基于阻尼最小二乘法的位场欧拉反演方法

Euler deconvolution of potential field based on damped least square method

欧拉反演方法是一种常用的估算场源位置的位场反演方法.在欧拉反演方法中如何获得稳定的解是一个还没有得到很好解决的难题,场源异常相互叠加干扰使反演系数矩阵极易奇异是造成反演结果发散的主要原因.我们基于阻尼最小二乘法对欧拉反演进行了进一步的分析研究,试图提高反演结果聚集度,获得可靠的反演结果.经过研究发现,阻尼因子的选取、系数矩阵的特征值、坐标系原点的位置设置等因素都会影响反演结果.阻尼系数大小与反演结果向原点压缩的程度呈正相关关系;系数矩阵特征值的大小与反演结果向原点压缩的程度呈负相关关系;并且特征值较小的系数矩阵对应的反演结果对坐标原点的位置变化较敏感.当阻尼系数确定后,采取变换坐标参考点的方法可以获得发散性小、稳定性好的反演结果,据此我们提出了变坐标系筛选方法.为了进一步地缩小反演结果的分布范围,我们根据反演结果与窗口中心点的空间关系对反演结果进行再次筛选.模型实验表明,阻尼最小二乘法欧拉反演方法和变坐标系筛选方法简单易行,可以明显地改善反演效果,增强反演结果的聚集程度.

Euler deconvolution is a popular method to estimate the source location.But the problem that how to obtain stable and reliable solutions has not been solved yet.The interference from adjacent sources which may be a main interference factor could cause the normal equation matrix(G T G)singular(G T G does not exist)and result in generating spurious solutions.And then in our study,the damped least square method which is often used to deal with singular matrices is applied to obtain Euler solution and we find that the damping factor,the eigenvalue of the normal equations matrix and even the relative position of the origin of coordinate could influence the accuracy of the Euler solutions.Specifically,the larger the damping factor,the closer the solution gets to zero,and the larger the size of the eigenvalue of the normal equations matrix,the smaller the impact of damping factor on solution,and also the matrix with small eigenvalue is sensitive to the change of the relative position of the coordinate origin.Accordingly,we propose a new method,called variable coordinate system selection method,to select best solutions.And in order to obtain more reliable solutions,an effective strategy based on the spatial relationship between the window center and the solution is used.Model test and real data application show that our selection methods are easy to perform and could dramatically reduce the number of spurious solutions.