Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data is missing or inaccessible. We propose to interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points, and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters – the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We have found that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contains noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. The proposed approach is first illustrated by a synthetic gravity dataset from a single survey line, then is generalized to the case over a survey grid. In both numerical experiments, the TSE method has demonstrated an improved interpolation accuracy in comparison with the minimum curvature method. Finally we apply the TSE method to a ground gravity dataset from the Abitibi Greenstone Belt, Canada, and an airborne gravity dataset from the Vinton Dome, Louisiana, USA.

Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)

The availability of geoids, especially in survey and mapping activities, is useful for transforming the geometric heights obtained from observations of the Global Navigation Satellite System (GNSS) into orthometric heights that have real physical meanings such as those obtained from waterpass measurements. If a geoid is available, the orthometric heights of points on earth can be determined using the GNSS heighting method. The use of modern survey and mapping instruments based on satellite observations such as GNSS is more efficient in terms of time, effort, and cost compared to the accurate waterpass method. According to the Indonesian Geospatial Information Agency (BIG) it is stated that the application of geoid as a national Vertical Geospatial Reference System has an adequate and ideal category if the accuracy is higher than 15 cm. Recent studies have shown that it is possible to generate local geoid models with centimetre accuracy by utilizing airborne gravity data. We calculate free-air gravity anomaly data is calculated by processing airborne gravity and GNSS data using the Stokes Integral method on AGR software. Next a geoid model is created by calculating the contribution of three components, namely the long wave component represented by the EGM2008 global geoid data model, the shortwave component represented by the Shuttle Radar Topography Mission (SRTM) data and the medium wave component represented by the free-air gravity anomaly data. The geoid model validation was carried out using the geoid fitting method for geoid accuracy by calculating the difference between the gravimetric geoid and the geometric geoid and comparing it with the global geoid model EGM2008 degrees 2190. As a result, the total geoid model accuracy value was determined to be 49.4 cm on gravimetric geoid undulations with a standard deviation of 7.1 cm. Meanwhile, the results of the EGM2008 geoid undulation accuracy test at 2190 degrees resulted in an accuracy of 51.9 cm with a standard deviation of 9.9 cm. These results indicate that the local geoid model from airborne gravity measurement data produces a geoid model with a higher accuracy than the global geoid model EGM2008 degrees 2190. However, the accuracy of the resulting data is still below the BIG standard of 15 cm, so further research is needed to produce a geoid model which conforms to the standard.

Assessment of high-degree reference models and Recent Goce/Grace Global Geopotential Models over Sudan based on the GPS/Leveling data

Nowadays, Global Geopotential Models (GGMs) can be used as a reference to develop more detailed regional/local geoids, or they can be used to provide geoid heights on their own. Since 2000, several GGMs have been released, and they are mainly derived from satellite gravity measurements, satellite-only models, terrestrial gravimetry, altimeter-derived gravity data in marine areas, and airborne gravity data. With a precise geoid model, ellipsoidal heights obtained from GPS can be converted to orthometric heights, which is reasonably quite needed in Geodesy, Civil Engineering, etc. These heights reflect changes in topography as well as local variations in gravity. This paper evaluates some of the latest releases of high degree reference models and the satellite-only global gravity field model over Sudan using 19 GPS/Leveling stations. We have been selected 6 GGMs based on Gravity field Goce and Grace, and they released in 2020, 2019, 2014, 2008, and 1996 as shown in the International Centre for Global Earth Models website (ICGEM). The accuracy evaluation of the GGM models have been discussed, the accurate GGMs over Sudan are XGM2019e_2159 and GOCO05s, which have indicated -0.019 and 0.046 meters, respectively. The evaluation results produce valuable information to academia and geoid modeling research topics in Sudan, which shows the precise model from the selected GGMs in Sudan by using the available GPS/Leveling data.

Quasi Geoid and Geoid Modeling with the Use of Terrestrial and Airborne Gravity Data by the GGI Method—A Case Study in the Mountainous Area of Colorado

This article concerns the development of gravimetric quasigeoid and geoid models using the geophysical gravity data inversion technique (the GGI method). This research work was carried out on the basis of the data used in the Colorado geoid experiment, and the mean quasigeoid (ζm) and mean geoid (Nm) heights, determined by the approaches used in the Colorado geoid experiment, were used as a reference. Three versions of the quasigeoid GGI models depending on gravity data were analyzed: terrestrial-only, airborne-only, and combined (using airborne and terrestrial datasets). For the combined version, which was the most accurate, a model in the form of a 1′×1′ grid was calculated in the same area as the models determined in the Colorado geoid experiment. For the same grid, the geoid–quasigeoid separation was determined, which was used to build the geoid model. The agreement (in terms of the standard deviation of the differences) of the determined models, with ζm and Nm values for the GSVS17 profile points, was ±0.9 cm for the quasigeoid and ±1.2 cm for the geoid model. The analogous values, determined on the basis of all 1′×1′ grid points, were ±2.3 cm and ±2.6 cm for the quasigeoid and geoid models, respectively.

High-Resolution Cooperate Density-Integrated Inversion Method of Airborne Gravity and Its Gradient Data

Airborne (or satellite) gravity measurement is a commonly used remote sensing method to obtain the underground density distribution. Airborne gravity gradiometry data have a higher horizontal resolution to shallower causative sources than airborne gravity anomaly, so joint exploration of airborne gravity and its gradient data can simultaneously obtain the anomaly feature of sources with different depths. The most commonly used joint inversion method of gravity and its gradient data is the data combined method, which is to combine all the components into a data matrix as mutual constraints to reduce ambiguity and non-uniqueness. In order to obtain higher resolution results, we proposed a cooperate density-integrated inversion method of airborne gravity and its gradient data, which firstly carried out the joint inversion using cross-gradient constraints to obtain two density structures, and then fused two recovered models into a result through Fourier transform; finally, data combined joint inversion of airborne gravity, and gradient data were reperformed to achieve high-resolution density result using fused density results as a reference model. Compared to the data combined joint inversion method, the proposed cooperate density-integrated inversion method can obtain higher resolution and more accurate density distribution of shallow and deep bodies meanwhile. We also applied it to real data in the mining area of western Liaoning Province, China. The results showed that the depth of the skarn-type iron mine in the region is about 900–1300 m and gives a more specific distribution compared to the geological results, which provided reliable data for the next exploration plan.

An Assessment of Recently Released High-Degree Global Geopotential Models Based on Heterogeneous Geodetic and Ocean Data

The development of the global geopotential model (GGM) broadens its applications in ocean science, which emphasizes the importance for model assessment. We assess the recently released high-degree GGMs over the South China Sea through heterogeneous geodetic observations and synthetic/ocean reanalysis data. The comparisons with a high resolution (∼3 km) airborne gravimetric survey over the Paracel Islands show that XGM2019e_2159 has relatively high quality, where the standard deviation (SD) of the misfits against the airborne gravity data is ∼3.1 mGal. However, the comparisons with local airborne/shipborne gravity data hardly discriminate the qualities of other GGMs that have or truncated to the same expansion degree. Whereas, the comparisons with the synthetic/ocean reanalysis data demonstrate that the qualities of the values derived from different GGMs are not identical, and the ones derived from XGM2019e_2159 have better performances. The SD of the misfits between the mean dynamic topography (MDT) derived from XGM2019e_2159 and the ocean data is 2.5 cm; and this value changes to 7.1 cm/s (6.8 cm/s) when the associated zonal (meridian) geostrophic velocities are assessed. In contrast, the values derived from the other GGMs show deteriorated qualities compared to those derived from XGM2019e_2159. In particular, the contents computed from the widely used EGM2008 have relatively poor qualities, which is reduced by 3.9 cm when the MDT is assessed, and by 4.0 cm/s (5.5 cm/s) when the zonal (meridian) velocities are assessed, compared to the results derived from XGM2019e_2159. The results suggest that the choice of a GGM in oceanographic study is crucial, especially over coastal zones. Moreover, the synthetic/ocean data sets may be served as additional data sources for global/regional gravity field assessment, which are useful in regions that lack of high-quality geodetic data.

3D constrained inversion of gravity and magnetic data to image basement and plutonic bodies: A case study from Dood Arale Basin, eastern Somaliland

We have developed 3D inversion models derived from airborne gravity and magnetic data, which are constrained by seismic and well data, in eastern Somaliland. The density model reveals a northwest–southeast-trending basin, 125 km long and 25 km wide and called the Dood Arale Basin. The basin comprises two subbasins separated by a basement high and is infilled by up to 2500–3200 m of sediments. Smaller and shallower subbasins are also identified to the west of Lafaweyne and northeast of Dararweyne. The density model shows that the top basement in the platform areas is at approximately 1500–1700 m in depth and shallows to approximately 300 m at the Bur Anod, Hagraajin and Hagrin Ranges and northwest of Eil Afwein. The basement depths in these areas are more uncertain and could be deeper because they occur in areas of high gravity anomalies caused by a combination of near-surface high-density sediments and high-density plutonic bodies within the basement. The susceptibility model indicates that the basement consists of very weakly magnetized metasediments of the Inda Ad Complex intruded by three northeast–southwest-trending magnetic bodies with upper surfaces at depths of approximately 300–3000 m. These magnetic bodies are interpreted as plutonic complexes of similar age and composition to the Lower Cretaceous syenite intrusions outcropping at Gorei in the Shilah Madu Range. Seismic reflection profiles image the sedimentary sequences, but they do not clearly map the top basement or detect any of the plutonic bodies. The plutonic bodies could have controlled the location of the basin’s border faults and contributed to the high geothermal gradient recorded at the Faro Hills-1 well. The Upper Cretaceous Gumburo and Jesomma Formations in the basin could potentially have reached maturation close to and above the plutonic bodies within the center of the basin.