Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
To illustrate the accuracy of the method, we use the Gaussian hill topography model presented in
Figure 1. The hill extends from a base elevation of 0 m to an elevation of 300 m at its peak. The total
number of observations locations is 625. We calculated the gravity gradient response of this terrain at
350 m above ground level for each component and allowed a 1 E error. Note that a separate
discretisation is determined for each observation location. We show the adaptive discretization of the
Gaussian hill for a single observation location in the bottom of Figure 1. Note that the asymmetry of
the discretisation in this instance is a consequence of the centre of the initial cells not being coincident
with the peak of the model.
(a)
Figure 1. (a) Gaussian hill with height equal to 300 m. (b) Automated adaptive quadtree
discretization of terrain to achieve a maximum of 1 E accuracy for all tensor components for an
observation made 50 m directly above the peak.
We compared the response of the Gaussian hill calculated with an adaptive quadtree-discretized DEM
(Figure 2) to the result for a regularly-gridded, surface-based forward modelling scheme. Although we
allowed the algorithm as much as 1 E error, the maximum difference between the two datasets was
0.17 E (Figure 3).
In order to evaluate the efficiency of the adaptive algorithm, we examine the number of calculations
performed. The full model contains 729,088 cells, which means that there are 455,680,000
calculations. Using the 1 E error level example, our method made 1,468,486 calculations, which is 310
times less (or 0.3%) of the full model calculation total. An overhead related to the evaluation of the
threshold conditions must be factored into this assessment. It is important to note that the degree of
efficiency is highly dependent upon the terrain and data locations.
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(b)