Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry,altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.     

The ITG-Goce02 gravity field model from GOCE orbit and gradiometer data based on the short arc approach

In this contribution, we describe the global GOCE-only gravity field model ITG-Goce02 derived from 7.5 months of gradiometer and orbit data. This model represents an alternative to the official ESA products as it is computed completely independently, using a different processing strategy and a separate software package. Our model is derived using the short arc approach, which allows a very effective decorrelation of the highly correlated GOCE gradiometer and orbit data noise by introducing a full empirical covariance matrix for each arc, and gives the possibility to downweight ‘bad’ arcs. For the processing of the orbit data we rely on the integral equation approach instead of the energy integral method, which has been applied in several other GOCE models. An evaluation against high-resolution global gravity field models shows very similar differences of our model compared to the official GOCE results published by ESA (release 2), especially to the model derived by the time-wise approach. This conclusion is confirmed by comparison of the GOCE models to GPS/levelling and altimetry data.     

利用先验重力场模型对GOCE卫星重力梯度观测值进行校准分析

GOCE卫星任务搭载了高灵敏度的重力梯度仪,其观测值用于恢复高精度高分辨率的地球重力场。本文利用EIGEN-5C、EGM2008、GOTIM3、GGM03S高精度全球重力场模型,确定了GOCE引力梯度张量的对角分量观测值(Vxx、Vyy、Vzz)的校准参数,分析了比例因子的稳定性,并讨论了相同模型不同阶次、同阶次不同模型以及是否估计漂移参数对比例因子、偏差参数及校准观测值的影响。研究表明比例因子的稳定性在10-4的量级,利用250阶的EIGEN-5C模型和EGM2008模型校准得到观测值的差异小于10-4 E,远远小于观测误差,以1d为周期估计校准参数时,是否估计漂移对校准结果的影响达到0.4E。同时,校准前后观测值差异的频谱说明校准过程主要影响Vxx、Vyy、Vzz观测值的低频部分,即来自先验重力场模型的中低(150)阶次,考虑到GOCE引力梯度的观测频带,校准后的观测值可用于恢复中高频的重力场信号。     

GOCE实测数据反演高阶重力场模型的Torus方法

不同于当前广泛使用的空域法、时域法、直接解法,本文尝试采用Torus方法处理GOCE实测数据,利用71 d的GOCE卫星引力梯度数据反演了200阶次GOCE地球重力场模型,实现了对参考模型的精化。首先,采用Butterworth零相移滤波方法加移去—恢复技术,处理引力梯度观测值中的有色噪声,并利用泰勒级数展开和Kriging方法对GOCE卫星引力梯度数据进行归算和格网化,计算得到了名义轨道上格网点处的引力梯度数据。然后,利用2D-FFT技术和块对角最小二乘方法处理名义轨道上数据,获得了200阶次的GOCE地球重力场模型GOCE_Torus。利用中国和美国的GPS/水准数据进行外部检核结果说明,GOCE_Torus与ESA发布的同期模型的精度相当;GOCE_Torus模型与200阶次的EGM2008模型相比,在美国区域精度相当,但在中国区域精度提高了4.6 cm,这充分体现了GOCE卫星观测数据对地面重力稀疏区的贡献。Torus方法拥有快速高精度反演卫星重力场模型的优势,可以在重力梯度卫星的设计、误差分析及在轨快速评估等方面得到充分应用。     

The height datum problem and the role of satellite gravity models

Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem.     

利用GOCE模拟观测反演重力场的Torus法

在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61dGOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022mm和0.099mm。在沿轨卫星引力梯度模拟数据中加入5mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58cm和1.45cm,累积误差最大值分别为6.37cm和5.55cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。     

联合高低卫-卫跟踪和卫星重力梯度数据恢复地球重力场的谱组合法

GOCE采用的高低卫-卫跟踪和卫星重力梯度测量技术在恢复重力场方面各有所长并互为补充,如何有效利用这两类观测数据最优确定地球重力场是GOCE重力场反演的关键问题。本文研究了联合高低卫-卫跟踪和卫星重力梯度数据恢复地球重力场的最小二乘谱组合法,基于球谐分析方法推导并建立了卫星轨道面扰动位T和径向重力梯度Tzz、以及扰动位T和重力梯度分量组合{Tzz-Txx-Tyy}的谱组合计算模型与误差估计公式。数值模拟结果表明,谱组合计算模型可以有效顾及各类数据的精度和频谱特性进行最优联合求解。采用61天GOCE实测数据反演的两个180阶次地球重力场模型WHU_GOCE_SC01S（扰动位和径向重力梯度数据求解）和WHU_GOCE_SC02S（扰动位和重力梯度分量组合数据求解）,结果显示后者精度优于前者,并且它们的整体精度优于GOCE时域解,而与GOCE空域解的精度接近,验证了谱组合法的可行性与有效性。     

GOCE引力梯度内部校准方法

GOCE卫星引力梯度仪的精确校准是反演高精度重力场的前提之一,本文利用GOCE卫星L1b数据中的引力梯度仪及恒星敏感器数据实现了卫星引力梯度的内部校准。以最小二乘联合多个恒星敏感器观测数据确定内部校准使用的角速度,有效避免了单个恒星敏感器低精度角速度分量对坐标转换过程的影响。考虑到恒星敏感器坐标系与梯度仪坐标系间旋转矩阵随时间的变化,本文在ESA官方内部校准方法的基础上,提出了顾及旋转矩阵校准参数的内部校准模型,并利用2009年11月的GOCE实测数据验证了该方法的效果。结果表明,该旋转矩阵校准参数数值约100″,且在该月存在3″~30″的漂移;与GOCE官方内部校准方法对比,从卫星引力梯度精度结果来看,在低于0.005 Hz频段内,同时解算旋转矩阵的校准参数与梯度仪内3个加速度计对的校准参数的内部校准模型优于仅考虑加速度计对校准参数的模型;除此之外,本文讨论了以该模型为基础的GOCE梯度仪数据校准的可能方法,为GOCE及后续重力卫星的数据处理工作提供参考。     

Exploring the possibilities for star-tracker assisted calibration of the six individual GOCE accelerometers

A method has been developed and tested for estimating calibration parameters for the six accelerometers on board the Gravity field and steady-state Ocean Circulation Explorer (GOCE) from star tracker observations. These six accelerometers are part of the gradiometer, which is the prime instrument on board GOCE. It will be shown that by taking appropriate combinations of observations collected by the accelerometers, by modeling acceleration terms caused by gravity gradients from an a priori low-degree spherical harmonic expansion, and by modeling rotational acceleration terms derived from star-tracker observations, scale factors of each of the accelerometers can be estimated for each axis. Simulated observations from a so-called end-to-end simulator were used to test the method. This end-to-end simulator includes a detailed model of the GOCE satellite, its instruments and instrument errors, and its environment. Results of the tests indicate that scale factors of all six accelerometers can be determined with an accuracy of around 0.01 for all components on a daily basis.     

联合EGM2008模型重力异常和GOCE观测数据构建超高阶地球重力场模型SGG-UGM-1

本文研究了联合卫星观测数据和重力异常数据确定超高阶重力场模型的理论方法,并使用EGM2008模型重力异常和GOCE（gravity field and ocean circulation explorer）观测数据构建了重力场模型SGG-UGM-1。重点研究了由球面格网重力异常快速构建超高阶重力场模型的块对角最小二乘方法,将OpenMP技术引入到块对角最小二乘中以提高计算效率,并基于模拟数据验证了方法及算法和软件模块的正确性。采用本文制定的联合解算策略,利用GOCE重力卫星观测数据构建的220阶次法方程和EGM2008模型重力异常构建的2159阶次块对角法方程,联合求解了2159阶次的重力场模型SGG-UGM-1。将SGG-UGM-1与EGM2008、EIGEN-6C2、EIGEN-6C4等超高阶模型在频谱域内进行了比较分析,结果表明SGG-UGM-1相对参考模型的系数误差较小,且在220阶次内的系数精度相比EGM2008模型有了提高。采用中国与美国的GPS/水准数据和毛乌素测区的航空重力观测数据对这些模型进行了外符合精度的检验。检核结果表明,在中国区域,SGG-UGM-1模型大地水准面的精度在EIGEN-6C2和EIGEN-6C4两个模型之间,优于GOSG-EGM模型和EGM2008模型,与美国区域几个模型的精度相当。利用毛乌素测区的航空重力数据对几个模型进行了检核,结果表明SGG-UGM-1模型计算的重力扰动精度与EGM2008、EIGEN-6C4模型相当,优于GOSG-EGM模型和EIGEN-6C2模型。     

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.     

First GOCE gravity field models derived by three different approaches

Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analysed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared with combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITG-Grace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-month GOCE gravity field models of 10?cm in terms of geoid heights, and 3?mGal in terms of gravity anomalies, globally at a resolution of 100?km (degree/order 200).     

GOCE gradiometer: estimation of biases and scale factors of all six individual accelerometers by precise orbit determination

A method has been implemented and tested for estimating bias and scale factor parameters for all six individual accelerometers that will fly on-board of GOCE and together form the so-called gradiometer. The method is based on inclusion of the individual accelerometer observations in precise orbit determinations, opposed to the baseline method where so-called common-mode accelerometer observations are used. The method was tested using simulated data from a detailed GOCE system simulator. It was found that the observations taken by individual accelerometers need to be corrected for (1) local satellite gravity gradient (SGG), and (2) rotational terms caused by centrifugal and angular accelerations, due to the fact that they are not located in the satellite’s center of mass. For these corrections, use is made of a reference gravity field model. In addition, the rotational terms are derived from on-board star tracker observations. With a perfect a priori gravity field model and with the estimation of not only accelerometer biases but also accelerometer drifts, scale factors can be determined with an accuracy and stability better than 0.01 for two of the three axes of each accelerometer, the exception being the axis pointing along the long axis of the satellite (more or less coinciding with the flight direction) for which the scale factor estimates are unreliable. This axis coincides with the axis of drag-free control, which results in a small variance of the signal to be calibrated and thus an inaccurate determination of its scale factor in the presence of relatively large (colored) accelerometer observation errors. In the presence of gravity field model errors, it was found that still an accuracy and stability of about 0.015 can be obtained for the accelerometer scale factors by simultaneously estimating empirical accelerations.     

利用引力梯度数据计算径向梯度的优化方法

根据重力梯度观测各分量的方差及协方差信息,提出了利用GOCE梯度数据计算径向重力梯度的优化方法。首先给出了径向重力梯度的计算方法,并深入分析了误差传播规律,通过建立相应的条件极值问题,给出了计算径向重力梯度最优组合因子的方法;通过模拟数据验证了本文所提出的优化因子的优越性。实际数据计算表明:相对于传统方法,采用优化组合因子可使反演所得引力位模型的累积大地水准面精度在250阶时提高约2 cm。由于径向重力梯度不仅可以用于地球引力场模型的求解,也可直接应用于地球物理问题的讨论,因此本文所提出的优化方法也可对部分地球动力学问题的讨论提供方便。     

GOCE卫星重力梯度数据反演重力场的滤波器设计与比较分析

地球重力场和海洋环流探测（gravity field and steady-state ocean circulation explorer,GOCE）卫星重力梯度数据有色噪声和低频系统误差的滤波处理是反演高精度地球重力场的一个关键问题。针对GOCE卫星重力梯度数据的滤波处理,基于移动平均（moving average,MA）方法和CPR(circle per revolution)经验参数方法设计了两类低频系统误差滤波器,并分别将这两类滤波器与基于自回归移动平均（auto-regressive and moving average,ARMA）模型设计的有色噪声滤波器组合起来形成级联滤波器。为了分析滤波器处理的实际效果,基于空域最小二乘法采用70 d的GOCE观测数据,并联合重力恢复与气候实验（gravity recovery and climate experiment,GRACE）数据分别反演了224阶次的重力场模型GOGR-MA(MA+ARMA级联滤波)和GOGR-CPR(CPR+ARMA级联滤波)。将反演模型与采用同期数据求解的第一代GOCE系列模型及GOCE和GRACE联合模...     

Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons

Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved.     

A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model

The Gravity and steady-state Ocean Circulation Explorer (GOCE) satellite mission measures Earth’s gravity field with an unprecedented accuracy at short spatial scales. In doing so, it promises to significantly advance our ability to determine the ocean’s general circulation. In this study, an initial gravity model from GOCE, based on just 2 months of data, is combined with the recent DTU10MSS mean sea surface to construct a global mean dynamic topography (MDT) model. The GOCE MDT clearly displays the gross features of the ocean’s steady-state circulation. More significantly, the improved gravity model provided by the GOCE mission has enhanced the resolution and sharpened the boundaries of those features compared with earlier satellite only solutions. Calculation of the geostrophic surface currents from the MDT reveals improvements for all of the ocean’s major current systems. In the North Atlantic, the Gulf Stream is stronger and more clearly defined, as are the Labrador and the Greenland currents. Furthermore, the finer scale features, such as eddies, meanders and branches of the Gulf Stream and North Atlantic Current system are visible. Similar improvements are seen also in the North Pacific Ocean, where the Kuroshio and its extension are well represented. In the Southern hemisphere, both the Agulhas and the Brazil-Malvinas Confluence current systems are well defined, and in the Southern ocean the Antarctic Circumpolar Current appears enhanced. The results of this preliminary analysis, using an initial GOCE gravity model, clearly demonstrate the potential of the GOCE mission. Already, at this early stage of the mission, the resolution of the MDT has been improved and the estimated surface current speeds have been increased compared with a GRACE satellite-only MDT. Future GOCE gravity models are expected to build further upon this early success.     

Evaluation of the first GOCE static gravity field models using terrestrial gravity,vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.     

GOCE地球重力场模型在青藏地区的评价及分析

2009年GOCE卫星升空以后,卫星重力梯度数据参与解算的GOCE系列重力场模型已有多家研究机构相继公布。本文分别采用青藏地区的GPS/水准和重力异常实测数据对GOCE重力场模型进行了外部测试,并在重力异常验证过程中引入了一种新的滤波方法,验证结果表明在青藏地区GOCE重力场模型相比其它系列模型的优势在于中波段。同时,探讨了GOCE重力场模型与其他系列模型在青藏地区主要差异值的空间分布以及首次利用统计分析方法找出模型之间主要差异值的阶次分布,得出如下结论：模型之间的较大差异值在空间水平方向上主要分布在喜马拉雅山脉、天山等地形起伏较大的区域,在垂直方向上主要集中在岩石圈。     

Space-Wise approach for airborne gravity data modelling

Regional gravity field modelling by means of remove-compute-restore procedure is nowadays widely applied in different contexts: it is the most used technique for regional gravimetric geoid determination, and it is also used in exploration geophysics to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.), which are useful to understand and map geological structures in a specific region. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are usually adopted. However, due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc., airborne data are usually contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations in both the low and high frequencies should be applied to recover valuable information. In this work, a software to filter and grid raw airborne observations is presented: the proposed solution consists in a combination of an along-track Wiener filter and a classical Least Squares Collocation technique. Basically, the proposed procedure is an adaptation to airborne gravimetry of the Space-Wise approach, developed by Politecnico di Milano to process data coming from the ESA satellite mission GOCE. Among the main differences with respect to the satellite application of this approach, there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. The presented solution is suited for airborne data analysis in order to be able to quickly filter and grid gravity observations in an easy way. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data retrieving the gravitational signal with a predicted accuracy of about 0.4 mGal.