Inversion of on-axis magnetic anomalies

Abstract

The theory for recovering crust magnetization from along-strike and, especially, axial magnetic profiles is examined. We develop a conventional Fourier technique that takes into account the special magnetic cross-section at a ridge axis including the thinning of layer 2A. Such an approach might be completely inappropriate because it is assumed that the observation path is perpendicular to all the magnetic variability, whereas in fact the path lies in the direction of least magnetic variation. To study this question and to overcome possible deficiencies, we consider a statistical modification of the theory in which the magnetization is treated as a planar stationary process in a thin layer with known power spectrum. The relationship between two signals is studied: the magnetic anomaly on a straight path at the sea surface, and the magnetization in the crust immediately under the observation track. The coherence between the two signals can be calculated, as well as the transfer function between them. We test the ideas with data from a long axial magnetic profile on the southern East Pacific Rise compiled by Gee and Kent. A model power spectrum is estimated from these data: the spectrum is red and, as expected, highly elongated perpendicular to the strike of the ridge. We find strong coherence (γ2 > 0.8) between the magnetic anomaly and the subtrack magnetization for wavelengths longer than 50 km, but coherence falls sharply for smaller scales. The naive, 1-D filter theory incorrectly predicts a close relationship down to much finer scales (3 km). Calculations for hypothetical surveys off-axis predict that there is always a band of high coherence, but only for an on-axis survey does the good correlation extend to infinite wavelength. We conclude that, in a wide variety of circumstances, the magnetic anomaly and the subtrack magnetization are highly correlated in a particular wavelength interval that depends on the shape of the power spectrum.