基于对称多项式约束的重力反演

Gravity inversion based on symmetric polynomial constraint

由于地球物理场的等效性、观测数据集的有限性和数据观测存在误差等问题,地球物理反演通常为不适定问题.Tikhonov正则化是应用最广泛的减少反演不适定性的方法之一,稳定函数的引入一方面提高了反演稳定性;另一方面将先验信息融入反演,提高了反演的效果.稳定函数的构建是正则化反演的关键之一,本文提出一种可以融入任意数量先验物性信息的对称多项式模型约束稳定函数.通过引入该函数,达到充分利用岩石先验物性信息、提高反演效果的目的.重力模型及实测数据反演表明,基于对称多项式的模型约束反演,可以实现任意数量岩石统计物性的利用,并获得理想的异常体边界和密度范围约束效果.

Geophysical inverse problem is usually ill posed because geophysical field has an intrinsic equivalence,the number of observational data is always finite and the observational data inevitably include noise.Tikhonov regularization is one of the most widely used methods to reduce ill-poseness of inverse problem.It not only improves inversion stability but also integrate prior information to get better inversion model.The design of stability function is one of the key steps of regularized inversion.In the paper,a symmetric polynomial constrained model stability function is proposed,which can integrate any number of prior physical property information into the inversion cost function,so as to make full use of the prior information and improve the inversion model.Both the gravity synthetic model and field data inversion show that the symmetric polynomial model constrained inversion can introduce any number geological unit physical property,and obtain the ideal boundary and density range of model.