Robust statistical methods for impulse noise suppressing of spread spectrum induced polarization data, with application to a mine site, Gansu province, China
Introduction
Induced Polarization (IP) methods performed in time or frequency domain are widely used at various stages of geophysical prospecting (Weller et al., 2010, Ntarlagiannis et al., 2010, Joyce et al., 2012). There have been great developments of IP in the aspects of the system of instruments, forward modeling and inversion methods (Khesin et al., 1997, Titov et al., 2002, Loke et al., 2006). Spread spectrum induced polarization (SSIP) is a new frequency-domain induced polarization (FDIP) method (Xi et al., 2013, Xi et al., 2014). For SSIP, the transmitter transmits pseudo-random m-sequence waveforms as source current, and the receiver measures the potential difference between two electrodes. Pseudo-random m-sequence is a kind of binary sequence generated using maximal linear feedback shift registers. This sequence is spectrally flat similar to the random signal. Practical application for m-sequence is in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping spread spectrum transmission systems (Golomb, 1994). Its application in electrical prospecting is emerging recently (Duncan et al., 1980, Ziolkowski et al., 2007). The major reason for transmitting pseudo-random m-sequence as source current is the broadband property of this signal. For SSIP, the complex resistivity at multiple frequencies can be obtained simultaneously. The underground geological structures can be estimated by calculating the IP parameters further (Chen et al., 2010).
However, SSIP measurements are contaminated by noise from a number of different sources, including telluric current, industrial current interference, major power lines and so on. When a survey area is located beside a mine, there will be a spike impulse interference appearing continuously, the amplitude of which is much higher than the Gaussian random noise and normal SSIP signal. This interference is mainly from the impulsive stray current and high-amplitude sferics pulses (Lou and Li, 1994). Stray current is caused by the electric power equipment. Sferics pulses are produced by lightning strokes propagating in the ionosphere-earth waveguide cavity (Jewell and Ward, 1963). There is a huge frequency overlap between SSIP signal and impulsive interference. If the interference is not effectively suppressed, the calculation of complex resistivity will be greatly affected.
Mean stack and digital filter are the common methods to reduce noise in FDIP data processing (Zonge and Wynn, 1975, Xi et al., 2014). Mean stack can effectively suppress the Gaussian random noise. If there is a little impulsive noise, this noise can also be reduced by prolonging observation time and increasing stack times. But when the interference is serious and impulsive noise is present continuously, mean stack is not effective. Digital filter based on the Discrete Fourier Transform (DFT) is widely used in a variety of FDIP instruments, which can suppress many kinds of noise by designing high-pass, low-pass, band-pass and notch filter. However there is a huge overlap between SSIP signal and impulsive interference in the frequency domain, which leads to an unsatisfactory result of digital filtering for impulsive noise suppressing. Many other practical methods have been developed for noise reduction in geophysics. These methods include the mean filter (Canales, 1984) and the median filter (Gallagher and Wise, 1981). Although the mean filter can suppress the Gaussian random noise effectively, it cannot suppress the spike impulsive noise. In contrast, the median filter can suppress the spike impulsive noise effectively but it cannot suppress the Gaussian random noise. Additionally, wavelet analysis is also applied in FDIP data processing, which may cause a signal distortion when impulsive noise is serious.
Robust processing of noisy (SSIP) data is investigated in this paper. Robust statistical methods are a generalized conception (Huber, 1981). This method has been widely used in geophysical signal processing. It is routinely used for estimating high-quality Magnetotelluric (MT) transfer functions (Egbert and Booker, 1986, Chave et al., 1987, Chave and Thomson, 1989). In addition, the technique is also applied for gravity and magnetic interpretation (Silva and Cutrim, 1989), controlled-source electromagnetic (CSEM) processing (Streich et al., 2013), transient electromagnetic (TEM) measurements processing (Buselli and Cameron, 1996), seismic data processing (Sabbione and Velis, 2013, Li et al., 2014) and geophysical monitoring problems (Lyubushin, 2002). In contrast, there have been few robust method applications in FDIP data processing. Whereas traditional method cannot suppress spike impulsive interference effectively, we implemented a robust statistical method to the SSIP data processing to improve the data quality. Specific applications include the following three aspects: robust least-squares regression is used to remove the linear trend from the original data. Robust M estimate is used to stack the data of all periods. Robust smooth filter is used to suppress noise in data after stacking. We first introduced the basic principle of robust M estimate for one-dimensional data and robust regression for multidimensional data. For robust statistical scheme, the most appropriate influence function and iterative algorithm are chosen by testing simulated data to suppress the outliers' influence. Then we introduced the basic principle and data processing procedure of SSIP. Finally, we demonstrated the effectiveness of this processing approach.
We carried SSIP testing for a 2D survey line beside a mine in Gansu province of northwest of China. There is a disseminated lead and zinc ore fault initially detected underground in the survey area. The SSIP profile was centered on the top of the target using intermediate gradient array protocol with multiple current electrode distance. The transmitter transmits 5-order m-sequence as source current, and the receiver array is based on GPS sync and ZigBee network, 25 receivers or 100 channels are supported for data acquisition. We applied robust methods to improve the data quality. Gaussian random noise and peak noise are suppressed effectively. There is a good agreement between the apparent resistivity anomalies and the geological target body with high polarization and low resistivity, which can help to improve the interpretation of previous geophysical surveys in the survey area.
Section snippets
Robust statistical method
There are outliers in original data inevitably due to the observation error and spike interference in the process to obtain SSIP data. Some ordinary statistical methods are quite sensitive to outliers. A few outliers can change the statistical results significantly. The objective of a robust statistical method is to deal with the assumed model using a reasonable method and suppress outliers' influence (Huber, 1981).
Application to a field case
We applied the robust processing methods to SSIP data recorded in a test site beside a mine in Baiyin city, Gansu province of northwest of China. The survey area is located in the east of Beiqilian Caledonian fold. The lava in this area is developmental. The deposit is under the control of the regional structures. We carried SSIP testing in a 2D survey line. The design of the survey was based on a target concept and refined from the interpretation of previous geophysical surveys (CSAMT, TEM and
Conclusions
Our results demonstrated that the SSIP method transmitting pseudo-random m-sequence for current injection and calculating complex resistivity response at four frequencies is practically applicable in exploring for structurally controlled deposits in the survey area. We also show that the measuring time can be reduced and that the data quality can be generally improved by using the robust processing method to suppress the outliers caused by spike noise. Applications of the robust approach
Acknowledgments
This research is supported by the Fundamental Research Funds for the Central Universities of Central South University, China (2382014bks101). SSIP data measured in Gansu province, China were kindly supplied by Champion Geophysical Technology Ltd. We are grateful to the help of company technician Wu Hong, Yao Hong-chun, Shen Rui-jie, Shi Hong-hua and Qiu Jie-ting in SSIP method instruction, instrument and data processing. We thank reviewers and editor for their reviews and comments.
References (37)
- et al.
Spectral induced polarization response to nanoparticles in a saturated sand matrix
J. Appl. Geophys.
(2012) - et al.
Rapid methods for interpretation of induced polarization anomalies
J. Appl. Geophys.
(1997) - et al.
A robust method for analyzing the instantaneous attributes of seismic data: the instantaneous frequency estimation based on ensemble empirical mode decomposition
J. Appl. Geophys.
(2014) - et al.
A robust method for microseismic event detection based on automatic phase pickers
J. Appl. Geophys.
(2013) - et al.
A robust maximum likelihood method for gravity and magnetic interpretation
Geoexploration
(1989) - et al.
Theoretical and experimental study of time domain-induced polarization in water-saturated sands
J. Appl. Geophys.
(2002) - et al.
Robust estimates of location: survey and advances
(2015) - et al.
The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data
Technometrics
(1974) - et al.
Robust statistical methods for reducing sferics noise contaminating transient electromagnetic measurements
Geophysics
(1996) Random Noise Reduction: 54th Annual International Meeting, SEG, Expanded Abstracts, 525–527
(1984)
Some comments on magnetotelluric response function estimation
J. Geophys. Res. Solid Earth (1978–2012)
On the robust estimation of power spectra, coherences, and transfer functions
J. Geophys. Res. Solid Earth (1978–2012)
Distributed data acquisition unit based on GPS and ZigBee for electromagnetic exploration
Suppression of spike interference in magnetotelluric survey
Chin. J. Geophys.
Techniques for nonlinear least squares and robust regression
Commun. Stat.
The development and applications of a wide band electromagnetic sounding system using a pseudo-noise source
Geophysics
Robust estimation of geomagnetic transfer functions
Geophys. J. Int.
Recursive M-estimators of location and scale for dependent sequences
Scand. J. Stat.
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