the 25‐station network. Lower travel time error results in better location results (Fig. 4.6 b vs. f and d vs. h). S‐wave arrivals provide important constraint on the event location, particularly the depth (Fig. 4.6 d vs. b and h vs. f).
4.3.3. Location Accuracy for Different Surface Seismic Networks
We quantify the event location accuracy for each seismic network by calculating the mean error of the located events relative to their true locations. The relationship between the location accuracy and the total number of surface seismic stations for different scenarios is shown in Figure 4.7. The horizontal location (Fig. 4.7a) is generally better constrained than the depth (Fig. 4.7b). Adding S‐wave arrival times increases the event location accuracy in both the horizontal direction and vertical directions. Comparing the location results with the 4‐station and 5‐station networks, 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
