摘要
位场向下延拓技术在重磁位场领域作为重要的数据处理手段,其数学特性上的不稳定性始终是学界关注的焦点.正则化是解决位场向下延拓不稳定最有效的方法之一,目前有4种不同的正则化形式.本文从最小均方误差意义下的位场向下延拓维纳滤波器出发,结合位场源的分形径向平均功率谱,推导了位场向下延拓的最优正则化低通滤波器,并分析得到如下结论:(1)向下延拓的最优正则化低通滤波器只与源的集合质心埋深和分形结构指数相关,与下延深度无关;(2)现有文献中的4种不同正则化形式均是最优正则化向下延拓滤波器取特定参数的特例;(3)结合位场数据分形修正径向谱的最小值,最优正则化向下延拓滤波器仅需计算一次正则化参数即可下延不同深度.基于理论模型和实测数据的向下延拓对比试验验证了所提方法的有效性.通过理论模型和实际测量数据的向下延拓对比试验,结果表明,与现有的4种位场正则化方法相比,本文提出的最优正则化方法能获得更稳定、更准确的向下延拓结果.
The downward continuation technique of potential fields is an important data processing method in the field of gravity and magnetic potential fields.The mathematical instability of this technique has always been a focus of academic attention.Regularization is one of the most effective methods to solve the instability of downward continuation of potential fields,but currently there are four different forms of regularization.Starting from the Wiener filter of downward continuation of potential fields in the sense of minimum mean square error,and combining with the fractal radial average power spectrum of the potential field source,the optimal low-pass filter for regularized downward continuation of potential fields is derived.The following conclusions are obtained through analysis:(1)The optimal regularized low-pass filter for downward continuation is only related to the burial depth of the source's centroid and the fractal structure parameter,and is independent of the continuation distance;(2)The four different regularization forms in the existing literature are all special cases of the optimal regularization downward continuation filter with specific parameters;(3)The optimal regularization downward continuation filter combined with the minimum value of the fractal-corrected radial spectrum only requires calculating the regularization parameter once to downward continue to different depths.Through the comparison experiments of theoretical models and actual measurement data for downward continuation,the results show that,compared with the existing four kinds of potential field regularization methods,the optimal regularization method proposed in this paper can obtain more stable and accurate downward continuation results.
作者
曾小牛
刘天佑
张云
李鸿儒
杜爱民
刘代志
ZENG XiaoNiu;LIU TianYou;ZHANG Yun;LI HongRu;DU AiMin;LIU DaiZhi(School of Nuclear Engineering,Rocket Force University of Engineering,Xi′an 710025,China;National Engineering Research Center of Offshore Oil and Gas Exploration,Beijing 100028,China;CAS Engineering Laboratory for Deep Resources Equipment and Technology,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)
出处
《地球物理学报》
北大核心
2026年第3期1275-1285,共11页
Chinese Journal of Geophysics
基金
国家自然科学基金(41804136)
陕西省自然科学基础研究计划项目(2024-JC-YBQN-0253)资助.
关键词
位场
向下延拓
分形
正则化
径向平均功率谱
Potential field
Downward continuation
Fractal
Regularization
Radially averaged power spectrum
