gravity Gradient Anomalies

Historically, prediction of ocean floor depth, or bathymetry, has been based on the isostatic modeling and linearized relationships between gravity anomalies and bathymetry. The need for isostatic modeling limits the application of the resulting bathymetry predictions as constraints in geophysical models. An alternative technique making use of the Earth's vertical gravity gradient for predicting bathymetry is explored in this paper. This technique is based on the fact that the observed gravity gradient anomalies result primarily from local mass concentrations on the ocean floor, and that mass compensation by the oceanic crust has an insignificant effect on the gravity gradients, and can be neglected. The resulting bathymetry prediction therefore is independent of isostatic modeling assumptions, allowing it to be used as a constraint on models of lithospheric compensation and for other geodetic and geophysical applications.     

XGBoost算法在多光谱遥感浅海水深反演中的应用

在多光谱遥感浅海水深反演过程中,考虑到水体和底质影响,水深值和海水表面辐射亮度之间的线性关系不成立。本文以甘泉岛南部0～25m范围的沙质区域为研究区域,利用GeoEye-1多光谱遥感影像和多波束实测水深数据构建XGBoost非线性水深反演模型,研究了XGBoost算法用于水深反演的性能。以决定系数(R~2),均方误差(MSE)和平均绝对误差(MAE)作为评价指标,并与3种传统线性回归模型进行了对比分析。结果表明, XGBoost非线性水深反演模型的R~2、MSE和MAE分别为0.991、0.33m和0.44m,拟合程度最好,精度优于线性回归模型。为进一步探究各模型在不同水深的反演精度,将水深范围分成3段(0～8 m, 8～15 m, 15～25 m)分别进行精度验证和误差分析。结果表明, XGBoost模型在各分段的精度均优于线性回归模型, MSE依次为0.56 m, 0.14 m和0.43 m。可见,在单一底质区域下XGBoost模型的水深反演精度更高,且反演效果更稳定。     

Heterogeneous Gravity Data Fusion and Gravimetric Quasigeoid Computation in the Coastal Area of China

ABSTRACT

Different types of gravity observations are available over coastal areas. The main challenge for coastal geoid determination is the proper fusion of heterogeneous gravity data including land, shipborne, airborne, and altimetry-derived gravity data. This paper describes the gravity data fusion and the computation of the gravimetric quasigeoid in the coastal area of mainland China. An iterative procedure of the weighted least-squares prediction based on rectangular harmonic functions is used for merging the land, altimetric, shipborne, and airborne gravity data. Applying the analytical continuation method in Molodensky's theoretic frame, the merged gravity data are then used to determine the gravimetric quasigeoid model by using the generalized Stokes' integral in a remove-compute-restore fashion. The gravimetric quasigeoid model is compared with the height anomalies determined at 662 GPS leveling points over the coastal region of mainland China, where both the geodetic height and the normal height are known. The standard deviations of the differences in the coastal provinces range from 1.8 to 4.4 cm. For the entire computation area, the mean and standard deviation of the differences are 27.9 and 3.9 cm, respectively.     

海洋大地水准面的多尺度分析

利用径向基函数多尺度分析方法,将GOCO05S模型海洋大地水准面分解为3个尺度,并进行详细的分析统计。分解后重构的大地水准面精度达到了±0.02m,表明了径向基函数出色的多尺度分析能力。对不同深度层面上大地水准面异常的分布及成因做了深入探讨。浅层上地幔大地水准面异常主要分布于板块边缘,呈条状,与火山热点源分布类似;深层上地幔大地水准面异常和大洋中脊所在位置部分吻合,主要呈带状或块状,与上地幔的对流有关;中间层上地幔的大地水准面异常形态介于上述两者之间,主要受火山热点源和地幔对流的综合影响。     

On the Impact of Mispointing Error and Hamming Filtering on Altimeter Waveform Retracking and Skewness Retrieval

An adequate conceptual definition of the geoid is essential for the unambiguous combination of satellite tracking data, satellite al‐timetry, and surface gravity measurements to obtain sea surface topography. The factors influencing the selection of a particular level surface of the earth's gravity field include the purpose(s) for which the geoid is to be used at the 5‐cm level, and the types of data to be used in achieving these objectives. The principal reasons for high precision determinations of the shape of the geoid are: the determination of sea surface topography for applications in oceanography; and the unification of leveling datums with a resolution equivalent to that of first order geodetic leveling. A conceptual definition of the geoid acceptable to oceanographers would be: The geoid for a selected epoch of measurement is that level surface of the earth's gravity field in relation to which the average non‐tidal (or quasi‐stationary) sea surface topography is zero as sampled globally in ocean regions. In the geodetic context, it would be convenient, though not essential, to modify this definition in such a way that the global sea surface topography had zero mean as sampled for evaluations of the geodetic boundary value problem. In either case, a basis exists for unifying all leveling datums serving areas in excess of 10⁶ km², using either gravity anomaly data for the regions or precise determinations of position at first order bench marks. Unfavorable signal‐to‐noise ratios can pose problems when dealing with datums serving smaller areas. Elevation and gravity data banks must be correctly referenced to leveling datums prior to use in sea surface topography determinations. A recent attempt to upgrade the Australian gravity anomaly data bank indicates that all current data banks of this type are inadequate for the task. It is unlikely that time variations in the radial position of the geoid as conceptually defined above, will exceed ±5 cm per century, provided the rate of earth expansion was less than 1 part in 10¹⁰ yr^‐l and there is no dramatic change in the present rate of secular change in Mean Sea Level.     

First insights into the demography of the rare gorgonian Spinimuricea klavereni in the Mediterranean Sea

We present the results of the first study to highlight the demography, morphometry and growth rates of Spinimuricea klavereni, a rare Mediterranean endemic gorgonian exceptionally common in shallow depths of the Northeast Marmara Sea. In the study area, this species forms vast populations on rocks, boulders and attached to pebbles/stones/shells on soft substrates between 20 and 45 m depth, with a total average density of 0.3 colonies·m^?2 but comprising patches up to 3 colonies·m^?2. Colonies, which are on average 42.9 (±20.1) cm in height, can reach up to 110 cm. Unlike other Mediterranean gorgonians, the colonies studied here showed fast growth rates that decreased with increasing colony height, between 1.5–11.1 and 4.96 ± 3.01 cm·year^?1 on average. The low necrosis and high growth rates displayed by this species in the Northeast Marmara Sea confirm the previously hypothesized opportunistic behaviour of the species. The unique community consisting of S. klavereni and other rare gorgonian/soft corals has limited distribution in this area and should be considered to be a vulnerable marine ecosystem. Therefore we recommend that some conservation measures are taken, including the prohibition of all fisheries and anchoring over these assemblages.     

两种测高重力异常反演海底地形方法比较

针对基于测高重力异常反演海底地形理论众多、选取标准无法确定的情况,利用中国南海海域内的测高重力异常和船测水深数据研究比较了重力地质法(GGM)和SmithSandwell (SAS)法两种精度高、计算速度相对较快的海底地形反演理论。其中,GGM方法的密度差异常数Δρ由向下延拓技术确定为2.15 g·cm-3,SAS方法采用移去-恢复技术得到反演波段内重力异常和水深数据。结果表明:测线分布条件一定时,水深多在-1 000 m左右或反演区域岛礁、海山等复杂海底地形较多时选取SAS方法,水深主要在-3 000 m以深的区域或海底地形复杂程度不高时选取GGM方法则能获取更好的效果,其效果最优处与船测水深在检核点处的差值最优平均值能达-0.61 m,标准差可达14.67 m。