# Four-Dimension Seismic Analysis in Carbonate: A Closed Loop Study
## 3 Results & Discussion
### Seismic Inversion and Supervising Machine Learning Neural Network  
After completion of 4D seismic co-processing, 4D seismic interpretation was performed to investigate the 4D time shift between the baseline and the monitor's final migrated stack volume. The time shift is as important as the seismic 4D amplitude differences. A dynamic time shift was calculated for the final migrated seismic volume of the monitor with a time window of 1000 to 2000 ms and a threshold of \(\pm\)8 ms, using the baseline survey as a reference. Due to the 4D warping time shift, the baseline and monitor seismic volumes converged in time and amplitude compared to the volume without 4D warping. We calculated the velocity variation (DV) by scripting the 4D warping time-shift volume between the baseline seismic volumes and the final migrated seismic volumes. We calculated the low-frequency model of the warped seismic monitor volume using the DV changes in the volume as input with the low-frequency P-impedance model of the baseline survey. The baseline seismic volume and the warped monitor seismic volume were combined into a super group, as was the low-frequency model of the baseline and monitor surveys. A deterministic model-based 4D seismic inversion was created using well and seismic information for both the baseline and monitor surveys. The P-impedance, which is the result of the seismic inversion, was matched with the impedance calculated from the well logs to predict the 4D differences in rock properties such as density and porosity. We then used the Hampson-Russell (Emerge) software program, a procedure designed to merge well logs and seismic data. The general objective was to predict a property of the well log based on attributes of the seismic data. This property can be any measured log type, such as velocity or porosity, or even a derived lithologic attribute, such as shale volume. The seismic attributes can be calculated internally or provided as external attributes. The analysis was performed in several steps:  
Figure 6: Horizon slice of reservoir level: (**a**) NRMS of KPSDM seismic volume, and (**b**) NRMS of LSM seismic volume. 1. Examine the log and seismic data at well locations to determine which set of attributes is appropriate. 2. Derive a relationship using multi-linear regression or Neural Networks. 3. Apply the derived relationship to a 3D SEG-Y volume to create a volume of the desired log property. We tested six wells and thirteen wells with the baseline and monitor 4D seismic inversion volumes to train the data and investigate whether we could achieve a better match between the predicted density and the original density of the well logs using two approaches. The first approach was a single attribute regression curve to calculate the correlation coefficients for all attributes and rank their values by testing the nonlinear transformation applied to the target logs of wells penetrating the reservoir. The calculated average error is the root-mean-square difference between the target log values and the predicted values calculated over the analysis window for all selected wells. Note that applying a regression curve to the 1/(inversion) produces a result that reflects the general trend of the target logs but does not adequately predict the subtle features. This is because the inversion was blocked with a relatively coarse block size. The second task was to test the deep feed forward neural network (DFNN). In this deep machine learning approach, we used three hidden layers with a total of 50 training and validation iterations using six wells. For six wells, the agreement between the predicted density and the original density was better than for the thirteen wells, and the DFNN approach had the best match between predicted density (black curve) and the original density (red curve) (Figure 7c). It was clear that machine learning approach provided the best fitting between the predicted density and the actual density compared to the single attribute regression curve method using six wells for training and validation (Figure 7f).