3-D Time-domain Airborne EM Forward Modeling With Ip Effect Based On Implicit Difference Discretization Of Caputo Operator

As an efficient and effective geophysical tool,the time-domain airborne electromagnetic(AEM)method can be used to conduct exploration in areas with complex surface conditions such as dunes,swamps,or forest-covered areas.At present,it has been widely used in mineral resources exploration,groundwater and environmental engineering investigation and many other fields.With the continuous development of the time-domain airborne electromagnetic exploration system,the quality of its data collection is also constantly improved.People often find that the timedomain AEM response data has a sign reversal in the late time channels,which mostly occurs in the underground sulfide minerals or water-bearing areas.This phenomenon has been widely studied by scholars.It is believed that this phenomenon is often caused by the induced polarization effect.Since the conventional inversions only consider the non-dispersive conductivity,it cannot effectively recover the underground geoelectrical structures from the data containing IP effect.This will hinder the application of AEM technique.Therefore,it is meaningful to study the forward modeling and inversion algorithms for AEM with IP effect.In this paper,a 3-D time-domain airborne EM forward modeling with IP effect based on implicit difference discretization of caputo operator is proposed.The EM response is calculated and the influence characteristics of IP parameters are analyzed for typical geological body models.In this paper,the electric field diffusion equation is derived by using the constitutive relation from Maxwell’s equations in time-domain.Secondly,an unconditionally stable second-order backward Euler discretization scheme is adopted for the first-order time derivative.Then Cole-Cole model is introduced to describe the frequency variation of conductivity in polarized media and the time-domain expression of Ohm’s law in polarized media is derived.An implicit difference discretization scheme based on Caputo operator is used for discretization of fractional derivatives,and the electric field diffusion equation after time discretization is obtained.Then the space is discretized by vector finite-element method and the weak forms of finiteelement governing equation of AEM IP effect in time-domain is established by Galerkin’s method.The element matrix is calculated by the correlation between vector interpolation basis function and scalar interpolation basis function,and the electric dipole discrete processing method is used for the field source.The large linear equations are assembled and the sparse maxtrix is reduced by compressed sparse row storage method.Then the boundary conditions and initial conditions are determined.Finally,MUMPS solver is used to solve the equation and calculate the EM response.The effectiveness of the proposed algorithm is verified by comparing with the 1D semi-analytic solutions for a half-space model under different IP parameters.Meanwhile,compared with the frequency-time conversion algorithm,the computational efficiency of the proposed algorithm is significantly improved.The numerical results of theoretical model show that IP effect has a significant impact on AEM response.Among them,the conductivity and the chargeability have the biggest influence.Although there are differences in the characteristics and degree of influence for different parameters on EM responses,the IP effect will typically lead to the sign reversal of EM signal in late-time channels.Considering that for a concentric coil array in AEM,no other factor other than the IP effect can cause the sign reversal of EM responses,the proposed algorithm is beneficial to anomaly identification and feature extraction from time-domain AEM signal.The research in this paper is beneficial to anomaly identification and feature extraction of electromagnetic signals in the time-domain,and also provides theoretical and algorithm support for three-dimensional inversion of AEM IP effect.The research results of this paper have certain theoretical and practical value to the processing and interpretation of AEM data.