# Prestack Seismic Inversion via Nonconvex L\({}_{1-2}\) Regularization
## 4 Application  
In this case study, we used actual seismic data fromsampling the Pearl River Mouth Basin; this data consists of high-quality far-angle gathers suitable for a prestack AVA inversion study. The reservoir formation is comprised of sandstone, while the upper and lower layers surrounding the reservoir are mudstone. Previous work in this area indicates that this reservoir formation, known as the Pearl River Formation, is characterized by shallow deltaic deposits. This formation is deeply buried, structurally complex, and exhibits significant lateral variation [12]. Based on the results of our model experiments,  
Figure 11: The inversion results for angle gathers of 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\) using (**a**) our L\({}_{1-2}\) regularization inversion method and (**b**) the BP inversion method. The red, blue, and black curves represent the inverted, model, and initial values, respectively.  
Figure 10: The inversion results for angle gathers of 12\({}^{\circ}\),27\({}^{\circ}\), and 42\({}^{\circ}\) using (**a**) our L\({}_{1-2}\) regularization inversion method and (**b**) the BP inversion method. The red, blue, and black curves represent the inverted, model, and initial values, respectively.  
we separated the seismic data into three angle ranges: 3\({}^{\circ}\)-15\({}^{\circ}\), 18\({}^{\circ}\)-30\({}^{\circ}\), and 33\({}^{\circ}\)-45\({}^{\circ}\). We then used this data to generate seismic data sets with center angles of 9\({}^{\circ}\), 24\({}^{\circ}\), and 39\({}^{\circ}\), respectively (Figure 12a-c, respectively).  
We then perform prestack AVA inversions with these three data volumes. To enhance the lateral continuity of the inversion results, we use the logging data and horizon information to establish the low-frequency model required for the inversion (Figure 13a-c).  
Employing our L\({}_{1-2}\) inversion method, we performed the prestack AVA inversion and obtain three elastic parameters: P impedance, S impedance, and density (Figure 14a-c, respectively). In these figures, the black curves represent the logging curves corresponding to the prestack elastic parameters. The results in Figure 14 indicate that there are low P impedance and density anomalies and high S impedance anomalies. Because shear waves do not propagate in fluid media, the S-wave propagation velocity is comparable to that of the sandstone skeleton, which is in line with the actual geological interpretation of this study area. As shown in Figure 14d, our calculated P/S velocity ratio results not only allows us to pinpoint the location of our target formation, but they are also highly consistent with the P/S velocity ratios determined using the logging data (black curve in Figure 14d). As we have demonstrated, it is feasible to apply our L\({}_{1-2}\) prestack AVA inversion method to the task of reservoir prediction.  
Figure 12: Real partial angle stacks for angle gathers of (a) 12\({}^{\circ}\), (b) 24\({}^{\circ}\), and (c) 39\({}^{\circ}\).  
Figure 14: (**a**) P-impedance, (**b**) S-impedance, (**c**) density, and (**d**) VP/VS inversion results. The black circles denote the positions of gas-bearing sandstone units.  
Figure 13: (**a**) P-impedance, (**b**) S-impedance, and (**c**) density low-frequency models.