Airborne Gravity 2010 - Geoscience Australia

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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. 133 (b)
Airborne Gravity 2010 Figure 2. Gravity gradient response for each component on a horizontal surface 50 m above the peak of a 300 m high Gaussian hill. Units of measurement are eotvos (E). Figure 3. Difference between the terrain effect calculated with the adaptive quadtree method and that from a full-resolution surface-based method. The maximum error threshold specified for the adaptive mesh method was 1 E. Color bars range from -1 to 1 E. 134
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