Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions

The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

Research on Market-oriented Allocation of Scientific and Technological Financial Factors

Objectives: This paper combs and defines the related concepts of the elements of science and technology finance, and determines the composition of the innovation elements of science and technology finance and the market system of science and technology finance elements based on the correlation and function among the modules such as the goal, subject, object, environment and mode of the allocation of science and technology finance elements. It is proposed that the market-oriented allocation of scientific and technological financial factors includes two steps: one is the factor flow under the ecological environment of scientific and technological financial innovation and regional gravity, and the other is the factor distribution and combination under the market-oriented mechanism. Through the coordination between the government and the market, we have improved the supply and demand mechanism, competition mechanism, price mechanism and feedback mechanism of the market of scientific and technological financial factors, and established the market-oriented allocation mechanism of scientific and technological financial factors. From the aspects of improving the basic guarantee of environmental factors, promoting the free flow of capital factors, improving the efficient supply of labor factors, promoting the strong support of data factors, improving the pricing mechanism of technical factors, and strengthening the risk control system, this paper puts forward some suggestions to improve the market-oriented allocation mechanism of scientific and technological financial factors.

Delineation of subsurface features by gravity technique in parts of Shivpuri District, M.P.

This research paper represents the search of faults/ fractures/ shear zones/ altered zones, to find out mineral target zones in part of Shivpuri district, M.P. Geologically, the study area is represented by Vindhyan Supergroup of Meso to Neoproterozoic age. The area is mainly covered by alluvium which is characterized river gravels, sand and residual soil. The gravity survey was carried out with a station density of 1 gravity station per 2.5 sq km along with elevations of each gravity stations covered 2800 sq km. The rock samples have been collected from different litho-units of the study area for measurement of physical property (Density) which are useful for understanding & evaluating of geological response. The general trend of contour pattern of Bouguer gravity is NW-SE directions. Bouguer gravity anomaly contour map is characterized by broad gravity ‘high’ in southern part whereas ‘low’ in northern part which inferred depression of basement toward the north. The nosing in aligned approximately NW-SE direction is recorded in central part which may be interpreted as inferred lineament and it is clearly reflected on residual gravity map. The regional gravity anomaly aligned in NW-SE is characterized by broad gravity ‘high’ in southern part whereas ‘low’ in northern part which reflects basement deepening towards north. The majority of Euler 3D solutions are falling on linear bodies (inferred lineament) with varying depths from 0.5 to 2.5 km.

Penerapan Persamaan Trend Surface Analysis untuk Pemisahan Anomali Residual dan Regional pada Data Gayaberat

The separation of regional anomalies and residual anomalies in gravity data is an important part in interpreting gravity data. This process aims to obtain gravity anomalies that have been associated with exploration targets. The Trend Surface Analysis method is a mathematical approach to the earth field that can be used to separate maps into regional components and local components. The application of this method into gravity data can be used to separate regional anomalies and residual anomalies. The process of processing the trend surface analysis method can be done using Microsoft Excel. This method is tested first on synthetic gravity data, the purpose of this test is to determine the performance of the trend surface analysis method in performing anomaly separation. Based on the test results of the trend surface analysis method on synthetic gravity data, it was found that this method was quite good at separating regional anomalies and residual anomalies. This is evidenced by the anomalous pattern that is already the same between the regional gravity anomaly resulting from the separation of the anomaly using the trend surface analysis method and the regional anomaly resulting from synthetic data. The same anomaly pattern can also be seen in the residual anomaly resulting from the separation of the anomaly using the trend surface analysis method with the residual anomaly resulting from synthetic data. The application of the trend surface analysis method to field data has been carried out by producing regional anomalies and residual anomalies. This method is very good at separating regional anomalies and residual anomalies, especially in regional anomalies located at deep depths.Pemisahan anomali regional dan anomali residual pada data gayaberat merupakan bagian penting dalam melakukan interpretasi data gayaberat. Proses ini bertujuan untuk mendapatkan anomali gayaberat yang sudah berasosiasi dengan target eksplorasi. Metode Trend Surface Analysis merupakan teknik pendekatan matematika pada bidang kebumian yang dapat digunakan untuk memisahkan peta kedalam komponen regional dan komponen lokal. Penerapan metode ini ke dalam data gayaberat dapat digunakan untuk memisahkan anomali regional dan anomali residual. Proses pengolahan metode trend surface analysis dapat dilakukan dengan menggunakan microsoft excel. Metode ini diuji terlebih dahulu pada data gayaberat sintetis, tujuan pengujian ini adalah untuk mengetahui performa metode trend surface analysis dalam melakukan pemisahan anomali. Berdasarkan hasil pengujian metode trend surface analysis pada data gayaberat sintetis didapatkan bahwa metode ini cukup baik dalam memisahkan anomali regional dan anomali residual. Hal ini dibuktikan pada pola anomali yang sudah sama antara anomali gayaberat regional hasil pemisahan anomali metode trend surface analysis dengan anomali regional hasil data sintetis. Pola anomali yang sama juga dapat dilihat pada anomali residual hasil pemisahan anomali metode trend surface analysis dengan anomali residual hasil data sintetis. Penerapan metode trend surface analysis pada data lapangan telah dilakukan dengan menghasilkan anomali regional dan anomali residual. Metode ini sangat baik dalam memisahkan anomali regional dan anomali residual terutama pada anomali regional yang berada pada kedalaman dalam

A Simplification Method for Point Cloud of T-Profile Steel Plate for Shipbuilding

According to the requirements of point cloud simplification for T-profile steel plate welding in shipbuilding, the disadvantages of the existing simplification algorithms are analyzed. In this paper, a point cloud simplification method is proposed based on octree coding and the threshold of the surface curvature feature. In this method, the original point cloud data are divided into multiple sub-cubes with specified side lengths by octree coding, and the points that are closest to the gravity center of the sub-cube are kept. The k-neighborhood method and the curvature calculation are performed in order to obtain the curvature features of the point cloud. Additionally, the point cloud data are divided into several regions based on the given adjustable curvature threshold. Finally, combining the random sampling method with the simplification method based on the regional gravity center, the T-profile point cloud data can be simplified. In this study, after obtaining the point cloud data of a T-profile plate, the proposed simplification method is compared with some other simplification methods. It is found that the proposed simplification method for the point cloud of the T-profile steel plate for shipbuilding is faster than the three existing simplification methods, while retaining more feature points and having approximately the same reduction rates.

Functional approach to the search for quasi-optimal value of regularization parameter in downward continuation of potential field

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.

Improved the Accuracy of Seafloor Topography from Altimetry-Derived Gravity by the Topography Constraint Factor Weight Optimization Method

Gravity geologic method is one of the important to derive seafloor topography by using altimetry-gravity, and its committed step is gridding of regional gravity anomaly. Hence, we proposed a topography constraint factor weight optimization (TCFWO) method based on ordinary kriging method. This method fully considers the influence of topography factors on the construction of regional gravity grid besides horizontal distance. The results of regional gravity anomaly models constructed in the Markus-Wake seamount area show that the TCFWO method is better than ordinary kriging method. Then, the above two regional gravity models were applied to invert the seafloor topography. The accuracy of derived topographic models was evaluated by using the shipborne depth data and existing seafloor topography models, including ETOPO1 and V19.1 model. The experimental results show that the accuracy of ST_TCFWO (seafloor topography model inverted by TCFWO method) is better than ST_KR (seafloor topography model inverted by kriging method) and ETOPO1 model. Compared with the ST_KR, the accuracy of the ST_TCFWO has improved about 26%. In addition, the accuracy of seafloor topography is affected by the variation of depth, the distribution of control points and the type of terrain. In different depth layers, the ST_TCFWO has better advantages than ST_KR. In the sparse shipborne measurements area, the accuracy of ST_TCFWO is better than that of V19.1, ETOPO1 and ST_KR. Moreover, compared to other models, ST_TCFWO performs better in flat submarine plain or rugged seamount area.