基于L曲线法的位场向下延拓正则化参数选择  

The selection of regularization parameter in downward continuation of potential field based on L-curve method

作　　者：马涛[1] 陈龙伟[1] 吴美平[1] 胡小平[1] 

机构地区：[1]国防科技大学机电工程与自动化学院,长沙410073

出　　处：《地球物理学进展》2013年第5期2485-2494,共10页Progress in Geophysics

基　　金：国家自然科学基金项目(61174206);国防科学技术大学研究生创新资助项目(S110301)联合资助

摘　　要：正则化方法是处理位场向下延拓的一种有效方法,最优正则化参数的确定是位场向下延拓正则化方法的重要部分,参数选择优劣直接影响向下延拓结果的精度.本文采用L曲线法,通过曲率函数确定L曲线的拐点位置,进而选取合适的正则化参数.快速计算曲率函数值是算法的关键步骤,本文利用Parseval等式,结合快速傅里叶算法,实现了曲率函数值的频率域快速计算,提高了算法的运算效率.利用模型数据和实测航磁资料对L曲线法确定正则化参数的有效性进行了验证.结果表明,对于不同信噪比的观测数据,L曲线法表现出较强的适应性,将L曲线法确定的正则化参数代入Tikhonov正则化方法中进行位场向下延拓,取得了较高的精度.Regularization method is a powerful method in dealing with downward continuation of potential field. A very important part of regularization method is the selection of optimum regularization parameter, and the accuracy of result of downward continuation is affected by the selected parameter. In this paper, we adapt L-curve method to select the optimum regularization parameter. With the help of curvature function, we can find the maximum curvature point of L-curve, which corresponds to the optimum regularization parameter. How to efficiently calculate the value of aided function is crucial. Applying Parseval equation, we derive the frequency expression of curvature function, so that we can calculate the value of curvature function by using Fast Fourier Transform algorithm which makes the whole process very fast. We test the validity of L-curve method in selecting regularization parameter using modal data and aeromagnetic data. The result shows that the L-curve method has good adaptability in dealing with data with different signal to noise ratio, and downward continuation result shows high accuracy.

关 键 词：位场向下延拓 正则化参数 TIKHONOV正则化 L曲线法 曲率函数 PARSEVAL等式 

分 类 号：P312[天文地球—固体地球物理学] P318[天文地球—地球物理学]