An inverse approach for smooth magnetotelluric tranfer function estimation

Geophysical exploration of geothermal fields is largely based upon the Magnetotellurics method (MT), capable of reconstruct the underground resistivity distribution through the measurement of natural electric (E) and magnetic (B) fields at the Earth’s surface. The first assessment of the MT data quality is given by the inspection of the MT transfer function (TF), relating the E to the B field at the Earth's surface. Natural EM gives smooth transfer functions, and TF estimation can be carried out by the Least Squares method. However, in presence of noise generating non-stationary data, the estimation of the TF's can be very biased. This occurrence can be often identified by the sharp appearance of the TF's. Robust estimation methods can circumvent this problem only in case the noise affects the MT recordings for less than half length. However, when MT data are gathered in densely populated zones, artificial EM noise, often due to power lines occurs at the power line base frequency and its harmonics, is superimposed to the natural signal almost continuously. In this cases, the application of MT is severely hampered. Current practice foresees the posteriori smoothing of the TF, by means of splines or numerical smoothing procedures, but these approaches lack of physical foundation. Our method is a new heuristic algorithm aimed at get the smoothest MT TF's by an inverse method. The inversion operates an automatic event selection until the maximum TF's smoothness is reached. In this view, the TF smoothness represents the objective function, and the infinite set of threshold vectors constitutes the model space. After the process, the distribution of the event powers is demonstrated to be closer to Gaussian and suitable to LSQ estimation. We successfully applied our method to a geothermal prospect in the East African Rift System (Malawi), where strong coherent noise at the 50 Hz fundamental and its upper harmonics strongly biased the MT impedance. The method also successfully reduced the bias in the low-frequency band.