A new method to compensate for bias in magnetotellurics

Error estimates from statistical regression analysis are often obviously too small, leading to doubts about the given equations, the statistical method itself and finally, with resignation, to the conclusion that mathematical equations and reality never agree. However, for magnetotelluric data we have found an almost perfect fit between observed scattering and predicted confidence limits of regression coeYcients after accounting for a systematic error—the bias. DiVerent methods to compensate for bias in magnetotelluric impedance estimation have been described using additional data from a reference station. However, suYciently accurate reference data are often not available. A new method has been developed that enables bias compensation without additional data. For the new method we derive a linear relationship between the eVect of bias and an expression depending on the data fit. From this we extrapolate the solution for the unbiased impedance. The new method assumes a special model of uncorrelated noise as well as an approximation for the structure of the impedance tensor. From each pair of components of the unrotated impedance tensor corresponding to the same output channel, one of the pair can be compensated if its magnitude is large compared to that of the other. The method has been successfully applied in many cases. We claim that the solution is closer to the true impedance than any solution based on the selection of events. It gives a measure of the partitioning of noise between the electric and magnetic channels. We applied the method to measurements from the North Anatolian Fault Zone (Turkey) and from the Merapi volcano (Central Java) in the period range 10–2500 s. DiVerent instrumentation was used for the two sets of measurements, but in both cases we used fluxgate magnetometers to measure the magnetic variations. Key words: data processing, magnetotellurics, statistical methods.