重力位三阶梯度张量及其勘探能力初步分析

在重力位三阶梯度张量基本原理的基础上,给出均匀球体重力位零阶至三阶梯度张量的解析表达式,结合理论分析与模型实验,对比各阶梯度张量对场源参数(质量与埋深、水平位置与几何形状)的敏感性。结果表明,重力位三阶梯度张量随场源与观测点之间距离的增大衰减最快。重力曲率张量具有如下特征:对场源埋深变化具有最高的敏感性;对浅部的剩余质量探测能力最强,对深部的剩余质量探测能力最弱;对场源的水平分辨能力及几何形态的区分能力随场源埋深的增大而减小,但重力曲率张量的分辨能力最强;三阶梯度张量的独立元素个数最多,场空间分布形态的类型也最多样,在相同测点分布情况下能够捕获更多的场与场源信息,尤其是重力场的短波成分与浅部的剩余质量。

Third-Order Gradient Tensor of Gravitational Potential and Preliminary Analysis of Its Exploration Capacity

We first introduce the basic theory of the third-order gradient tensor of the gravitational potential, which is also called the gravitational curvature tensor(GCT). Second, we provide analytic expressions of the third-order gradient tensor of the gravitational potential caused by the homogenous spheroid. Finally, through theoretical analysis and synthetic model tests, we discuss the sensitivity of the source’s parameters(mass, buried depth, horizontal location and geometric shape) on the zero, first, second and third-order gradient tensors of the gravitational potential. Results show that, among the zero, first, second and third-order gradient tensors of the gravitational potential, the third-order gradient tensor of the gravitational potential decays most quickly as the distance between observation point and source increases. Therefore, the GCT has multiple characteristics, such as, highest sensitivity on the buried depth of the source; the best exploration capacity for shallow mass, and on the contrary the worst capacity for deep mass; and the highest sensitivity of the horizontal location of the source. This ability is weakened as the buried depth of the source increases. The type is also the most diverse, indicating that under the same distribution of points, the three-step tensor can capture more field and field source information, especially the short-wave component of the gravity field and the remaining mass of the shallow part.