# Feasibility of Identifying Shale Sweet Spots by Downhole Microseismic Imaging
## 3 Results
### Field Example  
We further apply our method to a field case involving a microseismic dataset created during hydraulic fracturing in the Barnett Shale reservoir [43]. To ensure sufficient raypath coverage and high-quality data, we select 156 effective events recorded by two nearby vertical receiver arrays during the fifth stage of hydraulic stimulation. Figure 6 shows recordings from one event by both arrays, where P and S wave arrivals are clearly identifiable. One vertical well employs a recording system consisting of 12 three-component geophones, while the other uses 8. These geophones are spaced approximately 15 m apart. The deployment geometry of these geophones is illustrated in Figure 7.  
We construct the initial Vp and Vs layer models from sonic logs, which provide velocity profiles along the wells, and convert these into 3D Vp and Vs grid models. From these grids, we calculate the Poisson's ratio model. Using our proposed method, we continue refining the event locations and Vp and Poisson's ratio models until the event locations stabilized. Figure 4: The Vp (**a**) and Poisson’s ratio (**b**) images extracted along two horizontal directions at a depth of 1.88 km of tomographic models. The green and red lines represent the images of true and inverted Vp or Poisson’s ratio models with our traveltime tomographic methods, the blue lines are the images of the Vp and derived Poisson’s ratio models from Vp and Vs models inverted separately using standard traveltime tomography. Figure 5: (**a**) Convergence curve of location error of 3D grid search over three loops in the synthetic case. (**b**) Misfit curves of the traveltime tomography of the last loop. The circle represents the data misfit of each loop, and the triangles and squares are the traveltime misfits over each iteration of P and S waves, respectively. Figure 7a illustrates the 3D distribution of our event locations (blue dots) alongside those provided by a service company (green dots), showing an average discrepancy of about 30 m. We further project both sets of event results in different views (Figure 7b-d), observing that our event locations maintain a similar distribution to the green ones but with greater convergence. The seven red stars in Figure 7 mark the perforations during the fifth stage. From the X-Y plan view, our event locations correspond closely with these perforations, a result of the constraints imposed by two observation wells. The depth positioning from the X-Z and Y-Z plan views also aligns well with the service company's data, reflecting the accuracy of our calibrated layer models. Figure 6: The different recordings of the same microseismic event from (**a**) eight-receiver array and (**b**) twelve-receiver array, respectively, in one field case. The P- and S-wave arrivals display a high signal-to-noise ratio and are easily picked (red and blue, respectively) on all 20 receivers. Figure 7: The survey geometry and event location results of the field case. The black reverse triangles stand for two receiver arrays installed in the two monitoring wells. The seven red stars are the perforations in one stage. The blue dots are our searched location results, and the green dots are the location results provided by service company. (**a**) The 3D view; (**b**) X-Y plan view; (**c**) X-Z plan view; and (**d**) Y-Z plan view. Figures 8d-f and 9d-f display the inversion results for Vp and Poisson's ratio, respectively. Across various plan views, we identify a region with a relatively low Poisson's ratio, marked by a black rectangle, located around a depth of 1.9 km. This low Poisson's ratio area delineates the sweet spot and helps estimate the stimulated hydrocarbon volume. Figure 10 presents the data misfit curve, demonstrating the convergence of our method. Despite numerous iterations, the data misfit stabilizes after four loops as shown in Figure 10a. Additionally, we include the misfit curves for P- and S-wave traveltime tomography from the final loop, illustrating detailed convergence behavior.