## 3 Method and Results
### Accuracy and Statistical Significance of Results  
The previous section explained the process followed to model and predict volumes and porosity maps. It also qualitatively compared the results obtained with the four attribute groups. In this section, statistical measures are implemented to determine the most accurate and statistically significant groups of attributes. The predicted porosity logs versus actual porosity logs filtered to 100 Hz (Figure 13) were cross-plotted with only data from blind wells that were not included in the training process. Figure 11: (**a**) Interpolation of the average porosity over a 20-ms window below the main reservoir top shown in Figure 10. (**b**) Group 1 map of average porosity over a 20-ms window below the main reservoir seismic pick in Figure 10. (**c**) Group 2 map of average porosity over a 20-ms window below the main reservoir seismic pick shown in Figure 10. (**d**) Group 3 map of average porosity over a 20-ms window below the main reservoir seismic pick shown in Figure 10. (**e**) Group 4 map of average porosity over a 20-ms window below the main reservoir seismic pick shown in Figure 10.  
Figure 12: Map of average porosity over a 20-ms window below the main reservoir top. The map was obtained by slicing the porosity volume from Group 4. Black dots are well locations. The black circle highlights an example of what could be channel-like features in a fan-delta environment. Figure 13: Cross-plots of the actual versus predicted porosity for predictions made using each of the attribute groups in three blind validation wells. Abbreviations: CC, correlation coefficient and MAE, mean absolute error. Data from the entire length of available logs were used in this cross-plot. Table 2 gives the resulting values of the correlation coefficient between the measurements and predictions, mean absolute error, standard error, F (Fisher's F-test), and significance F as measures of the regression statistical significance for each case. Figure 13 shows cross-plots of the predicted versus actual porosity for all attribute groups' predictions. The correlation coefficient (R) is a measure of the degree to which the observation and prediction vary linearly rather than being a direct measure of accuracy. Mean absolute error (MAE: the arithmetic average of absolute errors) measures the aver-age magnitude of discrepancy between pairs of predicted versus observed values. MAE is expected to be as small as possible. However, as the sign of the error is lost in the magnitude, it does not reveal bias. It indicates precision better than accuracy. To evaluate accuracy and bias, the standard error of the predicted mean is used. F is the ratio of the predicted variance to the error variance adjusted for the degrees of freedom (one less than the number of data points minus the number of attributes). When the ratio is less than 1, it can be concluded that the prediction is not useful. Significance F gives the probability that the correlation of the prediction and observation is a result of random chance [16]. A value below 0.05 is usually interpreted to mean the prediction is statistically significant. From Table 2, we can conclude that all the predictions are statistically significant, with bias and precision both being about two porosity units, approaching the accuracy of the logs. Compared to the measured log porosity, Group 4 has the best correlation, accuracy, and precision. Adding spectral decomposition to conventional attributes (Group 3) results in better incremental improvement compared to adding only relative geologic age (Group 2). From Table 2, the correlation coefficient increases from 0.64 (Group 1) to 0.79 (Group 4). F is much greater than 1 and Significance F is virtually zero for all cases, which indicates that none of the models provides a spurious correlation (a correlation by random chance) of the predicted versus actual porosity. All the statistics improve systematically from Group 1 to Group 4.