Research And Implementation Of Terrain Correction Using Sector Cylinder Models In Spherical Coordinate

Gravity is a traditional method of geophysical exploration. Gravity anomaliesreflect density variations of subsurface geological bodies. To eliminate the effects ofundulating terrain density bodies, measured gravity values need terrain correction sothat we can obtain gravity anomalies only caused by underground uneven densitybodies. In the condition of the geoid as an infinite plane, predecessors in terms of flatterrain correction have made a set of complete calculation method in the Cartesiancoordinate and utility program used in production practice. But for high-precisionground, airborne and satellite gravity measurements,the actual effect of the earth’ssphere can no longer be ignored. Therefore, it should be based on the actual shape ofthe geoid in order to ensure higher accuracy.So in order to meet the needs ofhigh-precision gravity data processing, this paper improves the traditional gravityterrain correction method. Respectively, from the theoretical approach, algorithmdesign and practical aspects, this paper comes up with a set of gravity terraincorrection method on a sphere with high accuracy and good effects, namely terraincorrection method using sector cylinder models in spherical coordinate.In this paper, terrain correction method in spherical coordinate is based on sectorcylinder seen as equivalent model of topographic materials. Next improve theaccuracy of terrain correction from the theoretical aspects. The first step is coordinatesystem transformation from Cartesian to spherical coordinate, derivation of gravityforward formula of sector cylinder in spherical coordinate and verification of validityof the formula. The second step, rotate spherical coordinate starting from the actualcomputing needs so that gravity observation points on the non-z-axis becomes a pointon the z-axis, and reconstruct the coordinates of the surrounding terrain points needed.The third step, the terrain area is divided into many rings and sectors in which sectorcylinder models are small near and large at a distance. The fourth step, grid digitalterrain data of far zone. Increasing and deleting original terrain points is to makeevery sector area with several terrain points distributed, not too much. Speed up the calculation of the average height of the top surface of sector cylinder. The fifth step,from the respects of simplification of the algorithm, the input and output data,parameter settings, the design of the main program and subprogram, etc., improvecomputational efficiency and accuracy of spherical terrain correction C++program.Through the computational experiments of theoretical models, terrain correctionin spherical coordinate is tested and evaluated.First using a simple theoretical model,by changing the parameters such as range and thickness of topographic materials,height of measuring point, theoretically assess the characteristics of gravity values onmeasuring points with different measuring points and different terrain. According tothe error between spherical terrain correction and flat terrain correction method,compare and comprehensively judge the conditions of the two methods. Then to testthe calculation effect of the program modules, set a digital terrain model on theEarth’s surface. Spherical terrain correction C++program and forward formularespectively calculates the gravity values on a measuring point caused by the digitalterrain model. According to the above values, verify the correctness of sphericalterrain correction C++program.Finally, using data of a local real terrain, calculate gravity terrain correctionvalues of the survey area and survey line. Discuss the characteristics of gravity valueson measuring points at different heights caused by topographic materials of differentrange. According to the error between spherical terrain correction and traditional flatterrain correction method, analyse the characteristics of the two methods. From theresults of the analysis and computational efficiency, illustrate the necessity andfeasibility of spherical terrain correction method using sector cylinder models inspherical coordinate.