A fuzzy logic-based filter for the removal of spike noise from 2D electrical resistivity data Jalal Ferahtia a, ⁎, Nouredine Djarfour a , Kamel Baddari a , Aissa Kheldoun b a Laboratoire de physique de la Terre (LABOPHYT), Université M'hamed Bougara, Faculté des hydrocarbures et de la chimie (FHC), 35000 Boumerdès, Algeria b Institute of Electrical and Electronical Engineering (IGEE), Université M'hamed Bougara, 35000 Boumerdès, Algeria abstract article info Article history: Received 7 March 2012 Accepted 17 August 2012 Available online 25 August 2012 Keywords: Electrical resistivity data Filtering Fuzzy logic Inversion Pseudosection Spike noise In this paper, a filter based on fuzzy logic is proposed to remove spike noise from 2 dimensional electrical re- sistivity data. The noise detection used in this paper is based on differentiating noisy samples from the central sample inside a moving window. These fuzzy derivatives are used by the fuzzy inference system to detect corrupted samples. To assess the performance of the proposed filter for the removal of spike noise, the root-mean squared error as well as the signal-to-noise ratio were used as an objective criterion. It has been demonstrated by synthetic and real examples that the proposed filter achieves quite good results com- pared to the standard median filter as well as to the very effective SD-ROM filter. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Until the late‐1980s, conventional electrical resistivity sounding and profiling methods have been routinely used in geotechnical engi- neering (Ogilvy et al., 1980), groundwater (Kossinski and Kelly, 1981), mining (Peric, 1981), and archaeology (Noel and Xu, 1991). The past decade has seen significant advances in two- and three‐ dimensional electrical resistivity imaging (ERI) data acquisition systems and inversion techniques. These developments allow im- aging of relatively complex structures and improving the interpre- tation models. Recently, ERI technique has been successfully used in environmental and pollution surveys (Dahlin, 1996; Daily et al., 1998; Grellier et al., 2008; Guérin et al., 2004; Zouhri and Lutz, 2010). Nevertheless, as for most geophysical measurements, ERI data are fre- quently corrupted by various types of noise. Some of these are coherent noise, such as near-surface inhomogeneities (NSIs) (Ritz et al., 1999); others are random noise such as telluric currents or electrode polarization (Cornacchiulo and Bagtzoglou, 2004). Both types of noise will have a sig- nificant effect on the inversion process, and hence, the quality of the inter- pretation model (LaBrecque et al., 1996). Therefore, to improve the inversion process, removal of such noise is very important. For that purpose, a large number of filtering techniques have been proposed so far. Among them are linear averaging filters (such as the low-pass filters). Their mathematical simplicity has made them methods of choice for many years (Patella, 1986). They are usually used to remove additive Gaussian noise. However, in the presence of impulsive noise they do not produce convincing results. To over- come this problem, nonlinear filters are often used. One of nonlinear filters family includes filters based on order statistics (OS). The stan- dard median filter (Tukey, 1974) is a good example of OS filters; it is among the most commonly used filter for spike noise removal (Gonzalez and Woods, 1992). Median filter is characterized by sim- plicity and robustness. Basically, it outputs the median of the samples contained in its filtering window. Nevertheless, it has the undesirable property of altering both noise and signal of interest. To overcome this problem, a variety of OS filters have been proposed; among them is the signal dependent rank ordered mean (SD-ROM) filter (Abreu et al., 1996; Chandra et al., 1998; Moore and Mitra, 2000; Moore et al., 1999). This filter is a detection–estimation filter; it was demonstrated to be highly effective in filtering spike noise (Ferahtia et al., 2009). The SD-ROM filter uses a spike detector that aims to de- cide whether the sample under consideration is corrupted or not. If the sample is considered by the spike detector as corrupted, it is re- placed by an appropriate estimate (the ROM). Otherwise, i.e., if the sample under consideration is uncorrupted, it passes unchanged through the filter. Recently, fuzzy set theory and fuzzy logic emerged as an alterna- tive and flexible approach to solve complex problems even with inac- curate, incomplete and/or noisy information which is often the case with geophysical data. However, to our knowledge the application of fuzzy logic to ERI data processing is not fully tested. This paper addresses the problem of removing spike noise from 2D ERI data using a fuzzy logic-based filter. We show that fuzzy logic helps the automatic detectability and removal of spike noise Journal of Applied Geophysics 87 (2012) 19–27 ⁎ Corresponding author. E-mail address: jalelferahtia@yahoo.fr (J. Ferahtia). 0926-9851/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jappgeo.2012.08.007 Contents lists available at SciVerse ScienceDirect Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo