Application of the curvelet transform to synthetic and real magnetic data

Abstract

ABSTRACTCurvelets are multiscale and multidirectional operators that have many applications in image and data processing. Because of the effect of depth and source dimensions on the wavelength (or frequency content) of potential field anomalies, the study of magnetic data in the curvelet domain is of interest. In this paper, the consequences of transforming magnetic data to the curvelet domain are studied using synthetic models and real data for the first time. Based on the results of the theoretical models, we applied the method to airborne and ground magnetic survey data. We show the utility of the curvelet transformation for removing relatively large amounts of noise and its utility as a qualitative method for relatively robust delineation of magnetic sources, especially sources that are close, with overlapping anomalies. In the first step, the data in the curvelet domain are divided into scales or bands. Each scale is then split into multiple sub-bands that have different directional properties. We focus on the scale properties of magnetic data by studying the effects of debilitation or removing some scales in the curvelet domain. The first band (scale 1) of magnetic data in the curvelet domain corresponds to lower frequencies and contributes most to the energy of the signal. Thus, decreasing or removing this scale can highlight detailed (high-frequency) information. By contrast, the highest band has the highest frequency content and contains most of the noise. In this paper, we show that applying the inverse curvelet transform to the middle bands only (after deleting both low and high bands) gives the best results for the purpose of defining the horizontal locations of compact magnetic bodies.