A source-depth separation filter: Using the Euler method on the derivatives of total intensity magnetic anomaly data

Abstract

Derivatives of potential-field anomalies (or the anomaly gradients) enhance the field associated with shallow features and de-emphasize the field from deeper sources. The derivative approach of separating anomalies of shallow, intermediate, and deep sourves is, however, qualitative. Semiautomatic source location methods, such as the Euler method (also variously referred to in the literature as Euler's theorem on homogeneous functions, Euler's differential equation, EULDPH, and Euler deconvolution), the analytic signal method, and Werner deconvolution, developed since the 1980s use anomaly gradients to characterize sources of anomalies (i.e., the type of sources and their locations). In this article, we investigate the benefits of applying the Euler method on derivatives of anomalies to enhance the location of shallow and deep sources. Used appropriately, the method is suitable for characterizing sources from all potential-field data and/or their derivatives, as long as the data can be regarded mathematically as “continuous.” We also explain the reasons why the use of the Euler method on derivatives of anomalies is particularly helpful in the analysis and interpretation of shallow features.