正则化方法在比值类位场边缘识别方法中的研究

位场边缘识别方法有很多种,其中归一化标准差法(NSTD)、倾斜角法(Ta)和Theta Map(cosθ)等方法属于比值类方法.比值类方法在计算过程中会出现分母接近于0或者等于0这种情况,致使计算结果不稳定,并产生错误的边缘识别结果.为此,对比值类边缘识别方法计算公式中的分母加一个大于零的正则化因子,不但解决了比值类方法的数值计算稳定性问题,而且提高了部分比值类边缘识别方法识别结果的精度.通过理论模型和实际资料检验了新方法的稳定性、精度以及有效性.正则化因子的引入同样可以改善以比值类方法为基础构建的二阶导数类边缘识别方法的识别效果,如倾斜角总水平导数(Ta-THDR)的识别效果.正则化这一思想不但可以解决比值类位场边缘识别方法的数值计算问题,而且可以解决比值类方法的数值计算问题.

The research of the regularization method in the ratio methods of edge recognition by potential field

The ratio methods are one sort of edge recognition methods by using potential field,which contains the Normalized Standard Deviation method( NSTD),Tilt Angle method( Ta) and Theta Map( cosθ). If the denominator of ratio method closes or even equals to zero in the process of calculation,the result obtaining from ratio methods is unstable and may even bear little resemblance to the true geology. In order to relief this problem,a regularization factor,which is greater than zero,is added in the denominator of the ratio methods’ formula,which not only enhances the numerical stability of the ratio methods but also improves the accuracy of some ratio edge recognition methods. The stability,accuracy and effectiveness of the new method is verified by testing synthetic models and calculating real data. Also,the introduction of the regularization factor also can improve the effect of recognizing edge by the second-derivative edge recognition methods,which is based on the ratio methods,such as the Total Horizontal Derivative of the Tilt Angle( TaTHDR). The idea of regularization can not only solve the numerical calculation problem of the ratio methods of edge recognition for potential field,but also solve the numerical calculation problem of all ratio methods.