the vertical location accuracy improves greatly while the horizontal location accuracy improves moderately.
Figure 4.5 The initial (blue dots) and relocated (red dots) microseismic events obtained using different distributions of seismic stations (green triangles) for the synthetic study in Figure 4.4. The left column (a, c, e, g) is map view and the right column (b, d, f, h) is the corresponding depth view. These are the results using both P‐wave and S‐wave arrival times with the 0.02 s noise.
The overall hypocentral location accuracy is shown in Figure 4.7c, which combines both horizontal and vertical location accuracy. For all scenarios, the location accuracy in relation to the number of seismic stations improves rapidly when the seismic network consists of a relatively small numbers of seismic stations. However, further improvement of the location accuracy becomes slower with further increasing the number of seismic stations. To better analyze the relationship between the location accuracy and the total number of seismic stations, we normalize the mean location accuracy for each scenario studied (Fig. 4.7d). We choose the value obtained with the 5‐station network as the normalization value, because it shows dramatic change compared with the 4‐station network with only one station difference and should be the minimal number of stations required to have effective monitoring for a geometrically satisfactory network distribution shown in this work. The rapid improvement of event location accuracy from using four stations to five stations is also observed for optimal network distributions designed based on a statistical theory (e.g., Kijko, 1977b). The normalized curves between the mean location accuracy and the number of stations for all studied scenarios follow a similar trend. The best trade‐off point can be found by locating the corner of the L‐shaped curves. For the monitoring regions in this example, our result suggests that approximately 20 seismic stations are needed for cost‐effective monitoring.
Figure 4.6 The initial (blue dots) and relocated (red dots) microseismic events obtained using 25 seismic stations (green triangles) for the synthetic study in Figure 4.4. The results are for (a‐b) using P‐wave arrival times with the 0.02 s noise, (c‐d) using P‐wave and S‐wave arrival times with the 0.02 s noise, (e‐f) using P‐wave arrival times with the 0.05 s noise, (g‐h) using P‐wave and S‐wave arrival times with the 0.05 s noise.
Figure 4.7 Event location accuracy versus the total number of seismic stations: (a) mean horizontal location errors, (b) mean vertical location errors, (c) mean location errors, (d) mean location errors normalized relative to the error obtained with five seismic stations. Blue lines represent results obtained using P‐wave arrival times with different noise levels, red lines represent results obtained using both P‐wave and S‐wave arrival times with different noise levels.
The results shown in Figure 4.7 are for regularly distributed seismic networks. We also study irregularly distributed seismic networks to confirm that the results in Figure 4.7 are also approximately applicable to irregularly distributed seismic networks as long as the network has a reasonable geometry with adequate azimuthal and distance coverage. We take the 25‐station seismic network as an example. We create an irregularly distributed network by perturbing the regularly spaced network with random distances. We generate 10 randomly distributed 25‐station seismic networks, and Figure 4.8 shows two of them as an example. The mean location accuracy obtained with these 10 irregularly distributed 25‐station networks is similar to the value obtained with regularly distributed 25‐station networks (Fig. 4.9). For the specific monitoring regions in this demonstration example, we determine that approximately 20 stations with geometrically satisfactory distribution can achieve the best trade‐off between the cost and the event location accuracy. It should be noted, though, in this work, we only consider the square distribution around the fault for simplicity. This kind of square distribution covers a wide area, and can be useful for regions where seismic events may also occur on some unknown hidden fractures or faults around the focus fault. If the focus fault is long, an elongate distribution of seismic network surrounding the fault should be preferable.
Figure 4.8 (a,b) Two examples of the irregularly distributed 25 seismic stations (green triangles). The Black line shows the simplified surface location of a portion of the Pond‐Poso Creek fault.
Figure 4.9 Comparison between mean event location accuracy for regularly spaced 25 seismic stations (red dot) and irregularly spaced 25 seismic stations (blue dots). Ten different layouts of irregularly spaced 25 seismic stations are studied. The mean event location accuracy with irregularly spaced seismic stations is similar to the one obtained with regularly spaced seismic stations.
4.4. OPTIMAL DESIGN OF A BOREHOLE GEOPHONE ARRAY
For the case with borehole geophones, similar steps as above for surface seismic networks can be applied to obtain the optimal design of a borehole geophone array. For demonstration, we consider a synthetic case with target microseismic events within the reservoir, at depths between 2.2 km and 2.5 km and within a horizontal region of 2 km. We place a vertical geophone string above the center of the target monitoring region of microseismic events, at depths between 0.2 km and 2.1 km (Fig. 4.10). We consider regularly spaced geophones along the geophone string. We fix the top and bottom locations, and increase the number of geophones from 5 to 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. For each geophone distribution, we compute synthetic P‐wave and S‐wave arrival times for the true locations of microseismic events (Fig. 4.10) using the velocity model in Figure 4.3. We add a random Gaussian error with standard deviations of 0.02 s to the computed travel times. We then use these travel times to solve for the