Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

Abstract

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained.In a test using real data, the wavelet transform showed a significant improvement in the signal-tonoise ratio over the conventional Fourier transform.

New application of wavelets in magnetotelluric data processing: reducing impedance bias

“…Another approach was the use of wavelet techniques to look for MT sources or remove noise in the time series. Zhang and Paulson (1997) applied the continuous wavelet transform (CWT) on high-frequency data to select sferics events. They thus increased the signal-to-noise ratio in the response function determination in a straightforward way by the selection of useful signal parts.…”

“…Geomagnetic pulsation signals contain several oscillations so they are very localized in the time and frequency domains simultaneously. Thus, like previous authors (e.g., Zhang and Paulson 1997;Garcia and Jones 2008 for atmospherics signals), we have chosen the Morlet wavelet, which represents the best compromise between the time and frequency resolution. Use of the Cauchy wavelet would be hazardous because of its low-frequency resolution.…”

“…In the low-frequency band of extremely low-frequency (ELF) waves, sferics consist of a high-amplitude To analyze ELF waves using the CWT, we have chosen the Cauchy wavelet. Most of the previous work on MT methods with wavelets was based on the Morlet wavelet stemming from its properties of good resolution in terms of both the time and frequency (Zhang and Paulson 1997;Garcia and Jones 2008). However, the shape of the ELF wave (Fig.…”

“…Robust statistics are still necessary, but we considerably increase the signal-to-noise ratio on all selected events. Zhang and Paulson (1997) worked in a single station configuration and used conventional least-squares analysis to resolve Eq. (7).…”

“…11, we show an example of such a VLF wave and its time-frequency analysis. These waves were already used in an MT processing study by Zhang and Paulson (1997).…”