The Local Gravity Field Model Is Constructed Based On The Least Square Configuration

The gravity field is an important geophysical information on Earth.From a static point,the earth's gravity field is a comprehensive reflection of all the earth's mass;From a dynamic point,the earth's time-varying gravity field reflects the changes of the earth's mass or density in time-space domain.The earth interior material distribution,structure,and migration can be fully reflected in the earth's gravity field.Understanding on the earth's gravity field is very important to solving many geophysical phenomena and problems,such as the shape of earth,the inversion of the density structure of the lithosphere and asthenosphere,and the detection of mass transfer in the process of volcanoes and earthquakes.The earth's gravity field provides important basic information for solving these problems.In addition,the earth's gravity field also plays an important role in other scientific fields,such as geodesy geology,geodynamics,oceanography and so on.The study of these problems urgently needs a reliable and precise gravity field model(global gravity field model or local gravity field model)as support.Therefore,the study of the earth's gravity field is an important and basic scientific task in the geosciences.The earth's gravitational field model can be represented by spherical harmonic functions,such as EGM2008 and EIGEN-6c.It requires global coverage of gravity observations.For the construction of local gravity field model,it is difficult to solve spherical harmonic model because of the limited coverage area of gravity data.This is mainly because the spherical harmonic model approximates the actual earth's gravity field optimally from the global scale,and the change of any spherical harmonic coefficient will always affect the earth's gravity field model from the global scope.Therefore,the spherical harmonic function method is not applicable to the construction of local gravity field model.Two problems need to be solved in the construction of the local gravity field model:the surface gravity measurement data in local areas are often distributed unevenly and discreetly in space,and even there are data gaps in some areas.In the process of measurement,gravity data are inevitably affected by environmental noise.This paper studies how to reduce the influence of these factors on the construction of local gravity field model and the related problems.EGM2008 earth gravity field model was used for simulation data in this paper,and north China was selected as the research area(29°n-43°N;109°E-124 °E).The free air gravity anomaly field in north China was extracted from the EGM2008 model and sampled at a grid interval of 0.1°.To simulate the irregular distribution of measuring points,the absence of gravity data within the region and the white noise in the data,the least square collocation method was used to restore the gravity field model of the region.Compared with the results of the least curvature method and inverse distance weighting method,the results of the various methods were evaluated by the residual standard deviation of the gravity field model,and the applicability of the gravity field modeling methods in local areas was discussed.The main achievements of this paper are as follows:(1)When randomly selecting gravity sampling points and adding different levels of noise,the least square collocation method,inverse distance weighting method and minimum curvature method have better modeling effects.In the case of 50%random sampling,with the increase of noise level,the least square collocation method significantly enhances the noise suppression effect compared with other methods.(2)Through the use of actual gravity point location in north China,with discrete sampling EGM2008 gravity anomaly model,using the least square collocation method to reconstruct the highest accuracy of regional gravity anomaly,among them,the least square collocation method residual standard deviation is 0.8 mGal,minimum curvature method residual standard deviation is 1.4 mGal,inverse distance weighting method residual standard deviation of 4.1 mGal;(3)By forward the gravity field source model,the gravity anomalies with resolution of 0.5°,1.5°and 3°in north China are respectively predicted,and the resolution ability of the existing gravity measurement network for gravity anomaly of different scales is tested by the least square collocation method.The results show that the gravity anomaly with the field source scale of 0.5°is poor in somewhere with a few measuring points.As for gravity anomalies with field source scales of 1.5°and 3°,the existing gravity measurement network in north China can be fully resolved.