航空重力异常数据稳定高精度向下延拓方法研究  

Study on the stable and high-precision downward extension method of airborne gravity anomaly data

作　　者：柯宝贵[1,2] 赵予菲 徐凡凡 赵翠 李泰航 Ke Baogui;Zhao Yufei;Xu Fanfan;Zhao Cui;Li Taihang(Chinese Academy of Surveying and Mapping,Beijing 100036,China;National Precise Gravity Measurement Facility,Huazhong University of Science and Technology,Wuhan 430074,China;Faculty of Geomatics,Lanzhou Jiaotong University,Lanzhou 730070,China;College of Applied Science and Technology,Beijing Union University,Beijing 102200,China)

机构地区：[1]中国测绘科学研究院,北京100036 [2]华中科技大学精密重力测量研究设施,武汉430074 [3]兰州交通大学测绘与地理信息学院,兰州730070 [4]北京联合大学应用科技学院,北京102200

出　　处：《地球与行星物理论评(中英文)》2025年第3期264-277,共14页Reviews of Geophysics and Planetary Physics

基　　金：中央级公益性科研院所基本科研业务费(AR2404);北京联合大学科研资助项目(ZK20202204)。

摘　　要：航空重力异常向下延拓的本质是求解第一类Fredholm方程,属于不适定性的问题.稳定高精度向下延拓方法一直以来都是该领域的研究热点.为抑制边缘效应和提升计算效率,分别对所用数据进行扩边和快速傅里叶变换处理.为增大向下延拓距离、提高稳定性和延拓精度,利用模拟重力异常数据和实测航空重力数据对比分析了积分迭代法、Tikhonov正则化迭代法、Barzilai-Borwein法、迭代最小二乘法和半迭代方法、改进的共轭梯度法向残差法等六种向下延拓方法.结果表明:在数据没有噪声的理想情况下,Barzilai-Borwein法的收敛速度最快,且初始延拓均方误差值低,延拓精度高,优势明显.迭代最小二乘法不够稳定.Tikhonov正则化迭代方法在达到延拓稳定前,经历了误差增加的状态,且初始均方误差值较高,而其余的几种方法延拓效果类似较为一般.在模拟数据中添加噪声后,改进的共轭梯度法向残差法,对噪声的抑制效应最好.且该方法在实际数据向下延拓的过程中,能够实现稳定向下延拓,延拓精度优于其他五种延拓方法.The essence of the downward continuation of airborne gravity anomalies is to solve the first kind of Fredholm integral equation,which is an ill-posed problem.Stable and high-precision downward continuation methods have always been a research hotspot in this field.This research has been conducted on data expansion to suppress edge effects and enhance computational efficiency through the use of the fast Fourier transform.To increase the depth of downward continuation,improve stability,and enhance continuation accuracy,six downward continuation methods—the integral iterative method,Tikhonov regularization iterative method,Barzilai–Borwein(BB)method,iterative least squares method,semi-iterative method,and conjugate gradient normal residual(CGNR)method—were comparatively analyzed using simulated and actual airborne gravity anomaly data.The results indicated that the BB method has the fastest convergence rate under the ideal condition of no noise in the data,with a low initial mean square error of continuation and high accuracy,thus showing a clear advantage.The iterative least squares method is insufficiently stable.The Tikhonov regularization iterative method produces an increase in error before reaching a stable continuation state,and it has a relatively high initial mean square error with a continuation effect that is generally similar to that of the other methods.After adding noise to the simulated data,the improved CGNR method showed the best noise suppression effect.Moreover,this method is capable of achieving stable downward continuation in the process of actual data continuation,with a continuation accuracy that is superior to that of the other five methods.

关 键 词：航空重力数据 向下延拓 频率域 共轭梯度法向残差法 积分迭代法 

分 类 号：P312[天文地球—固体地球物理学]