Tikhonov正则化方法在航空γ测量数据处理中的应用

Application of Tikhonov Regularization Method in Airborne Gamma Ray Spectrometer Survey Data Processing

在航空γ测量中,当地形平坦且飞行高度变化不大时,采用传统的高度修正方法可得到良好的结果。实际测量中,地形崎岖不平、飞行高度突变等常见现象会导致高度修正后的结果仍存在偏差甚至错误。基于条带模型构设崎岖地形条件下的反演方程组,应用Tikhonov正则化方法求解可得到地面放射性核素的面活度浓度。Tikhonov正则化方法的应用结果表明:随机噪声较小时,采用广义交叉验证(generalized cross validation,GCV)方法选取正则化参数得到的反演结果较好;随机噪声较大时,采用L曲线方法选取正则化参数得到的反演结果较好。与传统高度修正方法的计算结果相比该方法好,且适用于飞行高度变化较大的情形。

In airborne gamma-ray measurements,traditional height correction method can yield good results when the terrain is flat and the flight altitude does not vary significantly.However,common phenomena such as rugged terrain and abrupt changes in flight altitude can lead to deviations or even errors in the actual measurement results after applying height correction.By constructing a strip model under rugged terrain conditions,an inversion equation set can be derived to estimate the surface activity concentration of ground radioactive nuclides by using the Tikhonov regularization method.The application of the Tikhonov regularization method shows that when the random noise is small,the inversion results obtained by selecting the regularization parameters using the generalized cross validation(GCV)method are better.When the random noise is large,the inversion results obtained by selecting the regularization parameters using the L-curve method are better.The method yields better computation results compared to traditional height correction methods and is suitable for situations where the flight altitude varies considerably.