Lateral constrained inversion of E-E x wide field data

In order to solve the problem of lateral discontinuity of inversion profile for E-E x wide field electromagnetic method,the constraint term of adjacent points is added on the basis of the original Occam inversion,so that not only the longitudinal smoothness of inversion model is considered in the inversion process,but also the continuity of crosssection inversion by adjacent points is made as far as possible.When there is logging prior data,this item can realize the vertical direction constraint on the measured points near the drilling well,and the inversion results of the other survey points are considered to be the least different from the previous one,so as to improve the lateral continuity. In order to make full use of prior data and reduce the accumulation of inversion errors,we adopts the method that the adjacent survey points or the measured points with stable field value and wide field apparent resistivityLMas the section segmentation points,and carries out piecewise inversion of the whole profile to reduce accumulation error of profile inversion.The objective function of onedimensional lateral constrained inversion is given,and the Lagrange multiplier is calculated by the combination of advance and backward method and golden section method. The onedimensional model test results show that the inversion convergence rate with the reference point constraint is faster ,and the inversion resistivity is closer to the model intrinsic resistivity in the middle layer,but it has little influence on the calculation error.The twodimensional model test results show that the crosssection resistivity obtained by inversion with lateral constraints has better continuity and smoother profile.The inversion with lateral constrains is superior to the interpretation of the fine stratification and quantitative interpretation of wide filed apparent resistivity section. In the survey inversion,measured data can be prepossessed and smoothed first to calculate the wide filed apparent resistivity,which can be used to the initial model of the inversion and quickly converge to the real model. Finally,the inversion of the observed data of wide field electromagnetic field somewhere of Shanxi Province is performed,the results show that one dimensional lateral constraint inversion is better than wide field apparent resistivity in lateral continuity,the vertical stratification ability is better than that of the apparent resistivity section,the results,the actual outlet water point and known goaf area,are in good agreement with the actual geological conditions,It shows that this method can improve the inversion accuracy of measured data in coal mine hydrogeology.