oa Magnetic depths to basalts -- extension of Spector Grant method

The Spector Grant method of estimating depths from magnetic power spectra is extended and automated to provide a regular set of depth estimates across the Northern Territory, where extensive magnetic basalts are otherwise poorly depthed.

Spector and Grant identified a simple exponential as being a common characteristic of prismatic sources, so that depth is a simple factor times a selected slope of the logarithmic power spectrum of the TMI. Whereas their method, now classic, requires a judicious choice of the characteristic slope of the power spectrum, automation requires that short line segments be fitted along a length of the spectrum. Their slopes constitute a slope spectrum, so the single Spector Grant factor is not sufficient to calculate the depth at the different frequencies. Forward modelling is used here to provide separate factors along the spectrum.

Maximum generality is attempted by using a magnetic dipole as the element in a convolution of 1000 elements in a thin flat box. Repeated across various depths, correlation between the various depths and the slope spectra arising from them has allowed calibration of the latter. Modelling has also identified where the correlation fails, providing a criterion for cutting off the spurious results from the high frequency end of the spectrum.

A result of the modelling is that the low frequency end of the power spectrum of a random convolution of many dipoles closely resembles the power spectrum of the dipole itself. Up to the cut-off, the depth factors along the slope spectrum for the dipole then provide the conversion factors for the ideal case of a finely lumpy slab.

Accordingly the formula connecting slope and depth has been extended, and a large number of depth profiles across the Northern Territory have been automatically calculated.