Interpretation of magnetic anomalies using analytic signal derivatives

Aeromagnetic surveys play an important role in the exploration of natural resources of economic interest, as well as in regional geologic mapping. Magnetic anomalies caused by the lateral variations of magnetization in the earth’s crust often are characterized by smooth regional gradients with isolated features. The main goal of magnetic prospecting is to infer both the geometry and the magnetization of the geologic structure that causes the observed magnetic anomalies. However, akin to other potential-field methods, interpretation of magnetic field anomalies is non-unique because more than one distribution of magnetization (i.e., magnetic dipole moment per unit volume) and source geometry can explain the same observed magnetic anomaly. One important goal in the interpretation of magnetic data is to determine the geometry and the location of the magnetic source. This has recently become particularly important because of the large volumes of magnetic data that are being collected for environmental and geological applications. To this end, a variety of semiautomatic methods based on the use of derivatives of the magnetic field have been developed to determine magnetic source parameters such as locations of boundaries and depths. As faster computers and commercial software have become widely available, these techniques are being used more extensively. Utilizing first-order derivatives of the magnetic field, Euler deconvolution was first applied on profile data and subsequently on gridded data. The method has come into wide use as an aid for interpreting magnetic data. The main advantage of the Euler method is that it can provide automatic estimates of the source location of the causative magnetic anomalies. However, it requires an assumption about the geometry of the body that is the actual source. In practice, assumption is achieved by specifying a structural index to define the source geometry in generalized situations, setting a good strategy for discriminating, and selecting meaningful solutions. Recent extensions to the Euler method allow to be estimated from the data, with the calculation of Hilbert transforms of the derivatives. The SPI method, which requires second-order derivatives of the field, uses a term known as the local wavenumber to provide a rapid estimate of the depth of buried magnetic bodies. The local wavenumber was defined as the spatial derivative of the local phase. The SPI method worked on gridded data, but assumed a contact model (=0). Later extensions to the method enabled calculation of, but these required third-order derivatives. The calculation of third-order derivatives from gridded data is problematic, so the use of profile data was advocated by Smith et al. (2005). In a more recent paper, a linearized least-squares method was applied to obtain information about the depth and nature of the buried sources from first- and second-order derivatives of the field (the analytic signal and its horizontal gradient). However, their approach requires knowledge of the horizontal position of the source, inferred from the peak of the analytic signal. Inappropriate sampling of the data and/or noise can make the selection of the horizontal position inaccurate. As a result, these inaccuracies lead to errors in the estimatation of both the depth and the nature of the sources. To overcome the limitations of the previous studies and to improve the process of estimating the source parameters using the analytic signal approach, an automatic method is presented to estimate horizontal location, depth, and the nature of 2D magnetic sources using derivatives of the analytic signal. Derivatives of the field of up to only the second order are used. First, a generalized equation is derived and solved using the least-squares method to provide source location parameters without any a priori information about the nature of the source. Then, using the estimated source location parameters, the nature of the source is obtained. To implement the method, the anomalies are first identified using the analytic signal peak. The method is then applied to a data window around the peak, where the signal-to-noise ratios of both the analytic signal derivative and the horizontal gradient of the analytic signal are relatively high. The determination of the number of data selected is based on the quality of the data and interference from nearby sources. The optimum number of selected data is small enough to see only a single anomaly and large enough to contain sufficient variations in the anomaly within the window. In this study, data for which the analytic signal values are greater than 10% of the peak value were used within each window. The presented method was applied successfully to synthetic magnetic data from 2D models with random noise as well as on a 3D synthetic Bishop model. In synthetic examples, we tested the feasibility of the proposed method; using theoretical anomalies of 2D magnetic models buried at different depths. These models were a horizontal cylinder with an infinite horizontal extent and a thin dike with infinite depth extent. The total-field anomaly values were calculated along a 100 km profile striking south–north at intervals of 1 km. Good results were obtained on a real magnetic dataset related to an ore field in Jalal-Abad,Iran, which has a broad correlation with drilling. In this regard, the results obtained by the proposed method were selected as start point in 2D modeling, and this shows a good fit with the measured profile.