利用低阶大地水准面异常反演大尺度核幔边界起伏

核幔边界（core-mantle boundary，CMB）是地球内部最重要的物理化学界面之一，地核和地幔通过核幔边界发生多种相互作用，这对地球重力场、地球自转及地磁场等都能产生重要影响。大地水准面异常是地球重力场的重要观测量，反映了地球内部的物质密度异常及界面变化等重要信息。推导了通过大地水准面异常反演核幔边界起伏的公式，利用2~4阶大地水准面异常反演了大尺度核幔边界起伏形态。结果显示，核幔边界起伏的径向幅度达±5 km、与Morelli的地震层析成像结果的幅度接近，但在形态上略有差异。以高为5 km、底边长为1 000 km的棱柱体模型模拟计算了核幔边界密度异常引起的大地水准面异常响应，结果与观测大地水准面异常比较接近。

Using Lower Degrees of Geoid Anomalies to Invert Large Scale Undulations of Core-Mantle Boundary

The core-mantle boundary (CMB) is one of the most important physical and chemical interfaces in the earth's interior, through which a variety of interactions occur between Earth's core and mantle. These interactions might have great impacts on Earth's gravity field, rotation and magnetic field. The geoid anomalies is an important observation of the earth's gravity field, which reflects significant information of the earth's interior, such as material density anomalies and interfaces, etc. A formula using the geoid anomalies to invert undulations of core-mantle boundary was derived. The large-scale undulations of the core-mantle boundary were calculated by this formula from degree 2 to 4. The result showed that the amplitude of core-mantle boundary undulations reached ±5 km, which corresponded to that obtained by Morelli using seismic tomography, but showed some differences in the worldwild distribution. We also simulated influences of the density anomalies in the core-mantle boundary to the geoid undulation using a prism model with height of 5 km and base length of 1 000 km. The result showed that it was closed to the observed value of geoid undulations.