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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 locations of the microseismic events assuming that the velocity models are known. The initial event locations (blue dots in Fig. 4.11) are generated by adding a random Gaussian error with a mean distance of approximately 100 m to the true locations. The final event locations are obtained using the same method described in section 4.3 for optimal design of a seismic surface array. Examples of the borehole geophone distribution and final event locations are shown in Figure 4.11.

Figure 4.10 The true locations of microseismic events (black dots) used for optimal design of a borehole geophone array.

We quantify the event location accuracy for each geophone distribution by calculating the mean accuracy of located events relative to their true locations. The relationship between the location accuracy and the total number of geophones for different scenarios is shown in Figure 4.12. We see that the event location accuracy does not change much when the number of geophones increases beyond 50. Therefore, 50 would be an optimal number of geophones needed to achieve a good balance between event location accuracy and the cost.

Figure 4.11 The initial (blue dots) and relocated (red dots) microseismic events obtained using different numbers of borehole geophones (green triangles) for the synthetic study in Figure 4.10. The number of geophones shown as examples is 5 (a‐b), 30 (c‐d), and 100 (e‐f).