# Fractal-Based Wavelet Filter for Separating Geophysical or Geochemical Anomalies from Background

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## Abstract

The widely used wavelet filtering technique holds potential to approach anomaly–background separation in geophysical and geochemical data processing. Wavelet statistics provide crucial information on such filtering methods. In general, conventional (Gaussian-type) statistical modeling is insufficient to adequately describe the heavily tailed and sharply peaked (at zero) distribution of the wavelet coefficients of irregular geo-anomaly patterns. This paper demonstrates that the cumulative (frequency) number of the wavelet coefficient yields a power-law scaling relationship with the coefficient based on wavelet transform of a fractal/singular measure. This wavelet coefficient–cumulative number power-law model is proven to be more flexible and appropriate than the Gaussian model for characterizing the scaling nature of the coefficient distribution. Accordingly, a fractal-based filtering technique is developed based on the wavelet statistical model to decompose mixed patterns into components based on the distinct self-similarities identified in the wavelet domain. The decomposition scheme of the fractal-based wavelet filtering method considers not only the coefficient frequency distribution but also the fractal spectrum of singularities and the self-similarity of real-world features. Finally, a synthetic data test and real applications from two metallogenic provinces of China are used to validate the proposed fractal filtering method for anomaly–background separation and identification of geophysical or geochemical anomalies related to mineralization and other geological features.

## Keywords

Wavelet transform Multifractal modeling Fractal filtering Anomaly–background separation## Notes

### Acknowledgements

This paper is based on the Ph.D. dissertation of the first author. Thanks are due to Eric Grunsky, Frits Agterberg, Jian Wang, and two anonymous reviewers for their comments that improved this manuscript. This research was jointly supported by the National Key Research and Development Program of China (no. 2016YFC0600508), National Natural Science Foundation of China (nos. 41702355, 416723328, and 41572315), and Fundamental Research Funds for Central Universities (CUG170635) and Most Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources (MSFGPMR09), China University of Geosciences (Wuhan).

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