# Single-Shot Time-Lapse Target-Oriented Velocity Inversion Using Machine Learning
## 3 Results
### Inversion in Non-Repeatability Scenarios  
The ML inversion methodology developed in this paper was designed to work on a perfect repeatability scenario. The ML inversion input is the seismic data difference, which in practice is contaminated by non-repeatability effects. In the industry, data non-repeatability is treated using several techniques such as 4D binning [2], matched filtering [28, 29], amplitude balancing [30] and time warping [31]. However, the complete removal of non-repeatability effects is impracticable. In this way, we test our methodology in this more challenging scenario in which some treatment to erase 4D noise was implemented, but a residual non-repeatability effect is still present. We model such a non-repeatability residual by introducing uniform-distributed random perturbations to the positions of receivers in the lateral direction. The new data-testing set was created similarly to the synthetic seismic data presented in Section 2.1, whereby the difference is the aleatory shaking in the receiver position. We employ two non-repeatability noises according to the maximal aleatory variation in the receiver position: \(\pm\)0.1 mand \(\pm\)0.5 m.  
The testing of the ML inversion methodology with non-repeatability noise is shown in Figures 7 and 8 for maximum receiver variation equal to \(\pm\)0.1 m and \(\pm\)0.5 m, respectively. The basic schema of these two figures repeats the previous Figure 6 that shows the inversion for the ideal case of perfect repeatability. The two upper rows show the true and the predicted velocity anomaly according to key percentiles of the SSIM distribution on the dataset: minimum (worst case), median case, maximum (best case), and two intermediary quartiles. The two lower rows of these Figures show the central vertical and central horizontal velocity profiles of the velocity anomalies. The medians of the estimated SSIM index of ML inversion are 0.69 and 0.48 for the \(\pm\)0.1 m and \(\pm\)0.5 m cases, respectively. The Kruskal-Wallis test for the SSIM shows significant difference among the three scenarios (\(\chi^{2}\) = 2082, df = 2, \(p\)-value \(<\) 0.00001). An analysis of the MAE reveals the same pattern of the SSIM quantifier. The median of MAE corresponding to the noiseless case is 0.38, while to the noisy case, the medians are 230 and 550 for the \(\pm\)0.1 m and \(\pm\)0.5 m cases, respectively. The Kruskal-Wallis test for the MAE also reveals significant difference among the three treatments (\(\chi^{2}\) = 2144.9, df = 2, \(p\)-value \(<\) 0.00001). Figure 7: Inversion results of individual samples for a scenario with non-repeatability, modeled by randomly moving the receivers in the lateral directions, with maximum perturbations equal to \(\pm\)0.1 m. The yellow pattern in the panels represent the velocity anomaly; the horizontal and vertical dimensions reproduce the reservoir region indicated by the rectangle in Figure 1. Comparison of true (first row) and predicted (second row) time-lapse velocity anomalies in the target region for specificsamples of a test dataset contaminated with geometry non-repeatability noise. The 4D noise was modeled by randomly shifting the receivers in the lateral direction, with maximum perturbations equal to \(\pm\)0.1 m. The shown samples are located at key percentiles of the SSIM distribution on the referred dataset: minimum (worst case), three quartiles, and maximum (best case). The last two rows compare, respectively, the central vertical and central horizontal velocity profiles of the velocity anomalies. The general overview of Figures 6-8 reveals that non-repeatability noise degrades inversion performance, as expected. The worsening of the ML methodology is observed by visual inspection of the velocity anomalies of the mentioned figures. In addition, the velocity profiles, both vertical and horizontal, are also affected by the non-repeatability noise. The difference between the true and predicted velocity profiles of Figure 6 contrasts with profiles of Figure 7 and, particularly, Figure 8, which has a strong noise.