مروری بر پردازش داده‌های مگنتوتلوریک

Magnetotelluric (MT) method is an important passive surface geophysical method which uses the Earth’s natural electromagnetic fields to investigate the electrical resistivity structure of the subsurface. The depth of investigation of MT is much higher than that of other electromagnetic (EM) methods (Vozoff, 1991). For a general conductivity distribution in the Earth, the horizontal electric field components are related to horizontal magnetic field components by the Impedance Tensor (Z):
(1)
Which shows vertical and horizontal variations of subsurface conductivity. Apparent resistivity ( ) and phase ( ) are the desired quantities which are calculated from Impedance matrix by the following expressions:
(2)
and are free space permeability and angular frequency. DET is determinant data. Time series are measured in frequency interval of 0.001-1000 and frequency spectra are used to estimate the Impedance Tensor as a function of frequency.The Impedance Tensor determinant (or effective impedance), , is as below (Berdichevsky and Dmitriev, 1976):
(3)
The advantage of using the determinant data is that it provides a useful average of the impedance for all current directions. Furthermore, no mode identifications (transverse electric, TE mode: current in parallel with the strike; or transverse magnetic, TM-mode: current perpendicular to the strike) are required, static shift corrections are not made, and the dimensionality of the data is not considered, since the effective impedance is believed to represent an average that provides robust 1D and 2D models.
MT data are as time series and information of the subsurface structure cannot be given. Then, MT data must be processed to be prepared for the inversion and interpretation. In the following sections, a review of MT processing steps consisting of time series analysis and also steps called manual processing is presented.
The analysis of the time series: The main problem in the processing of the MT data is that the field observations (raw data) are as time series (figure 1) but the basic theories are in the frequency domain. In this section, an explanation is given to how a single spectral matrix is computed from a specific time series section for all target frequency lines.
Transformation into frequency domain: The time series of each channel (2 electric field components and 3 magnetic field components) are transformed to the Fourier series by FFT (Fast Fourier Transform). Depending on the sampling rate in the specific
band and the adjusted section length, different resolution and frequency ranges are achieved.
The trend elimination: Before applying the Fourier transform, the raw data is processed with trend elimination. The trend elimination removes a possible systematic deviation from the x-axes. The mean value is set to zero and a straight line in the data (trend) which differs from the x-axis is removed. Figure 2 illustrates the trend elimination procedure.
The window function (windowing): After the trend elimination, the multiplication of the time series with a window function (windowing) follows. This is necessary in order to suppress side effects (discontinuities are generated at the edges) at the FFT and to obtain an optimum sharp mapping of the frequency spectra.
The fast Fourier transform (FFT): After the time series has been treated with the trend elimination and the windowing the fast Fourier transform (FFT) is applied to the data. The given time series has now been transformed into the frequency domain. All the further steps of computation are done with spectral data.
The calibration of spectra: When registrating the time series, the data is affected by the transfer function of the measurement instruments. In order to eliminate this influence, the data must be calibrated. The spectra are multiplied by the re