Controlled-source electromagnetic data processing based on gray system theory and robust estimation

We propose a novel method that combines gray system theory and robust M-estimation method to suppress the interference in controlled-source electromagnetic data. We estimate the standard deviation of the data using a gray model because of the weak dependence of the gray system on data distribution and size. We combine the proposed and threshold method to identify and eliminate outliers. Robust M-estimation is applied to suppress the effect of the outliers and improve the accuracy. We treat the M-estimators of the preserved data as the true data. We use our method to reject the outliers in simulated signals containing noise to verify the feasibility of our proposed method. The processed values are observed to be approximate to the expected values with high accuracy. The maximum relative error is 3.6676%, whereas the minimum is 0.0251%. In processing field data, we observe that the proposed method eliminates outliers, minimizes the root-mean-square error, and improves the reliability of controlled-source electromagnetic data in follow-up processing and interpretation.