Study on the apparent resistivity and magnetic field responses of a layered earth with arbitrary anisotropy
各向异性层状介质中视电阻率与磁场响应研究

The electric and magnetic responses to an arbitrary anisotropic formation have been checked through the direct current apparent resistivity and the magnetometric resistivity by using the potential of poloidal and toroidal scalars.The direct current apparent resistivity and the magnetometric resistivity responses to a multi-layer model have been calculated and applied to the analysis of the sensitivity of the apparent resistivity and the magnetometric resistivity methods to the anisotropic formation.In this study,the method of the state matrix analysis has been adopted.First of all,we construct the general solutions of the electric and magnetic fields by using of the poloidal and toroidal scalars.The current density and magnetic field are represented by potential of poloidal and toroidal scalars,and direct current(D.C.)apparent resistivity response due to point current sources in the layered half space with general anisotropy has been analyzed.The state matrix which propagates the electric and magnetic fields from upper layer to lower layers has been derived by adoption of the continuity of the electric and magnetic fields and the coupling of the source on the earth,and the fields are calculated recursively from the bottom layer to the top layer.Secondly,with regard to the unstable computation of the exponential term,a stable formulation has been deduced from the state matrix through the conversion to the stable exponential relationship.For the TI medium,an integral of the Green's function is used because of the decoupling of the poloidal and toroidal functions.Finally,the validity of the numerical method has been tested against an analytic solution of a simple half space anisotropic model.Results of multi-layer models have been shown to assess the feasibility of discerning the fractured formation and predicting the distribution of the fractures by using the D.C.current survey and magnetometric resisitity method.