反演地表质量变化的附有空间约束的三维加速度点质量模型法

Surface mass distribution derived from three-dimensional acceleration point-mass modeling approach with spatial constraint methods

重力卫星可以在相同误差尺度下对全球质量变化进行连续重复观测,并在近十余年来取得了巨大成功,探索重力卫星数据精化处理方法和相关应用研究具有重要意义.本文基于三维加速度点质量模型法的基本原理,进一步发展建立了时变重力场模型球谐位系数的变化和地面点质量变化的关系,可有效考虑地表质量变化导致的负荷形变的影响;引入等权形式、线性形式、指数形式和高斯形式的空间约束方法处理南北条带噪声和向下延拓导致的病态问题,并与零阶Tikhonov正则化方法进行对比分析.采用模拟数据和一个月的实测GRACE时变重力场模型计算全球质量变化,对三维加速度点质量模型法和几种空间约束方法进行对比分析验证.计算结果表明,对于3°等面积的全球格网质量点,高斯和指数形式空间约束方法的最优相关距离约为500km,等权和线性形式空间约束方法的最优相关距离约为600km,各方法均可有效处理条带噪声的影响,四种空间约束方法的计算效果优于零阶Tikhonov正则化方法,本文的相关方法为进一步利用三维加速度点质量模型法监测全球质量变化提供了借鉴.

Global mass distribution could be continuously and repeatedly detected by gravity satellites at the same error scale, and great success has been achieved in related work in the past decades. It is valuable to continue studying the refinement methods and related applications of gravity satellite data. In this study, the relationship between the spherical harmonic coefficient variation of time-variable gravity field models and the mass change on the Earth′s surface is developed, which is based on the basic principle of three-dimensional acceleration point-mass modeling approach (3D-PMA). The effect of the load deformation caused by the change of the Earth′s surface mass distribution can be effectively considered in this method. The uniform-type, linear-type, exponential-type and Gaussian-type spatial constraint methods are introduced to smooth the north-south strip noise and to stabilize the ill-posed problems caused by downward continuation, and at the same time, the four spatial constraint methods are compared with zero-order Tikhonov regularization method. In order to compare and validate the three-dimensional acceleration point-mass modeling approach and four spatial constraint methods, the global mass distribution is computed by simulation data and one-month GRACE time-variable gravity solution (CSR-RL05 version data). The calculation results show that the optimal distance of exponential-type, Gaussian-type and uniform-type, linear-type spatial constraint methods is about 500 km and 600 km when 3-degree equal-area grid is used to arrange mass point on the Earth′s surface. The influence of north-south strip noise can be effectively constrained by the spatial constraint methods, and four spatial constraint methods are better than zero-order Tikhonov regularization method. In general, it has provided reference for further use of gravity satellite data to monitor global mass change with relevant methods investigated in this paper.