基于Slepian方法和地面重力观测确定时变重力场模型: 以2011—2013年华北地区数据为例

时变重力场是研究地球系统内部物质运动和时空演化过程的有效途径.目前广泛使用的GRACE时变重力场模型受限于其空间分辨率（约400 km），难以探测较小空间尺度的重力变化.本文首次尝试利用Slepian局部谱分析方法和多期地面重力观测确定更高空间分辨率的时变重力场模型.Slepian方法通过构建研究区域内的正交基函数，将信号能量集中在研究区域内部，是构建球面局部重力场模型的理想方法.本文根据Slepian方法的特点给出了区域重力场建模及参数优化的步骤，以我国华北地区为例，基于2011—2013多期地面观测确定了区域时变重力场模型，并与同区域由Slepian方法和GRACE卫星数据确定的重力变化进行了对比分析.结果表明：（1）贝叶斯信息量准则可作为确定Slepian展开最佳截断数的有效手段；（2）基于研究区域内现有重复测点数据，能够恢复120阶时变重力场，空间分辨率（半波长）约150 km；（3）2011—2013年间研究区域内GRACE估计结果与120阶地面结果在时空分布的显著趋势上存在较好的对应，证明了本文利用Slepian方法和地面观测所得时变重力场模型的可靠性.本文研究结果可为区域重力场建模提供新的参考，也可为华北地区水资源变化监测、构造活动分析以及地震风险性评估等研究提供高分辨率的时变重力场模型支撑.

Time-variable gravity field determination using Slepian functions and terrestrial measurements: A case study in North China with data from 2011 to 2013

The time-variable gravity field (TVGF) provides an effective means of measuring the temporal and spatial variations of the mass redistribution within the Earth system. The widely used GRACE TVGF proves to be an excellent tool for studying large-scale mass redistribution. However, GRACE's low spatial resolution (~400 km) prevents the detection of the gravity changes at small regional scales. In this study, we attempt to determine the regional TVGF at a higher spatial resolution by using the Slepian localization analysis method and terrestrial gravity measurements for the first time. By constructing the orthogonal basis functions in a given region, the Slepian localization analysis optimally concentrates the signal energy inside the specific region and thus becomes an ideal method for modeling regional gravity fields. After reviewing the characteristics of the Slepian functions, we propose a procedure for selecting optimal parameters in the Slepian expansion. As a case study, we apply this procedure to the determination of TVGF in North China using terrestrial gravity measurements from multiple campaigns from 2011 to 2013. We then compare the results with gravity changes determined by the Slepian method and GRACE data in the same region. We find that: (1) the Bayesian information criterion can be used to determine the optimal truncation level of the Slepian expansion, (2) the maximum degree of the recovered TVGF in North China can be up to 120 (half-wavelength spatial resolution of~150 km) based on several simulations, and (3) the significant trends in GRACE estimations correspond well to those in the degree 120 TVGF results from 2011 to 2013, proving the reliability of the TVGF determined by the Slepian method and terrestrial measurements in this study. Our findings could benefit regional gravity field modeling, and the high-resolution TVGF determined in this study could support water storage change monitoring, tectonic activity analysis, and seismic risk assessment in North China.