## 3 Method and Results
### Porosity Prediction  
In this study, the Hampson-Russell EMERGE software package is used to perform the multi-attribute prediction. The objective is to model the relationship between porosity logs and seismic attribute traces at well locations, and to predict a porosity volume with this relationship by predicting porosity from traces at other locations. The following process was applied separately for each attribute group to obtain a different predicted porosity volume for each group of attributes. 1. To stabilize the prediction, porosity logs were filtered to 100 Hz. An initial multi-attribute list was generated to test convolutional operators with lengths from 1 to 51 samples incremented at every 10 samples and with a time sample rate of 1 ms. The operator length of 41 samples achieved the lowest validation error in all cases. Figure 7: Cosine of the instantaneous phase variation at 700 ms for porosity versus thickness wedge models. (**a**) Crossplot view and (**b**) 3D view. Figure 8 shows the resulting validation error versus the number attributes used in the regression. 2. Out of the 24 available wells, 21 were used for training the algorithm and 3 were left as out-of-sample tests for blind validation. 3. The transformation for each group was obtained using a 41-point operator length (representing 40 ms) and the attributes in Table 1.  
Figure 9 shows the measured and predicted porosity logs, filtered to 100 Hz, for one validation well. Group 4 attributes generally gave the best porosity prediction (quantified below). 4. Cross-validation among the training wells using the procedure described by [PERSON] [1] was used to restrict the number of attributes employed to 15. 5. Porosity volumes were built. Figure 10 shows an inline of the predicted porosity for each volume. The inserted curve is a porosity log filtered to 100 Hz from one validation well and the color background of the curve represents the filtered porosity log colored to the same scale as the volume. Notice a tradeoff between matching the well logs and lateral stability of the predictions. Average porosity maps over a 20-ms window below the seismic pick for the top of the most important reservoir layer were extracted to compare to interpolated average porosities from logs over the same window. Figure 11 shows average porosity maps for predictions made using the four attribute groups. Figure 8: Average training error versus the number of attributes testing convolutional operator lengths from 1 to 51 samples every 10 points. The black arrow indicates the point of the lowest validation error achieved using a 41-point operator. The example shown corresponds to the Group 4 attribute selection process. As the sample rate is 1 ms, the 41-point operator represents 40 ms.  
Figure 10: Inline of the predicted porosity volume obtained using each of the attribute groups. The inserted curve is a porosity log filtered to 100 Hz from one validation well and the color background of the curve is the log colored to the same scale as the volume. The dashed black line indicates the top of the main reservoir. Abbreviation: SD, spectral decomposition. Figure 9: Comparison of resulting predicted log (**red**) and actual porosity log filtered to 100 Hz (**black**) for a well not used in the training process using the different attribute groups. Error is the mean absolute error over the prediction interval. The blue rectangle highlights the main reservoir unit. A small time–depth error at the reservoir level is more obvious for Groups 3 and 4. Maps were obtained by horizon-slicing porosity volumes. Black dots are well locations. Although all maps in Figure 11b-e follow a similar general trend, when compared to the interpolated porosity map from the logs (Figure 11a), Group 1 fails to accurately predict average porosity at well locations. The other three maps better match values from logs but away from well control, they behave differently.