Spectral Methods for Magnetic Anomalies

Spectral methods, that is, those based in the Fourier transform, have long been employed in the analysis of magnetic anomalies. For example, Schouten and MaCamy's Earth filter is used extensively to map patterns to the pole, and Parker's Fourier transform series facilitates forward modeling and provides an efficient algorithm for inversion of profiles and surveys. From a different, and perhaps less familiar perspective, magnetic anomalies can be represented as the realization of a stationary stochastic process and then statistical theory can be brought to bear. It is vital to incorporate the full 2-D power spectrum, even when discussing profile data. For example, early analysis of long profiles failed to discover the small-wavenumber peak in the power spectrum predicted by one-dimensional theory. The long-wavelength excess is the result of spatial aliasing, when energy leaks into the along-track spectrum from the cross-track components of the 2-D spectrum. Spectral techniques may be used to improve interpolation and downward continuation of survey data. They can also evaluate the reliability of sub-track magnetization models both across and and along strike. Along-strike profiles turn out to be surprisingly good indicators of the magnetization directly under them; there is high coherence between the magnetic anomaly and the magnetization over a wide band. In contrast, coherence is weak at long wavelengths on across-strike lines, which is naturally the favored orientation for most studies. When vector (or multiple level) measurements are available, cross-spectral analysis can reveal the wavenumber interval where the geophysical signal resides, and where noise dominates. One powerful diagnostic is that the phase spectrum between the vertical and along-path components of the field must be constant 90 degrees. To illustrate, it was found that on some very long Project Magnetic lines, only the lowest 10% of the wavenumber band contain useful geophysical signal. In this case the spectra and cross spectra show that the source of the noise is instability in the gyro platform. Spectral techniques should always be applied to vector data in order to avoid overinterpretation of short-wavelength features.