6.4. Large data set example

In the next example a synthetic data set is introduced, where a Wenner array is combined with a pole-dipole array and covers an 8-km long profile. The synthetic model is a 1000 Ohm- m half space covered by a 50-m thick overburden of variable electrical resistivity (200 Ohm-m section on the left, followed by 50 Ohm-m section in the middle, followed by 500 Ohm-m section on the right. The background resistive media is hosting two rectangular bodies at 150-m depth each. The prism on the left side is resistive (10,000 Ohm-m resistivity) and the prism on the right side is conductive (50 Ohm-m) (Figure Fig. 6.28 a).

For the Wenner array the following configuration was used: number of stations = 400; minimum a-spacing = 80 m; maximum a-spacing 1367 m (spreading coefficient: 1.5 to accommodate up to 8 spreads per station). The spreading coefficient in this case is the multiplier used to calculate the increased spread distance between the potential electrodes for each station, given the minimum separation ) The total number of data for Wenner array (considering number of stations and all possible separations) was 2610 (Figure Fig. 6.28 b).

The pole-dipole synthetic survey used a=75 m and n=1,10. The current pole was fixed on the right hand side of the array. This resulted in a total number of pole-dipole data of 1005 (Figure Fig. 6.28 c). The combined Wenner and pole-dipole data set contains 3615 data (Figure Fig. 6.28 d).

This synthetic model was discretized with a mesh, composed of 17918 cells (including padding), with the smallest cells reaching 30 m horizontally and 15 m vertically for the core region (depth to 1 km).

../_images/synLarge.png

Fig. 6.28 (a) The true model create for a large-scale synthetic data set by combining Wenner and Pole-dipole configurations. (b) The synthetic data from the Wenner array and (c) pole-dipole array are combined to get the (d) synthetic data for the entire data set.

This synthetic data set was contaminated with 5% Gaussian noise and inverted using \(l_1\) measure for model objective function in order to accommodate a more blocky inversion result. The inversion control file is provided below:

../_images/dcinv_largedata.png

The inversion converged in 17 iterations (Figure Fig. 6.29 a)) and was able to reconstruct all of the features shallower than 500-m of depth. This is consistent with the depth of investigation for this survey, based on the sensitivity (Figure Fig. 6.29 b)).

../_images/synLargeRec.png

Fig. 6.29 (a) The true model create for a large-scale synthetic data set by combining Wenner and Pole-dipole configurations. (b) The recovered model from inversion of the large synthetic data set with the Ekblom norm showing the DOI based on sensitivity analysis (threshold = 0.4). (c) The convergence curves show how the inversion performed.

The observed data were compared with the predicted data. The misfit is shown in Figure Fig. 6.30. The predicted data error does not exceed 3.9 standard deviations and overall data misfit is 3597.6.

../_images/synLargeMisfit.png

Fig. 6.30 (a) Observed apparent resistivity (mixed Wenner/Pole-dipole data set) and the (b) data misfit, which is normalized by the standard deviation.

Finally, the parallelization of  with OpenMP was analyzed on this example. It was inverted twice using 1 and 12 threads (6 cores with hyper-threading capability) with identical results. Running this example on one thread took 1:15:50.68 of CPU time, while running it on 6 cores (12 threads) resulted in convergence in 0:25:16.86 of CPU time, which is almost a threefold increase in productivity since the last release.