A new two-dimensional (2D) magnetotelluric (MT) inversion scheme is proposed in this paper. This scheme is based on a locally two-dimensional analysis in order to minimize computational time and computer memory. The MT governing equation is linearized in terms of the magnetic field and electrical conductivity for the perturbation analysis. The perturbed equation is then multiplied by a test function and integrated over the cross section. Integrating by parts and then substituting this test function with local magnetic fields, a new equation is obtained that is a 2-D variational integral for the electrical conductivity. The new equation is general in the sense that it can explicitly include the horizontal derivative of the magnetic field. If the horizontal derivative term is eliminated, the new equation becomes identical to the Rapid Relaxation Inversion (RRI) scheme proposed by Smith and Booker (1991).


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