二维井间电磁场的非线性反演方法

Nonlinear inversion algorithm for two-dimensional cross-hole electromagnetic fields

采用高精度的非线性反演方法,对轴对称二维井间模型的电导率分布进行了成像。该成像方法既考虑到雅可比矩阵的线性项,也考虑了其偏微分项,因而反演精度高且稳定性强。采用矩阵求逆技术计算了纵向成层背景地层Green函数的系数,可以很方便地得到Green函数对空间坐标的积分,从而使雅可比矩阵的计算更方便、准确。反演实例表明,井间电磁成像技术更适宜于对相对高电导率异常区域进行成像。由于井间电磁成像技术对异常区块的垂向探测范围大于径向探测范围,测量数据中包含的垂向信息多于径向信息,因而垂向分辨率高于径向分辨率。

A high-precision nonlinear inversion algorithm was applied to image the conductivity distribution in the two-dimensional cross-hole model with cylindrical symmetry. Since both the linear term and the differential term of the Jacobian Matrix are considered in the algorithm, the inversion process is more accurate and stable. The coefficients of the Green's function in longitudinal layered background medium were calculated by inverting the coefficient matrix, and the integral of the Green's function with respect to the space coordinates could be conveniently obtained. Thus the calculation of the Jacobian Matrix becomes more convenient and accurate. Inversion examples showed the effectiveness of this algorithm. The cross-hole electromagnetic imaging technique is more suitable for imaging the anomalous domain with relatively high conductivity compared with the background conductivity. These examples also indicate that the vertical detecting range is broader than the radial detecting range of this technique. Therefore the vertical information is more than the radial information in the measured data, and the vertical resolution is higher than the radial resolution.