Efficient equivalent-layer technique for processing irregularly spaced magnetic data on uneven surfaces

ABSTRACT We develop a new rapid and robust equivalent-layer method for processing large magnetic data sets that can deal with irregularly spaced data points on undulating surfaces. Our method estimates an equivalent layer by numerically solving the upward continuation integral for a given set of magnetic data. Although this estimated layer allows performing specific spatial transformations, such as interpolation and continuations of any potential-field data, it cannot be used to perform conventional phase transformations on magnetic data, such as the reduction to the pole, because this layer requires a magnetic moment distribution over the equivalent layer of dipoles. To overcome this drawback, we transform the estimated equivalent layer into a planar equivalent layer of dipoles that equally reproduces the observed magnetic data. To carry out this transformation, we first use the fact that the estimated layer obtained by solving the upward continuation integral is a scaled version of the magnetic data on the layer plane, i.e., it can be considered a harmonic function. Then, we use the upward continuation integral to continue the estimated layer into a planar and regular grid, which results in a second equivalent layer. Finally, we apply a fast 2D discrete convolution to transform this second layer into a planar equivalent layer of dipoles that also fits the observed magnetic data. Applications to synthetic and real data show that our methodology is able to efficiently process magnetic data, combining the robustness of accommodating irregularly spaced data with the ability to perform phase transformations.