Fast, simultaneous and robust VLF-EM data denoising and reconstruction via multivariate empirical mode decomposition

The measurement of Very Low Frequency Electromagnetic (VLF-EM) is important in many different applications, i.e, environmental, archeological, geotechnical studies, etc. In recent years, improving and enhancing VLF-EM data containing complex numbers (bivariate) was presented by several authors in order to produce reliable models, generally using univariate empirical mode decomposition (EMD). Applying univariate EMD separately on each data is problematic. This results in a different number of misaligned Intrinsic Mode Functions (IMFs) which can complicate the selection of some IMFs for denoising process. Thus, a filtering method based on the multivariate empirical mode decomposition (MEMD) approach to decompose simultaneously bivariate data is proposed. In this paper we address two issues by employing the recently introduced noise assisted MEMD (N-A MEMD) for improving bivariate VLF-EM data. Firstly, the N-A MEMD to decompose bivariate measurement of the VLF-EM data into IMFs and a residue is defined as VLF-EM signal or unwanted noise. Secondly, the proposed method is used to enhance VLF-EM data and to reject unwanted noise. Finally, the proposed method is applied to a synthetic data with two added sinusoids. To demonstrate the robustness of the N-A MEMD method, the method was tested on added-noise synthetic data sets and the results were compared to the Ensemble EMD (EEMD) and Bivariate EMD (BEMD). The N-A MEMD gave more robust and accurate results than the EEMD and BEMD methods and the method required less CPU time to obtain the IMFs compared to EEMD. The method was also tested on several field data sets. The results indicate that the filtered VLF-EM data based on the N-A MEMD make the data easier to interpret and to be analyzed further. In addition, the 2D resistivity profile estimated from the inversion of filtered VLF-EM data results was appropriate to the geological condition. & 2014 Elsevier Ltd. All rights reserved.