Reduction to the pole near the equator with a Fourier-domain equivalent dipole layer

Abstract

Reduction to the pole (RTP) transforms the phase of the observed total-field anomaly, making magnetic interpretation easier. However, RTP operations are notoriously unstable at low latitudes and produce singularities at the equator. The equivalent-source approach is an appropriate method to address the well-known difficulties of RTP at low latitudes. Although we routinely use equivalent-source RTP algorithms in the spatial domain, they consume massive computational resources. In contrast, the equivalent-source method in the Fourier domain is more efficient and also invalid for RTP because of the inevitable use of the RTP operator in the inversion. To overcome this problem, we introduce a simple approximation of the RTP operator instead and then develop a novel algorithm to calculate the magnetic moments of the equivalent dipole layer from the total-field anomaly near the equator. Because the calculations are mainly performed in the Fourier domain, this algorithm is more efficient than the conventional spatial-domain method. We also impose a nonnegative constraint on the dipole layer to improve the results and significantly reduce the undesired striation associated with the low-latitude RTP. We evaluate the effectiveness of our approach with synthetic data near the equator, and the results indicate that the algorithm can produce an RTP field that is an accurate representation of the real field at the pole, even when accounting for the existence of noise. The new approach is applied to field data collected near the geomagnetic equator in the South China Sea. In the central part of the anomaly, we obtain a robust spindle shape of the RTP field, which is identical to the shape of a basalt formation in that location. Recent 1:1,000,000 scale marine geologic mapping has confirmed this presence, proving that our solution is an applicable approach to the problem.