The magnetic permeability inversion is very important for environmental contamination and ferro-mining exploration. In the magnetic permeability inversion, we should suppose that the magnetic permeability is variable cell by cell. In this case the magnetic field is discontinuous and electric field is continuous.
In this paper we present the following contents: (1) to use a new electric integral equation on the boundary and electric differential equation in the domain to construct a GILD electric field modeling; (2) to use a Global Integral equation on subdomain CSI and a Local variation electric field Differential equation on subdomain CSII to construct a GILD inversion for updating the permeability; (3) to use a new particle tracking to connect magnetic permeability and ferrofludis permeability; (4) to describe applications.