Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
Changes in DEM resolution can have a dramatic effect on local features. Changing the resolution from
1 to 30 m for our test example (Figure 4a) introduced a local error of over 400 E, while the RMS error
remained below 1 E. When studying the adequacy of a particular resolution in terrain correction, RMS
differences between maps can be a misleading measure of validity since the power is concentrated
over DC and long-wavelength signals that are largely unaffected.
(a)
Figure 5. (a) Euclidian norm ( L 2 ) of the unfiltered Tzz gravity gradient component of the terrain
model as a function of terrain resolution. The rapid decrease beginning at 15 m indicates a loss
of total energy in the system, analogous to a loss in accuracy with decreasing resolution. (b)
Euclidian norm of the acquisition filtered Tzz gravity gradient component of the terrain model as a
function of terrain resolution. Note the change in scale from (a). There is no appreciable reduction
in accuracy with resolutions less than 20 m.
We calculated the 2 L (Euclidian) and L � (i.e., maximum of the absolute values) norms and errors as
functions of decreasing resolution (Figure 5 and Figure 6). The norms of the calculated Tzz
components are related to how much energy is lost with decreasing resolution. While the Euclidian
norm indicates how much energy is lost in the whole map, the L� norm is a measure of the reduction
of the largest anomaly when compared across decreasing resolutions.
Figure 5a shows that the non-acquisition filtered corrections do not improve in accuracy with a
horizontal resolution better than 15 m since the terrain clearance acts as a low-pass filter on the
acquired data. The post-acquisition filtered corrections (Figure 5b) do not improve in accuracy with a
resolution better than 20 m. Decreasing the resolution past 20 m, the amount of energy lost with
decreasing resolution is 10 times slower for the acquisition-filtered dataset than for the non-filtered
data. Therefore, the gains in accuracy for increasing the resolution for the terrain correction diminish
faster when the data have been low-pass filtered. Figure 6 shows the same result through an L� norm
in terms of errors. For this case, the optimal terrain correction will be performed with a DEM that has
20 m horizontal resolution.
The above quantitative conclusions are based on a specific example that is representative of common
survey conditions and methodology. In particular, terrain clearance will be an important consideration
when performing this modelling. As the terrain clearance increases, the required resolution will, at
some point, cease to be a function of acquisition filtering and instead become a function solely of
terrain clearance.
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(b)