A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform
Jianhua CaiDepartment of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China. Email: cjh1021cjh@163.com
Exploration Geophysics 48(3) 192-200 https://doi.org/10.1071/EG15014
Submitted: 16 February 2015 Accepted: 1 April 2016 Published: 2 May 2016
Abstract
The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.
Key words: Hilbert-Huang transform, magnetotelluric signals, response function estimation, time-frequency method.
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