## 3 Method and Results
### Resolution  
The limit of vertical resolution (\(\lambda/4\)) is 10.04 m for the spectrally broadened seismic data used as input for this study.  
Figure 15 shows thin hydrocarbon-bearing intervals evidenced on gamma-ray and resistivity logs, as well as associated porosities for a blind validation well that was not included in the training process.  
Figure 14: Cross-plots of the actual versus predicted average porosity extracted over a 20-ms window below the main reservoir. Abbreviations: CC, correlation coefficient and MAE, mean absolute error.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Average** & **Group 1** & **Group 2** & **Group 3** & **Group 4** \\
**Porosity** & 0.4 & 0.5 & 0.65 & 0.73 \\ \hline
**Correlation** & 2.11 & 1.81 & 1.7 & 1.33 \\
**Mean Absolute** & 2.11 & 1.81 & 1.7 & 1.33 \\
**Error** & 1.86 & 1.83 & 1.59 & 1.39 \\ \hline
**F** & 0.83 & 1.55 & 8.29 & 17.11 \\ \hline
**Significance F** & 3.70 \(\times\) 10\({}^{-01}\) & 2.20 \(\times\) 10\({}^{-01}\) & 9.20 \(\times\) 10\({}^{-03}\) & 5.11 \(\times\) 10\({}^{-04}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Correlation coefficient and mean absolute error (PU), standard error, F, and Significance F for the actual versus predicted average porosity over a 20-ms window below the main reservoir.  
All highlighted intervals in Figure 15 are at or above the limit of vertical resolution for the input bandwidth-extended seismic data. The four groups can detect such layers but only Groups 3 and 4 can accurately predict log porosities in them above 30 PU. The lowest reservoir just above a record time of 900 ms (black ellipse in Figure 15) is best detected by Group 4.  
The Group 4 porosity volume is also useful to identify geologic features not seen on the seismic sections alone.  
Figure 16 shows examples of channel-like bodies evident on the Group 4 predicted porosity volume that are not obvious on the original seismic data.  
Figure 16: Right: sections from the Group 4 porosity volume showing channel-like features. Left: same sections from the seismic volume used as input for multi-attribute analysis. Polarity: an increase in amplitude corresponds to an increase in acoustic impedance.  
Figure 15: Thin hydrocarbon-bearing intervals seen on logs and predictions made using the four attribute groups. The inserted curve is a porosity log filtered to 100 Hz. The well shown was not used for training. Black ellipse highlights a reservoir of interest, most detectable using Group 4 prediction.  
High porosity features on the right of Figure 16 resemble incised and stacked-high porosity channels. This response is expected in the area given that the reservoirs are fluvial and are lacustrine fan delta deposits. These features are imperceptible or are not clearly defined on seismic sections on the left.  
Another example is shown in Figure 17. In this case, one well passes through the channel-like feature. Porosity and gamma-ray logs are shown, as well as the corresponding seismic section.  
The computed porosity section in Figure 17 shows a high porosity possible channel and this interpretation is supported by well log porosity and gamma-ray responses, which indicate a very porous clean sand. The blocky shape of the sand layer suggests that the interval may correspond to a fluvial or deltaic distributary channel. The feature is about 10 m thick at the limit of seismic resolution and it is not obvious on the spectrally broadened seismic section. Thinner sand intervals are not resolved by the predicted porosity volume.