2D Discrete wavelet transform for denoising magnetic data Felipe F. Melo*, Valéria C. F. Barbosa and Yolanda Jiménez-Teja, Observatório Nacional Summary Discrete wavelet transform (DWT) is a valuable tool in signal and imaging processing, in particular for denoising. Its performance in denoising potential-field data has been proven to be superior to that of traditional techniques. We analyze the most common thresholding techniques: soft and hard with cycle spinning, for denoising magnetic data. To certify the efficiency of denoising and improvement of the filtered data we use qualitative and quantitative analysis. Tests on noise-corrupted Bishop model prove that the soft thresholding changes the amplitude of the data while hard thresholding with cycle spinning generates better results. We show the quality of hard thresholding with cycle spinning applying it to real aeromagnetic anomaly over the Goiás Alkaline Province, Brazil, and quantifying the improvement of the denoised data. Introduction In 2017, the Brazilian Geological Service (CPRM) made publicly available a set of 95 airborne surveys called series 1000. These surveys were flight between 1953 and 2006 and consist of magnetic and gamma-ray data. In order to deal properly with these datasets some reprocessing and/or preprocessing is often required. Discrete wavelet transform (DWT) has been used over the past 20 years to denoise potential-field data successfully (e.g. Ridsdill-Smith and Dentith, 1999; Fedi et al., 2000; Leblanc and Morris, 2001; Zhang et al., 2017). This technique has proven to be a valuable tool in enhancing the quality of the denoised data. A common property of the random noise is the presence of significant power in the high-frequency band. On this case, the Fourier transform is commonly used to denoise potential- field data (Naidu and Mathew, 1998). However, the Fourier transform has the cumbersome that the space resolution is absent for any given frequency (Fedi and Quarta, 1998). This means that we cannot directly correlate a signal in Fourier domain to its position in space/time domain. This characteristic is because all the data is transformed together to Fourier domain, thus the high-frequency spectral content produced by noise maybe not properly separated from the high-frequency spectral content produced by geologic bodies (e.g., shallow-seated sources). Namely, the noise cannot be removed by Fourier domain filtering because it may have the same spectral content as the signal. One way to around these limitations is the windowed Fourier transform but it has the drawback that it uses the same window size for all frequencies. Hence, the frequency resolution analysis is the same at all locations (Graps, 1995) and once more maybe is not possible to separate the high- frequency spectral contents due to noise from those produced by geologic bodies. The DWT overcomes these limitations allowing the decomposition of the data into a linear combination of scaled and translated versions of the basic wavelet (Mallat, 1989; Chui, 1992). In the literature, we can find several works where the DWT is applied to denoise one-dimensional data: for instance, Ridsdill-Smith and Dentith (1999) applied it to a magnetic dataset using hard threshold and Lyrio et al. (2004) employed it on gravity gradiometry data using an adaptive thresholding. For denoising two-dimensional gridded magnetic data sets, Leblanc and Morris (2001) applied the DWT using soft threshold and Fedi and Florio (2003) applied it to decorrugate and remove directional trends using the local threshold parameter with soft thresholding. Fedi et al. (2000) applied the DWT on vertical derivatives of a gravity dataset using the local threshold parameter with soft thresholding and Zhang et al. (2017) applied it to gravity gradiometry data with an adaptive Bayesian threshold and mixed thresholding. In addition to denoising of potential- field data, some authors applied the wavelet transform to filter undesired anomalies (Fedi and Quarta, 1998; Fedi et al., 2004; Paoletti et al., 2007) and to perform interpretations (Chapin, 1997; Oruç and Selim, 2011; Oruç, 2014). Most of the above-mentioned authors compared the results of DWT with the Fourier filtering, and other techniques for denoising, proving that the DWT performed better in all cases. Therefore, in this work, we focus on the use of the DWT with different thresholding methods: soft and hard. For the hard thresholding case, we will consider a variant: the cycle spinning algorithm (Coifman and Donoho, 1995). In the literature, the consequences of using noisy data or improperly denoised data to the interpretation are well known. For example, Florio et al. (2014) shown that improperly denoised data lead to wrong depth estimates of the geologic bodies using Euler deconvolution as the interpretation method. Therefore, as qualitative quality control for denoising we analyze the input data, the denoised data and the noise. Moreover, quantitative enhancements are measured with the signal-to-noise ratio (SNR) and root mean square (RMS) of the predicted noise. Here, we compare the use of DWT with soft thresholding and hard thresholding using the cycle spinning algorithm for denoising and noise determination. Applications to theoretical magnetic data of the Bishop model corrupted by additive pseudorandom Gaussian noise show that the DWT with hard thresholding using cycle spinning yields better results, both quantitatively and qualitatively, than the DWT 10.1190/segam2018-2998295.1 Page 1469 © 2018 SEG SEG International Exposition and 88th annual Meeting Downloaded 09/01/18 to 189.122.99.170. 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