Magnetic field of direct current in heterogeneous ground

We derive solutions of the steady state magnetic field due to a DC current source in four types of heterogeneous earth models. Four two-layered continuously earthed models are considered : an exponentialearth with a homogeneous overburden, a homogeneous earth with an exponential overburden, a homogeneous earth with a linear varying overburden, and a linearly varying conductivity earth with a homogeneousoverburden. These solutions are critical to interpret the magnetometric resistivity (MMR) data. Our solutions are achieved by solving a boundary value problem in the wave number domain and then transforming backto the spatial domain. The propagator matrix techniques are used. The curves of magnetic field are plotted to show the behavior of the field while some parameters are given approximately. To determine the conductivityparameter, the inverse problem is introduced via the use of optimization technique.