基于不等式约束的重力三维聚焦反演

聚焦反演是目前较受关注的重力反演方法之一，能较好地还原异常体的紧凑构造和物性差异较大的边界，此外，不等式约束可以将反演参数限制在有意义的范围内，可以改善反演的多解性。基于此，本文将这两种思路融入重力三维反演中，引入对数转换函数法，实现了基于不等式约束的三维重力聚焦反演。模型试验表明：聚焦反演可以较准确地还原密度异常体的形状和范围，但在深部仍然存在虚假异常现象，而基于不等式约束的聚焦反演方法可以有效压制假异常，改善反演多解性问题；此外，分区域不等式约束可以提高先验物性信息应用的灵活性，获得更逼近真实模型的解。

Research on Three-dimensional Focusing Inversion to Gravity Data Based on Inequality Constraints

The focusing inversion is one of the most popular methods gravity inversion, which can better recover compact features and tectonic boundary with large difference in physical properties of abnormal bodies. In order to avoid non-uniqueness problem of inversion, inequality constraints are introduced to restrict inversion parameters to a meaningful range. Based on this, this paper integrated these two ideas into the 3D gravity inversion, and adopted the logarithmic transformation function method to realize the gravity 3D inversion based on inequality constraints. Model tests show that the focusing inversion can accurately recover the shape and range of density anomalies. However, there are still some false anomalies in the deep areas. Meanwhile, the focusing inversion using inequality constraints can effectively suppress the false anomalies and improve the non-uniqueness of the inversion solutions. In addition, the subregional inequality constraints can improve the flexibility of the application of prior physical information, and obtain the inversion solutions which are closer to the real model.