Susceptibility Inversion

Use the Calculate > Lateral Susceptibility Inversion option to perform lateral susceptibility inversion on a layer in the GM-SYS 3D model. This is a two-stage process, optionally running both Parker-Huestis and Apparent Susceptibility Sharpening methods to optimize the layer susceptibility.

Lateral Susceptibility Inversion dialog options

Top of inversion layer	Drop down list of the model’s layers, filtered to show only those with susceptibility defined by a grid. The layer's corresponding lateral susceptibility distribution grid will be altered.
Method	Select which inversion method(s) to use: Options are Both (default), Parker-Huestis, or Apparent Susceptibility sharpening. Subsequent fields are enabled or disabled according to their relevance to the selected method(s).
Max Parker-Huestis iterations	Run up to this number of iterations using the Parker-Huestis method, stopping whether or not the convergence target has been reached.
Max sharpening iterations	Run up to this number of iterations using the Apparent Susceptibility sharpening method, stopping whether or not the convergence target has been reached.
Convergence limit (nT)	Inversion will stop when either the mean error or the standard deviation of the error is less than this limit. Note that under certain conditions, the calculations may not converge at all. The code will detect divergence and terminate the appropriate method accordingly.
Lower high-cut limit	A cosine roll-off high-cut filter is applied to the misfit before it is passed to the Parker-Huestis method. Enter the beginning of the cosine taper. The default wavelength is equivalent to 0.5 times the Nyquist.
Upper high-cut limit	Enter the short-wavelength end of the taper. The default wavelength is equivalent to 0.7 times the Nyquist. If you enter numbers that are > 1.0, they will be interpreted as wavelengths (distances) in ground units. If you enter numbers that are <= 1.0, they will be interpreted as fractions of the Nyquist.
Nominal top of surface	The misfit will be downward continued to this elevation. This level should be at or above the highest elevation of the layer being inverted; if it is too deep, the inversion will fail to converge. The default value is the magnetic survey elevation.
Nominal mean of surface	Mean elevation of the layer being inverted relative to sea level, which must be deeper than Nominal top of surface. The default value is the calculated mean of the selected layer's relief surface.
Regional offset	This constant will be subtracted from the observed magnetic data before inverting.
Constraints grid	Designated constraint grid for restriction of calculated values.

Application Notes

In order to perform a lateral susceptibility inversion, the susceptibility of the layer must be defined by a lateral susceptibility grid.

The Parker-Huestis method (based on Parker and Heustis (1974) - see References link below) typically does a good job of fitting the long wavelength aspects of the anomalies. However, more than 1 or 2 iterations using this method is usually counterproductive. The Apparent Susceptibility sharpening method (MAGMAP Apparently Susceptibility filter) does a better job of fitting the short wavelength features (hence "sharpening"). However, too many sharpening iterations will eventually cause "ringing"; 5 or 6 iterations are usually adequate.

If the Nominal top of surface is set below the observation level, the inversion involves a downward continuation of the magnetic anomaly data to the Nominal top of surface elevation. In this case, a high-cut filter is often necessary to prevent the input anomaly from "blowing up" when the highest frequencies are amplified by the downward continuation filter. If the input anomaly grid has high frequency noise from survey resolution limits or high frequency signal from shallow magnetic sources (e.g., volcanics or culture), the inversion algorithm may not be able to produce a susceptibility distribution at the layer's elevation that can account for the high frequency portion of the input residual anomaly. The inversion algorithm will cause the susceptibility to oscillate rapidly in its attempt to fit the high frequency signal. The user-specified high-cut filter can help stabilize the inversion and prevent the inversion process from oscillating. However, you should also avoid over-filtering, as the inversion results may be smoother than desired. You can test by repeatedly running the inversion, filtering heavily on the first attempt and then gradually lessening the filter.

Magnetic susceptibility inversion can be improved by an understanding of the effect of the vertical distance between the observation level and the top of the target layer relative to the grid interval (i.e. depth/width ratio). In cases where the chosen grid interval is small, (less than one third of the depth), the number of Taylor Series terms used in the calculations needs to be increased to a larger odd number (say 7, 9 or 11) in order to allow enough high frequency variation into the inversion grid to fit the rapidly varying susceptibility. Unfortunately, there are limits to how much the Taylor Series order can be increased to fit short wave-length changes at significant depth because the inversion can oscillate and "blow up". Even high-cut filtering of the magnetic anomaly does not completely solve this problem of the inversion "blowing up". The ratio of the depth to the target layer divided by the grid spacing is critical. If this ratio is greater than ~3:1, and the Taylor Series Order is increased to 9 or 11, the process can still "blow up" even with a moderate high-cut filter. Until the user is comfortable with the simultaneous influences of vertical relief/depth of inversion surface, noise and filter cutoffs - stick to a ratio of 3:1 or less.