Reservoir Characterization. Группа авторов
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Название: Reservoir Characterization

Автор: Группа авторов

Издательство: John Wiley & Sons Limited

Жанр: Физика

Серия:

isbn: 9781119556244

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СКАЧАТЬ show expected versus posterior FDR for randomly sampled training and test sets. Continuous lines represent regression of the mean expected vs. the mean posterior FDR. Both regression lines are averaged over 1000 randomly sampled sets. On average, expected and posterior false discovery rates are about the same for both sizes of the training set. On the other hand, random differences between expected and posterior FDR are much larger for the training sets with a smaller number of records.

Schematic illustration of expected versus posterior false discovery rate for two sizes of the training set.
AD method Expected false discovery rate (%) Mean of posterior false discovery rate (%) Mean of posterior true discovery rate (%)
Sparsity 20 20.44 60.85
Distance 20 20.44 71.32
Divergence 20 20.49 85.71

      Since the divergence classifier was specifically designed for detection of gas-filled sand anomalies, it outperforms two universal classifiers. Its mean the posterior true discovery rate is as high as 85%.

      The ROC curve analysis presented in this section is based on the analysis of results of anomaly detection with 1000 bootstrap sampled training and test sets of different size. Two input petrophysical parameters, Poisson’s Ratio and Vp/Vs, were used for calculation of AD classifiers for each of the pair training - test sets. For every training set, the expected value of the false discovery rate was assigned, and distributions of posterior true and false discovery rates were calculated on anomaly detection results.

      In the case of multiple bootstrap sampled training and test sets, ROC curve analysis has to deal with multiple ROC curves. In that case, quantiles of the true and false discovery rates, and quanties of area under ROC curve may be used for a compact description of a set of multiple ROC curves.

      The writers distinguish two types of ROC curve analysis: (a) posterior ROC curve analysis, which is identical to traditional ROC curve analysis and (b) expected - posterior ROC curve analysis. Posterior ROC curve is a plot of posterior true discovery rate versus posterior false discovery rate, both calculated on the test set. Expected-posterior ROC curve is a plot of posterior true discovery rate (posterior TDR) versus expected false discovery rate (expected FDR), where posterior TDR is calculated on the test data and expected FDR assigned using training set data.

      Two of the three AD classifiers with AUC shown in Figure 3.3 do not rely on the use of information about properties of petrophysical parameters within potential anomalies. This is their advantage since they may be used for detection of any type of anomaly with unknown properties. Although they underperform compared to the divergence classifiers that rely on the use of known anomaly properties, they still can produce median AUC values as high as 0.75.

Schematic illustration of median of posterior AUC for three AD classifiers as a function of the size of the training set.