Robert L. Parker
A closed-form solution is given for a 2-dimensional, transverse electric mode, magnetotelluric problem. The model system consists of a finite vertical thin conductor with variable integrated conductivity over a perfectly conducting base. A notable property of the solution is that the frequency response possesses a single pole in the complex plane. Systems with finitely many resonances play a central role in the 1-dimensional magnetotelluric inverse problem based on finite data sets, but until now, no 2-dimensional system of this kind was known. The particular model is shown to be just one of a large class of thin conductors with same the property, and further examples are given. The solutions of the induction problem for members of this family can often be written in compact closed form, making them the simplest known solutions to the 2-dimensional magnetotelluric problem.