Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
Images of the cube root of the second invariant of the tensor signal in Figure 2 illustrate the response
around a non-economic kimberlitic pipe in Botswana before (a) and (b) after applying 100 iterations of
a MITRE smoothing kernel. The distortions to the tensor curvature field apparent in Figure 2a are
clearly being smoothed (Figure 2b), but without introducing distortions to the geometry of the pipe.
This is a good example of the need for careful de-noising of the full tensor signal before going any
further with local interpretation.
(a)
Figure 2. Detail of a pipe structure from Botswana, shown as an image of the cube root of the
second invariant of the tensor signal, (a) before, and (b) after 100 iterations of a MITRE
smoothing kernel.
Compensation / levelling methods
The most popular FTG levelling method currently used is a variation on a ‘heading’ correction. It is
reasonable to apply the method once but not 40 or 50 times as is sometimes done in practice. The
reason that in-line and cross-line, as well as tensor data is subjected to this excessive ‘correction’ is
the lack of an alternative approach. Using the Amplitude / Phase treatment of tensors, it is possible to
define a heading correction that works similarly to the well-known heading correction for scalar data.
All that is needed is to define a tensor average that preserves the intrinsic physical properties of
tensors. The heading correction can then be applied in the same manner as the traditional algorithm.
This correction, as we traditionally know it, adjusts the observed TMI by a variable amount based upon
the azimuth of the acquisition line. Compensation traditionally also adjusts TMI based upon a function
derived from figure of merit aircraft manoeuvres at high altitude. The inaccuracies in determining the
three rotational angles of an aircraft mean that we need more sophisticated de-rotational methods for
tensor data, with its inherent high curvatures, rather than simple linear adjustments. The year 2010
should see these emerge.
Furthermore, we examined perhaps the simplest of levelling procedures from surveying – the ‘Loop
Closure’ method (Green, 1983). This is a least squares minimisation technique that works very well in
weak gradient situations. The requirement of a least squares solution is that the sum of the observed
differences around every intersection be equal to the sum obtained from the estimated values. In
implementing this method for FTG data, the Frobenius Norm of the delta mis-closure tensor (i.e., the
matrix norm of an m by n matrix defined as the square root of the sum of the absolute squares of its
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(b)