Evaluation of Gravity Data by EIGEN-2 (CHAMP-only) Model in China

<p>In this study, we investigate the optimal combination of local gravity observations and their contributions to the regional quasi-geoid model. The study area is located in Colorado, USA, with two types of regional data sets, namely terrestrial gravity data and airborne gravity data, available within the “1 cm geoid experiment”. The approach based on series expansions in terms of spherical radial basis functions (SRBF) is applied, which has been developed at DGFI-TUM in the last two decades. We use two different types of basis functions covering the same spectral domain separately for the terrestrial and the airborne measurements. The Shannon function is applied to the terrestrial data, and the Cubic Polynomial (CuP) function which has smoothing features is applied to the airborne data for filtering their high-frequency noise.</p><p>To assess the contributions of the regional terrestrial and airborne gravity data to the final quasi-geoid model, four solutions are compared, namely the combined solution, the terrestrial only, the airborne only, and finally the model only solution, i.e., only the global gravity model and the topographic model are used without any gravity data from regional measurements. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the quasi-geoid model w.r.t the validation data (the mean solution of independent computations delivered by fourteen institutions from all over the world) drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data.</p>

This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity data, and the third grid from combined downward-continued airborne and terrestrial gravity data. Gravimetric geoid models with the three gravity anomaly grids were determined using the least-squares modification of Stokes’ formula with additive corrections (LSMSA) method. The absolute and relative accuracy of the computed gravimetric geoid models was estimated on GNSS/levelling points. Results exhibit the accuracy improved by 1.1 cm or 20% in terms of standard deviation when airborne and terrestrial gravity data was used for geoid computation, compared to the geoid model computed only from terrestrial gravity data. Finally, the spectral analysis of surface gravity anomaly grids and geoid models was performed, which provided insights into specific wavelength bands in which airborne gravity data contributed and improved the power spectrum.

In this study, a tailored gravity-field model is developed to fit and recover local terrestrial gravity data by integrating gravity from global gravity-field models, residual gravity derived from topographic data and observed terrestrial gravity over two study sites in Africa (Cameroon and South Africa). During the modelling phase, two-thirds of the terrestrial gravity data is utilised, reserving the remaining one-third for validation purposes. Additionally, an independent validation is conducted by comparing computed quasigeoid models (derived from tailored gravity data) with height anomalies from GPS/levelling data over the two study sites. The accuracy of the tailored gravity model in reproducing observed gravity data is noteworthy, with a ±8.9 mGal accuracy for the study site in South Africa at 2867 test points and a ±10.4 mGal accuracy for the study site in Cameroon at 637 test points. Comparing height anomalies from GPS/levelling with the SATGQG quasigeoid model (developed from tailored gravity data) and the recent CDSM09A quasigeoid model at 11 GPS/levelling data points reveals comparable accuracies of ±0.10 m and ±0.05 m, for SATGQG and CDSM09A, respectively for the site in South Africa. For the Cameroon site, the differences between height anomalies from GPS/levelling and the CTGQG quasigeoid model (developed from tailored gravity data), along with the recent CGM20 quasigeoid model at 38 GPS/levelling data points, show practically equal accuracies of ±0.15 m for CTGQG and ±0.11 m for CGM20. These findings underscore the potential of tailored gravity-field model in developing accurate quasigeoid models, particularly in regions with limited gravity data coverage. This approach holds promise for gravity recovery and precise geoid modelling in developing countries and regions with insufficient coverage of terrestrial gravity data.

ABSTRACTThe pan-sharpening scheme combines high-resolution panchromatic imagery (HRPI) data and low-resolution multispectral imagery (LRMI) data to get a single merged high-resolution multispectral image (HRMI). The pan-sharpened image has extensive information that will promote the efficiency of image analysis methods. Pan-sharpening technique is considered as a pixel-level fusion scheme utilized for enhancing LRMI using HRPI while keeping LRMI spectral information. In this article, an efficient optimized integrated adaptive principal component analysis (APCA) and high-pass modulation (HPM) pan-sharpening method is proposed to get excellent spatial resolution within fused image with minimal spectral distortion. The proposed method is adjusted with multi-objective optimizationto determine the optimal window size and σfor the Gaussian low-pass filter (GLPF) and gain factor utilized for adding the high-pass details extracted from the HRPI to the LRMI principlecomponent of maximum correlation. Optimization results show that if the spatial resolution ratio of HRPI to LRMI is 0.50, then a GLPF of 5 × 5 window size and σ = 1.640 yields HRMI with low spectral distortion and high spatial quality. If the HRPI/LRMI spatial resolution ratio is 0.25, then a GLPF of 7 × 7 window size and σ = 1.686 yields HRMI with low spectral distortion and high spatial quality. Simulation tests demonstrated that the proposed optimized APCA–HPM fusion scheme gives adjustment between spectral quality and spatial quality and has small computational and memory complexity.

A Stokesian approach is formulated to update the geoid model for a specific spherical harmonic band by spectrally combining a GOCE-based satellite global geopotential model with terrestrial gravity data. A simulation test shows that the GOCE-based model can be combined into a geoid solution with an accuracy better than 3 mm for the band between degrees 90 and 180. A comparison of the GOCE-based model GOCO03S and the Canadian terrestrial gravity data for the spherical harmonic band between degrees 90 and 180 shows that the geoid update by GOCO03S reaches 1.6 cm in RMS in the Yukon Territory, 1.8 cm in northern British Columbia, and 1.6 cm in the Maritimes. This may suggest a slight improvement of the GOCE model over the Canadian gravity data considering the standard deviation of 1.0 cm given by GOCO03S. However the analysis indicates comparable accuracy between the terrestrial gravity data and GOCE models for the rest of Canada where topography is relatively flat. The comparisons at the GPS-levelling points suggest that GOCE has improved our existing knowledge of the Earth’s gravity field for wavelength components longer than 200 km over the Yukon Territory, northern British Columbia, the Maritimes, and Newfoundland.KeywordsSatellite gravity modelStokes integralTerrestrial gravity data

<p>The maintenance of leveling benchmark is both laborious and costly due to distortions caused by geodynamic activities and local deformations. It is necessary to realize geoid-based vertical datum, which also enables calculation from ellipsoidal heights obtained from GNSS to orthometric heights that have physical meaning. It can be considered as an important step for height system unification as it eliminates the problems stem from the conventional vertical datum. The ongoing height modernization efforts in Turkey focus to improve quality and coverage of the gravity data, eliminate errors in existing terrestrial gravity measurements in order to achieve a precise geoid model. Accuracy of the geopotential model is crucial while realizing a geoid model based vertical datum as well as unifying the regional height systems with the International Heights Reference System. In this point of view, we assessed the accuracies of recently released global geopotential models including XGM2019e_2159, GECO, EIGEN-6C4, EGM2008, SGG-UGM-1, EIGEN-6C3stat, and EIGEN-6C2 using high order GNSS/leveling control benchmarks and terrestrial gravity data in Turkey. The reason for choosing these models in the validations is their relatively higher spatial resolutions and improved accuracies compared to other GGMs in published validation results with globally distributed terrestrial data. The GNSS/leveling data used in validations include high accuracy GNSS coordinates in ITRF datum with co-located Helmert orthometric heights in regional vertical datum. 100 benchmarks are homogeneously distributed in the country with the benchmarks along the coastlines. In addition, the terrestrial gravity anomalies with 5 arc-minute resolution were also used in the tests. In order to have comparable results, residual terrain effect has been restored to the GGM derived parameters. Numerical tests revealed significant differences in accuracies of the tested GGMs. The most accurate GGM has the comparable performance with official regional geoid model solutions in Turkey. The drawn results in the study were interpreted and discussed from practical applications and height system unification points in conclusion.</p>

<p>The objective of this study is the combination of different types of basis functions applied separately to different kinds of gravity observations. We use two types of regional data sets: terrestrial gravity data and airborne gravity data, covering an area of about 500 km × 800 km in Colorado, USA. These data are available within the “1 cm geoid experiment” (also known as the “Colorado Experiment”). We apply an approach for regional gravity modeling based on series expansions in terms of spherical radial basis functions (SRBF). Two types of basis functions covering the same spectral domain are used, one for the terrestrial data and another one for the airborne measurements. To be more specific, the non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The Cubic Polynomial (CuP) function is applied to the airborne data as a low-pass filter, and the smoothing features of this type of SRBF are used for filtering the high-frequency noise in the airborne data. In the parameter estimation procedure, these two modeling parts are combined to calculate the quasi-geoid.</p><p>The performance of our regional quasi-geoid model is validated by comparing the results with the mean solution of independent computations delivered by fourteen institutions from all over the world. The comparison shows that the low-pass filtering of the airborne gravity data by the CuP function improves the model accuracy by 5% compared to that using the Shannon function. This result also makes evident the advantage of combining different SRBFs covering the same spectral domain for different types of observations.</p>

This study presents a recent combined regional gravity field model over Egypt, developed by integrating satellite and terrestrial data via applying the remove-compute-restore (RCR) principle and the least-squares collocation (LSC) procedure. A high-resolution digital terrain model was exploited for the computation of the terrain and residual terrain corrections. Hereby, all the signals that can be modelled or deterministically computed are considered known and then removed in order to reduce the order of magnitude of the input gravity data prior to applying the LSC. Several GOCE-only and combined global geopotential models (GGMs) have been thoroughly investigated with respect to the EGM2008, in which the space-wise (SPW) solution, namely the SPW-R5 model, demonstrated the best performance. For the development of the combined model, the SPW-R5 GGM has been integrated with both the EGM2008 GGM and the terrestrial data retrieved from 56,250 gravity stations of the Getech data, acquired in the framework of the African Gravity Project. The combined regional gravity model was compared to the state-of-art XGM2016 global gravity model. The standard deviation of the differences is 18.0 mGal in terms of Bouguer anomalies. The combined regional model fits well with the terrestrial gravity data along the chosen North–South oriented profile through the Nile Delta region. The improvements of the developed combined regional model over the XGM2016 are due to the use of a more extensive terrestrial dataset. In conclusion, our model is more suitable than solely using the ground data or GGMs for regional density modelling over Egypt. As an example, the comparison of using a global or regionally defined gravity model with the forward gravity modelling based on Saleh (Acta Geodaetica et Geophysica Hungarica 47(4):402–429, 2012) density model is performed.

GNSS/INS applications are being developed, especially for direct georeferencing in airborne photogrammetry. Achieving accurately georeferenced products from the integration of GNSS and INS requires removing systematic errors in the mobile mapping systems. The INS sensor's uncertainty is decreasing; therefore, the influence of the deflection of verticals (DOV, the angle between the plumb line and normal to the ellipsoid) should be considered in the direct georeferencing. Otherwise, an error is imposed for calculating the exterior orientation parameters of the aerial images and aerial laser scanning. This study determines the DOV using the EGM2008 model and gravity data in Sweden. The impact of the DOVs on horizontal and vertical coordinates, considering different flight altitudes and camera field of view, is assessed. The results confirm that the calculated DOV components using the EGM2008 model are sufficiently accurate for aerial mapping system purposes except for mountainous areas because the topographic signal is not modelled correctly.

A method for implementing Gaussian low-pass filter by using switched-current technique has been presented in this paper. The stable rational transfer function for Gaussian-shaped low-pass filter is approximated by the multiplication of the follower-integrator functions based on central limit theorem. An SI filter structure constructed from the inverse follow-the-leader feedback configuration has been proposed to synthesize the obtained transfer function, in which the switched-current bilinear integrator is employed as the building cell. Explicit design formulas are also derived. The 8th-order Gaussian low-pass filter is selected as the example to elaborate the design details. Simulation result shows that the proposed design method has high approximation precision and low magnitude sensitivity.

To estimate Moho depth, geoid, gravity anomaly, and other geopotential functionals, gravity data is needed. But, gravity survey was not collected in equal distribution in Ethiopia, as the data forming part of the survey were mainly collected on accessible roads. To determine accurate Moho depth using Global Gravity Models (GGMs) for the study area, evaluation of GGMs is needed based on the available terrestrial gravity data. Moho depth lies between 28 km and 32 km in Afar. Gravity disturbances (GDs) were calculated for the terrestrial gravity data and the recent GGMs for the study area. The model-based GDs were compared with the corresponding GD obtained from the terrestrial gravity data and their differences in terms of statistical comparison parameters for determining the best fit GGM at a local scale in Afar. The largest standard deviation (SD) (36.10 mGal) and root mean square error (RMSE) (39.00 mGal) for residual GD and the lowest correlation with the terrestrial gravity (0.61 mGal) were obtained by the satellite-only model (GO_CONS_GCF_2_DIR_R6). The next largest SD (21.27 mGal) and RMSE (25.65 mGal) for residual GD were obtained by the combined gravity model (XGM2019e_2159), which indicates that it is not the best fit model for the study area as compared with the other two GGMs. In general, the result showed that the combined models are more useful tools for modeling the gravity field in Afar than the satellite-only GGMs. But, the study clearly revealed that for the study area, the best model in comparison with the others is the EGM2008, while the second best model is the EIGEN6C4.

Terrestrial gravity anomalies selected from three extended continental regions having a smooth gravity field were used in order to determine the appropriate size of the area for gravity data collection as well as the required data-sampling for calibration of the GOCE satellite gravity gradient (SGG) data. Using Least Square Collocation (LSC), prediction of gravity gradient components was carried out at points on a realistic orbit. Based on the mean error estimation it was shown that up to 80% of the signal of the gravity gradient components, as it is expressed through the covariance function of the terrestrial gravity data, can be recovered in the case of an optimal size of the collection area and of the optimum resolution of the data. These optimal conditions e.g. for the Australian gravity field, correspond to an 10° × 12° area extend and a 5′ data-sampling. It was also numerically demonstrated that it is possible to calibrate the GOCE SGG data for systematic errors such as bias and tilt.

The ground-based gravity data reveals diverse anomaly signatures in areas of the Main Ethiopian rift where active volcanic and tectonic activities are dominant. In such a region ground-based data collection is restricted to existing roads and relies on accessible stations. These resulted in gaps in data, either missing, uneven, or insufficient spatial coverage that must be estimated with proper interpolation techniques. Comparison and evaluations of the spatial interpolation methods that are commonly used in potential field geophysical data analysis were made for the terrestrial gravity and elevation data of the central Main Ethiopian rift. In this research, two widely used interpolation techniques, minimum curvature interpolation, and Ordinary Kriging were compared and assessed. A 10 % hold-out validation was employed, where 90 % of the data points were used to generate interpolated surfaces, which were then evaluated against the remaining 10 %. Following interpolation with each technique, the generated grid was converted into discrete data points (estimated values). These are then compared with the available gravity data, which were deliberately excluded from the gridding process (10 % remaining dataset). The accuracy of each method was assessed by evaluation metrics such as mean value, variance, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), correlation coefficient (r), and R-squared. The results showed that the ordinary Kriging interpolation method outperformed the minimum curvature interpolants for gravity data with all performance metrics, while both interpolants seem to perform equally well for the elevation dataset. Therefore, it is proposed to use the Kriging interpolation method for potential field gravity studies conducted in the central Main Ethiopia rift.

Over the past few decades, convolutional neural networks (CNNs) have achieved outstanding results in addressing a broad scope of computer vision problems. Despite these improvements, fully convolutional Siamese neural networks (FCSNN) still hardly adapt to complex scenes, such as appearance change, scale change, similar objects interference, etc. The present study focuses on an enhanced FCSNN based on convolutional block hyperparameters optimization, a new activation function (ModReLU) and Gaussian low pass filter. The optimization of hyperparameters is an important task, as it has a crucial ascendancy on the tracking process performance, especially when it comes to the initialization of weights and bias. They have to work efficiently with the following activation function layer. Inadequate initialization can result in vanishing or exploding gradients. In the first method, we propose an optimization strategy for initializing weights and bias in the convolutional block to ameliorate the learning of features so that each neuron learns as much as possible. Next, the activation function normalizes the output. We implement the convolutional block hyperparameters optimization by setting the convolutional weights initialization to constant, the bias initialization to zero and the Leaky ReLU activation function at the output. In the second method, we propose a new activation, ModReLU, in the activation layer of CNN. Additionally, we also introduce a Gaussian low pass filter to minimize image noise and improve the structures of images at distinct scales. Moreover, we add a pixel-domain-based color adjustment implementation to enhance the capacity of the proposed strategies. The proposed implementations handle better rotation, moving, occlusion and appearance change problems and improve tracking speed. Our experimental results clearly show a significant improvement in the overall performance compared to the original SiamFC tracker. The first proposed technique of this work surpasses the original fully convolutional Siamese networks (SiamFC) on the VOT 2016 dataset with an increase of 15.42% in precision, 16.79% in AUPC and 15.93% in IOU compared to the original SiamFC. Our second proposed technique also reveals remarkable advances over the original SiamFC with 18.07% precision increment, 17.01% AUPC improvement and an increase of 15.87% in IOU. We evaluate our methods on the Visual Object Tracking (VOT) Challenge 2016 dataset, and they both outperform the original SiamFC tracker performance and many other top performers.

This study outlines the newly identified N–S dextral shear zone within the Egyptian Nubian Shield. The N–S Shear Zone (600–590 Ma) is a significant north-trending geological feature in the Egyptian Nubian Shield, extending over 140 km in length and reaching widths of up to 10 km. The N–S shear zone area is composed mainly of mylonitic schist, metavolcanics, metasediments, augen gneisses, and molasse sediments. The combination of remote sensing, magnetic analysis, and fieldwork in structural mapping has been extensively used, with developments in remote sensing technologies facilitating comprehensive structural geology mapping. Two Landsat-8 OLI/TIRS scenes with 30 m spatial resolution were used to upgrade the geologic map and extract major geological structures in a study area. Image kinematic indicators of the N–S shear zone (N–SSZ) were enhanced using processed remote sensing data. Geophysical magnetic and gravity data were used to unravel shallow and deep structures, with geophysical data analysis and edge detection interpretation revealing significant structural directions in the region. The gravity and magnetic data were upward continued to altitudes of 1, 2, and 4 km. Then, the Enhanced Horizontal Gradient Amplitude (EHGA) was applied to RTP and Bouguer and their upward continued data to delineate shallow and deep structures. The Bouguer anomalies outline N–S, NW, and E–W-directed structures, while magnetic data underline a previously unrecognized N–SSZ. The N–SSZ is characterized by a transpressive deformation regime, featuring a sub-horizontal pure shear component operating in conjunction with simple shear. As the deformation gradient intensifies, the influence of the simple shear component escalates, becoming the dominant factor in the ultramylonites located at the core of the shear zone. The N–S shear area is characterized by conjugate shear zones that emerged during the Najd Orogeny. The dominant shear plane is oriented in a NW–SE direction, while additional shear zones trending NE–SW and N–S serve as conjugate structures. Riedel structures create a network of shear bands, with the N–S dextral shear recognized as the X-shear. The N–SSZ plays a crucial role in controlling gold mineralization as well as other ore minerals such as chromite, copper, and nickel.