基于不等式约束的重力三维聚焦反演

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

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,但仍然存在着多解性较强的问题。为了解决该问题,引入不等式约束将反演参数限制在有意义的范围内,从而降低反演的多解性。基于此,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。因此,基于不等式约束的三维聚焦反演可以降低反演的多解性,提高解的准确性。

The focusing inversion is the main method of gravity inversion,which can better recover the compact structure of anomalies and differentiate the boundary having large difference in physical properties.However,the problem of non-uniqueness of the inversion remains strong in some cases.To solve the problem,inequality constraints were introduced to restrict inversion parameters in a meaningful range.Afterwards,the focusing inversion and inequality constraints were integrated into the three-dimensional(3D)gravity inversion,and the logarithmic transformation function method was introduced to realize the 3D gravity inversion based on inequality constraints.Model tests showed that the focusing inversion could accurately recover the shape and range of density anomalies.However,some false anomalies remain in deep areas.Meanwhile,the focusing inversion based on inequality constraints could effectively suppress the false anomalies and improve the non-uniqueness problem of the inversion.Furthermore,inequality constraints in different regions could improve the flexibility of the application of prior physical information,and obtain the inversion solutions that are closer to the real model.Therefore,the 3D focusing inversion based on inequality constraints can effectively reduce the multiplicity of inversion,and improve the accuracy of the inversion solutions.