基于Huber范数的地震曲率计算方法

Seismic curvature calculation based on Huber norm

本文分析了基于L2范数的曲率计算方法的不足,指出常规曲率计算方法采用二维中值滤波或距离加权的均值滤波,会导致异常值数据拟合出的曲面严重形变,计算出的曲率误差较大。针对此类问题,笔者给出了基于Huber范数的曲率计算方法:在Huber范数误差较小时,运用L1范数;反之,则运用L2范数。模型试算验证了基于Huber范数计算曲率在刻画异常值和跳跃值方面要优于传统的最小二乘法。实际资料的应用结果表明,基于Huber范数的曲率计算方法能够获得比常规的最小二乘法更加清晰而准确的结果。

There are some drawbacks in curvature calculation based on L2 norm.Using 2D median filtering or distance-weighted median filtering,this conventional method leads fitting surface deformation and large curvature errors for data with anomalies.To solve this problem,seismic curvature calculation based on Huber norm is proposed in this paper,which treats large residuals with L1 norm and small residuals by L2 norm.Model tests suggest that the method can describe more fine properties about abnormal values and jump values than the least squares method.Field data tests indicate that finer and more accurate seismic curvature results can be obtained by the method.