Trend Removal And Detection Of Overlapping Magnetic Field Anomalies By Wavelet Analysis

Total magnetic field data measured for geophysical exploration purposes comprise the superposition of the effects of all underground magnetic sources. Usually the targets in magnetic<br>exploration are small, shallow buried bodies, and their magnetic field is superimposed on the regional field that arises from larger and/or deeper source or sources located further away. Sometimes inaccurately removed core fields or large scale topographic features also give rise to regional components. The regional field is generally smooth, adding a trend to the data. The estimation and subtraction of this trend field yields the residual field that corresponds to the target sources. Evidently, the reliability of the interpretation of the residual field depends on the correct estimation of the regional field. In this work the regional-residual separation in the wavelet domain is performed with the aid of the discrete wavelet transformation (DWT) realized with the use of compactly supported wavelets (Daubechies, 1990) with two or three vanishing moments. These wavelets are orthogonal to first or second order polynomials. This means essentially that the regional field (usually represented by a first or second order polynomial) is invisible to the wavelets and thus the regional field is almost entirely hidden in the coefficients of the coarser level of the wavelet transformation. However, in the realization of the DWT as decimated and periodized, the periodic assumption produces some non-zero contribution in a few detail coefficients. Therefore the suppression of all detail coefficients degrades the calculated regional field. To avoid such a distortion we can process a relatively large symmetrical extension of the<br>data sequence from both sides. Alternatively, we can use an internal model for the polynomial field that controls the separation. Because of the spectral overlap, the approximation of the regional field contains some of the energy of the residual field. We can tackle this problem by analyzing the reconstructed approximation of the regional field in a proper new wavelet basis (with the same number of vanishing moments) and repeating the separation procedure. The choice of the model is empirical; thus it depends on the interpreter’s experience. The wavelet that concentrates the energy of the regional field in the low-resolution coefficients and spreads the energy of the residual field in the high-resolution coefficients gives best results. A good choice of<br>wavelet pairs for the first order model is the Db4 and the triangular biorthogonal wavelet. For the second order model, the combination of the Db6 and Villasenor2 wavelets gives a very good separation. The proposed method preserves the signal’s features and has the ability to detect the possible local variations of the regional field. The same method can be used for the detection of overlapping magnetic field anomalies. Although the method may have application in more general settings we are mostly focused on archaeological geophysics, a fact that limits the kind of regional-residual problems which occur in certain ways.