关键词: 可控源音频大地电磁法, 一维反演, 最小二乘法, 初始模型

Abstract: In the application of CSAMT,the sounding curve is often distorted with the impact of electric dipole source,which produces confusions in data inversion and interpretation.Based on the 1-D layered earth conventional least-square inversion for CSAMT data,this paper introduces an optimized technique to get better result by discussing the forward modeling calculation,mechanism of inversion,selection of initial model,and iteration model controlling.Formulas of electromagnetic field components,E_x and H_y,given as integrations which contain Bessel functions of first kind of order 0 and 1,can be obtained using numerical method.During the calculation,the kernel functions of integrations are changed respectively in order to get better convergence properties.Taking the short transmitter-receiver distance into account,the relatively long grounded linear wire source should be assumed as an accumulation of dipoles,thus the theoretical apparent resistivity can be calculated by the field responses of dipole series.The forward calculation of CSAMT needs configuration parameters such as source location,measuring point position,current amplitude and so on,which are different from MT modeling.A primary objective of inversion is to recover a geologically interpretable model that can reproduce the set of observations.Based on the least square inversion theory,the method iteratively updates the vector of model parameters to get the minimum of the vector of relative mean square errors,where the Jacobi matrix can be obtained by difference method.Singular value decomposition method is adopted in equations solving,and we replace small singular value with zero.To get rid of falling into local minimum point during the iteration,it is necessary to control the model parameter excess when the model becomes abnormal.Actually the action will destroy the convergence,but it also increases the chance to find out the global minimum point.Numerical experiments show that the inversion result is better than the conventional one.The selection of initial model has an impact on the inversion results.Based on the theoretical similarity of CSAMT far-field data and MT data,the semi-quantificational Bostick resistivity-depth curve can be used as the base of initial model.Then,by decreasing the layers number according to the resistivity trend with apparent depth,and abandoning the deformed thin layers produced in layer cutting if necessary,the appropriate initial model is created.Some synthetic studies and a case of field data are followed to validate the inversion mechanism,and their resultant response fits the observed data well with acceptable inversion precision and computing time.In conclusion,it is available to adopt semi-quantificational Bostick resistivity-depth curve as the base of initial model for the CSAMT 1-D inversion.The multiplicity of solutions can be suppressed by the number of inversion parameters cut down using the Bostick curve optimization techniques.Appropriate initial models and iteration controlling are introduced to help enhance the capability of algorithm to find the global minimum,which satisfies the geophysical exploration requirements.

Key words: CSAMT, 1-D inversion, least-squares algorithm, initial model