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Equivalent Sources: Rapid Calculation in the Frequency Domain and Application to Leveling Correction

The equivalent source is usually calculated by an iterative method, designed to converge on the observed potential field, magnetic or gravitational. Each iteration involves two Fourier transforms, one forward and one inverse. As the number of grid point increases the time penalty may become prohibitive. However, the number of transforms can be dramatically reduced by the a priori transformation of the observed potential field to the frequency domain. We describe this method which reduces the number of Fourier transforms from n to two, and demonstrate its use on a simple magnetic anomaly. An extension of this equivalent source technique is also given for the case of a draped magnetic survey that requires leveling correction. The observed data is separated into layers according to the height changes, and the equivalent source is iteratively calculated via comparisons of the upward continued data. Whilst this process is computationally intensive, it is designed to scale with the complexity, and hence the discretisation, of the topographical changes. This gives the method a speed advantage compared with similar Taylor series approaches. A synthetic example containing multiple dipole sources is used to test the method, and to illustrate the advantages and differences of draped surveys and the need to reduce the data to a common datum.