Theoretical Consideration on the Application of Continuous Wavelet Transform to Time-Series Processing for Magnetotelluric Data

Abstract

In the magnetotelluric (MT) method, the responses of the natural electromagnetic fields are evaluated by transforming time-series data into spectral data and calculating the apparent resistivity and phase. The continuous wavelet transform (CWT) can be an alternative to the short-time Fourier transform, and the applicability of CWT to MT data has been reported. There are, however, few cases of considering the effect of numerical errors derived from spectral transform on MT data processing. In general, it is desirable to adopt a window function narrow in the time domain for higher-frequency components and one in the frequency domain for lower-frequency components. In conducting the short-time Fourier transform, because the size of the window function is fixed unless the time-series data are decimated, there might be difference between the calculated MT responses and the true ones due to the numerical errors. Meanwhile, CWT can strike a balance between the resolution of the time and frequency domains by magnifying or reducing the wavelet, according to the value of frequency. Although the types of wavelet functions and their parameters influence the resolution of time and frequency, those calculation settings of CWT are often determined empirically. In this study, focusing on the frequency band between 0.001 Hz and 10 Hz, we demonstrated the superiority of utilizing CWT in MT data processing and determined its proper calculation settings in terms of restraining the numerical errors caused by the spectral transform of time-series data. The results obtained with the short-time Fourier transform accompanied with gradual decimation of the time-series data, called cascade decimation, were compared with those of CWT. The shape of the wavelet was changed by using different types of wavelet functions or their parameters, and the respective results of data processing were compared. Through these experiments, this study indicates that CWT with the complex Morlet function with its wavelet parameter k set to 6 ≤ k < 10 will be effective in restraining the numerical errors caused by the spectral transform.

Novel approach in static shift correction for magnetotellurics data using 2D electrical resistivity imaging

“…Fourier Transformation was applied onto the data to resolve from time domain into their constituent frequencies. MT transfer function, which mainly consists of impedance tensor and phase tensor, was calculated from electric and magnetic elds data measured on site using robust estimation (Ogawa et al, 2020;Smaï & Wawrzyniak, 2020). The data was then exported as .edi le format that is readable by third party software for further analyses.…”