基于边界约束有限内存的拟牛顿CSAMT一维反演及应用

LBFGS CSAMT 1D inversion of limited memory based on boundary constraint and its application

可控源音频大地电磁法(CSAMT)正演具有计算耗时、精度低的特点;常规的反演方法边界处理简单,占用内存大,搜索方向也难以精准,严重影响反演效果。为了实现CSAMT快速高精度正演,改善边界处理方法以减少内存占用,优化搜索方向以减少迭代反演次数,提出基于边界约束有限内存的拟牛顿CSAMT一维反演方法。首先,在CSAMT正演中基于高斯积分与并行算法实现了一维介质模型条件下有限长导线源激发的水平电场快速高精度计算。其次,在反演方法中,分别构建了基于相对误差和绝对误差的两种目标函数,并引入光滑模型约束,采取自适应正则化策略更新正则化因子,并采用基于边界约束的有限内存拟牛顿算法(LBFGS_B算法),实现了CSAMT一维准确快速反演。以含低、高阻薄层的多层地电模型的水平电场Ex振幅为反演数据进行直接反演和模型检验。结果表明,该方法能够反映出地层电阻率随深度变化的趋势,并对高、低阻薄层有较好的分辨能力,低阻薄层分辨效果更佳。实际CSAMT资料的反演剖面的分辨率优于常规的连续介质反演方法,地质效果明显,表明该方法具有良好的应用前景。

CSAMT is characterized by time-consuming calculation and low accuracy.The conventional inversion method has simple boundary processing,needs big memory,it is difficult to have accurate search direction,influencing severely the effect of inversion.In order to achieve rapid and high-precision forward modeling of CSAMT,to improve the boundary processing method,to reduce memory usage,to optimize the searching direction to reduce the times of iterative inversion,LBFGS CSAMT 1D inversion method based on boundary constraint and limited memory was proposed.Firstly in CSAMT forward modeling,double-precision and parallel algorithm was adopted,realizing rapid and high-precision calculation of the horizontal electric field excited by a wire source with limited length under conditions of 1D medium model.Secondly in inversion method two objective functions based on the relative error and the absolute error were constructed respectively.The constraints of smooth model were introduced.Self-adaptive regularization strategy was adopted to renewal the regularization factors.LBFGS-B algorithm of limited memory based on boundary constraint was adopted.1D precise and rapid inversion of CSAMT was realized.The amplitude of the horizontal electric field Ex of the geoelectric model of multiple thin layers with low and high resistivity was used as inversion data to conduct direct inversion and model test.The results illustrate that this method can reflect the trend of the variation of formation resistivity with depth,and has higher resolution for thin layers with high and low resistivity,the resolving effect is better for a thin layer with low resistivity.The resolution of the inversion profile of the actual CSAMT data is superior to that of the conventional inversion method for continuous medium.The geological effect is evident,indicating that this method has good application prospect.