共轭梯度法向残差法的重力异常向下延拓研究

Downward continuation of gravity anomaly by conjugate gradient normal residual method

针对重力异常向下延拓的不适定性导致求解难度大的问题,该文采用了共轭梯度法向残差(CGNR)法与频率域积分迭代法,使用模拟重力异常数据进行向下延拓,并对两种方法的延拓效果进行对比。实验结果表明:二者均需对变量的数据进行扩边,以更好地消除边缘效应;CGNR法结合快速傅里叶变换(FFT)可以提高计算效率,有利于抑制噪声的影响,算法稳健性强且相比频率域积分迭代法具有较高的延拓精度,向下延拓深度可达20倍点距,且保持良好的延拓精度。

In view of the difficulty of solving the problem caused by the ill-posed of downward continuation of gravity anomaly,conjugate gradient normal residual(CGNR)method and frequency domain integral iterative method were adopted in this paper to downward continuation of simulated gravity anomaly data,and the continuation effects of the two methods were compared.The experimental results showed that both of them needed to expand the edge of variable data to better eliminate the edge effect.The CGNR method combined with fast Fourier transform(FFT)could improve the calculation efficiency and suppressed the influence of noise.Compared with frequency domain integral iterative method,the CGNR algorithm had strong robustness and higher continuation accuracy,and the downward continuation depth could reach 20 times the point distance,and maintained good continuation accuracy.