A two-dimensional, self-consistent impedance method has been derived and used to calculate the electromagnetic surface impedance above buried objects at very low frequencies. The earth half space is discretized using an array of impedance elements. Inhomogeneities in the complex permittivity of the earth are reflected in variations in these impedance elements. The magnetic field is calculated for each cell in the solution space using a difference equation derived from Faraday's and Ampere's laws. It is necessary to include an air layer above the earth's surface to allow the scattered magnetic field to be calculated at the surface. The source field is applied above the earth's surface as a Dirichlet boundary condition, whereas the Neumann condition is employed at all other boundaries in the solution space. This, in turn, enables users to use both finite and infinite magnetic field sources as excitations. The technique is shown to be computationally efficient and yields reasonably accurate results when applied to a number of one- and two-dimensional earth structures with a known surface impedance distribution. ¿ 2001 American Geophysical Union