Noise reduction and data recovery for a VLF-EM survey using a nonlinear decomposition method

Geologic noise and background electromagnetic (EM) waves often degrade the quality of very low frequency electromagnetic (VLF-EM) data. To retrieve signals with significant geologic information, we used a new nonlinear decomposition technique called the empirical mode decomposition (EMD) method with the Hilbert transform. We conducted a 2D resistivity model study that included inversion of the synthetic data to test the accuracy and capabilities of this method. Next, we applied this method to real data obtained from a field experiment and a geologic example. The filtering procedure for real data starts with applying the EMD method to decompose the VLF data into a series of intrinsic mode functions that admit a well-behaved Hilbert transform. With the Hilbert transform, the intrinsic mode functions yielded a spectrogram that presents an energy-wavenumber-distance distribution of the VLF data. We then examined the decomposed data and their spectrogram to determine the noise components, which we eliminated to obtain more reliable VLF data. The EMD-filtered data and their associated spectrograms indicated the successful application of this method. Because VLF data are recorded as a complex function of the real variable distance, the in-phase and quadrature parts are complementary components of each other and could be a Hilbert transform pair if the data are analytical and noise free. Therefore, by comparing the original data set with the one obtained from the Hilbert transform, we could evaluate data quality and could even replace the original with its Hilbert transform counterpart with acceptable accuracy. By application of both this technique and conventional methods to real data in this study, we have shown the superiority of this new method and have obtained a more reliable earth model by inverting the EMD-filtered data.