Smooth MT Transfer Function Estimation by An Inverse Scheme

Magnetotellurics (MT) is the main geophysical tool applied to geothermal exploration. The method exploits the measurement of the low-power natural EM field at the Earth's surface, and through the estimation of the MT transfer functions (TF), the subsurface resistivity distribution can be inferred. Due to the diffusive nature of the low-frequency EM waves in the Earth, the MT TF's are inherently smooth, and this characteristic is the main criterion adopted by EM scientists to evaluate the quality of the TF and the presence of noise. If noise is Gaussian, the frequency-domain the least squares (LSQ) estimation provides the best possible TF estimate; natural MT data, however, contains a significant amount of non-stationary data that constitute outliers. This fact makes the TF's sharp at several frequencies, according to the nature of the noise. If non-stationarity occurs at a minor portion of the record, this problem is circumvented by robust estimation methods. However, is expectable that geophysical investigation of geothermal resources in the next future will be carried out in densely populated and industrialised areas, where high-power artificial EM noise, typically at the the power line frequency and its harmonics is superimposed to the weak natural signal. In this case, preliminary analog filtering aimed at mitigate this issue can be ineffective due to the high power of the noise, and robust methods can fail since the disturbance signals can be persistent. Moreover, EM noise is often coherent, making coherence pre-sorting ineffective. Therefore, the application of MT is severely hampered. Current practice can foresee to artificially smooth the MT TF, by means of splines or numerical smoothing procedures, and smoothness can also be part of estimation methods. However, these approaches lack of physical foundation or imply the adoption of some arbitrary assumptions, such as the representability of the TF by polynomials and the validity of the dispersion relationship between its real and imaginary parts. We propose a new heuristic and effective algorithm which goal is to get the smoothest MT TF's, via an inverse method applied to event selection. The frequency domain selection is done through variable power thresholds that reject powerful events making the TF sharp. The TF smoothness represents the objective function, and the infinite set of threshold vectors constitutes the model space. After the completion of the process, the distribution of the event powers is closer to Gaussian, and the LSQ residuals are consequently closer to a Rayleigh distribution. We found that the algorithm greatly reduces the effects of artificial strong-power signal on the MT acquisitions. Moreover, it can be combined with the MT remote-reference technique. Physical consistency of the TF has been checked by 1D inversion. Successful application of the technique to MT data collected over a geothermal prospect in the East African Rift System is here presented, where strong coherent noise at the 50 Hz fundamental and its upper harmonics strongly biased the MT impedance. The method was also successful at reducing bias in the low-frequency band.