# Feasibility of Identifying Shale Sweet Spots by Downhole Microseismic Imaging
## 3 Results  
### Synthetic Example  
To evaluate the efficacy of our proposed method, we conduct a synthetic test featuring two observation wells and a simulated red cloud of 726 microseismic events as depicted in Figure 1. Each well is equipped with 20 receivers spaced 20 m apart. We design two-layered grid models for Vp and Vs, incorporating an abnormal volume within each layer, from which we derive the true Poisson's ratio model. As illustrated in Figures 2a-c and 3a-c, these anomalies represent the zones of hydraulic fracturing for a stimulation stage. We hypothesize that the red event cloud (shown in Figure 1) is triggered by fractures due to shear or tensile failure, which could increase porosity and permeability while significantly lowering the Poisson's ratio. This stimulated region, or anomaly, is identified as the shale sweet spot. We initialize the models by altering the true Vp and Vs layered models by 5% and 10%, respectively, based on sonic logs or calibrated models. The initial Poisson's ratio model is further obtained based on initial Vp and Vs models. Figure 1: The survey geometry and event location results in the synthetic case. The black reverse triangles denote two receiver arrays installed in two wells. The red and blue dots are the true and searched event locations, respectively. (**a**) 3D view; (**b**) X-Y plan view; (**c**) X-Z plan view; and (**d**) Y-Z plan view. After establishing the velocity models and survey geometry, we employ 3D wavefront raytracing to compute the traveltime data based on the true event locations within the models. The synthetic data are treated as the observed or picked arrival times typically encountered in field situations. We iteratively invert the Vp and Poisson's ratio and refine the event locations using the grid search method during each iteration loop. This process continues until the event locations stabilize and no longer change. As shown in Figure 1, the event locations determined by the grid search method closely match the true locations, with a maximum discrepancy of about 30 m. Notably, the error in the Y-axis positioning is less than that in the X-axis, which can be attributed to the constraints imposed by the two receiver arrays. In addition to event localization, the final inversion results for the Vp and Poisson's ratio models incorporate the initial models' layer constraints. Figure 2 displays the Vp models--true, initial, and inverted--highlighting that the abnormal area (indicated by a black rectangle) near the event cloud is accurately recovered. Similarly, a comparison between the true and inverted Poisson's ratio models in Figure 3 shows effective recovery of the abnormal area around the event cloud. These comparisons confirm that the embedded anomaly is well inverted, demonstrating the effectiveness of our methodology. Figure 2: True, initial, and inverted P-wave velocity models in the synthetic case. (**a,d,g**) Plan view (Y = 1.0 Km), (**b,e,h**) plan view (X = 0.86 Km), and (**c,f,i**) cross-sectional view (X = 0.86 Km, Y = 1.0 Km, and Z = 1.9 Km). (**a–c**) Map views of true 3D P-wave velocity model. (**d–f**) Map views of initial 3D P-wave velocity model. (**g–i**) Map views of the inverted 3D P-wave velocity result. The black rectangle denotes the border of the embedded anomaly in the true model. We also perform traditional traveltime tomography to invert Vp and Vs separately and subsequently derive Poisson's ratio. We extract Vp and Poisson's ratio profiles from both tomographic methods along two horizontal axes at a depth of 1.88 km. Figure 4 illustrates the comparison of the Vp and Poisson's ratio images obtained from the traditional and our tomographic methods. The green lines represent the true models, while the blue and red lines depict results from our proposed and the traditional methods, respectively. The comparison reveals that the red lines, indicating our method, more accurately recover the abnormal area compared to the blue lines, demonstrating superior Vp and Poisson's ratio solutions.