基于“浅层海水”质量法确定海洋内部层面重力值

Determination Internal Layer Gravity of Ocean Based on Surface Shallow Layer

经典物理大地测量学利用斯托克斯方法和莫洛金斯基方法解算大地测量边值问题并给出地球外部重力场表达,若忽略1~2 m量级的动力学海面地形,静止的平均海面可认为是大地水准面,后者是与平均海平面最为接近的重力等位面。经典理论无法求解海洋内部,即地球内部重力场问题,为解决这一局限,基于地表浅层法引入“浅层海水”的概念,“浅层海水”上下界面由平均海面高模型DTU21确定,利用牛顿积分和球谐展开算法确定了最优球谐分析迭代次数,分析了“浅层海水”厚度与积分区域半径大小的关系,确定了“浅层海水”厚度为100 m、500 m和1 000 m时的最优积分区域半径为1°,厚度4 000 m时为1.5°;评估了“浅层海水”质量法移去-恢复海洋表面重力值的精度,“浅层海水”厚度100 m、500 m、1 000 m和4 000 m的均方根误差分别为0.13 mGal、0.61 mGal、1.21 mGal和3.93 mGal,验证了该方法的可靠性。基于此理论,计算了不同厚度“浅层海水”下表面的层面重力值,得到了100 m、500 m、1 000 m和4 000 m深度处层面重力值与“浅层海水”上表面重力值差的均方根,分别为22.11 mGal、110.50 mGal、220.87 mGal和877.31 mGal。

Objectives: Classical physics geodetic mainly focuses on the solution of the geodetic boundary value problem, which is usually given by the theorems of Stokes and Molodensky. Solving the internal gravity field of the ocean is a problem of solving the internal potential of the earth, to which classical theoretical method cannot be applied. In order to solve this limitation, the concept of shallow seawater is introduced based on the surface shallow method to calculate the internal ocean gravity at different depths.Methods: Using high-resolution data of DTU21 mean sea surface and EGM2008, combined with Newton’s integration, spherical harmonic analysis, and spherical harmonic comprehensive theoretical methods, the internal ocean gravity field in the western Pacific region((131.5°±0.25°) E,(19.5°±0.25°) N) was determined. The number of iterations of spherical harmonic analysis was determined, and the relationship between the depth of shallow seawater and the integral area radius was analyzed.Results and Conclusions:An optimal integral area radius of 1° was determined for 100 m, 500 m and 1 000 m and the depth of 1.5°for 4 000 m. The accuracy of the shallow seawater method to remove-restore the ocean surface gravity is evaluated and the root mean square error is 0.13 mGal at a depth of 100 m, 0.61 mGal at a depth of 500 m,1.21 mGal at a depth of 1 000 m, and 3.93 mGal at a depth of 4 000 m. Compared to surface gravity, gravity of the inner layer of the ocean increases by 22.11 mGal at 100 m depth, 110.50 mGal at 500 m depth,220.87 mGal at 1 000 m depth, and 877.31 mGal at 4 000 m depth.