Efficiency of Surface Monitoring Layouts for Retrieving Accurate Moment Tensors in Hydraulic Fracturing Experiments

Abstract

We study the sensor layouts of surface monitoring systems for injection areas in hydraulic fracturing experiments, which maximize the accuracy of retrieved moment tensors. The moment tensors (MTs) are determined using noisy synthetic P-wave amplitudes of microearthquakes with varying mechanisms. An optimum sensor layout is searched by minimizing a difference between the true and inverted MTs. First, we tested the efficiency of the circular networks. We focused on one-circle and two-circle layouts of various sizes and numbers of sensors on each circle and with their centre in the epicentral region. The results show that the optimal layout for events distributed within a circular epicentral area is characterized by: (1) one sensor fixed in the centre of the area; (2) about 1/10 of the total number of sensors gathered near the centre; and (3) the rest of sensors evenly distributed on a circle surrounding the area with the take-off angle of 135°. In homogeneous media, this angle corresponds to the radius of the circle comparable with depth of microearthquakes. Second, we compared the efficiency of the circular layout with other layouts: regular-grid, star-shaped and uniform focal-sphere layouts. Taking 25 sensors and 81 sensors as examples, we show that the two-circle layout is always the best, which means that we can achieve more accurate MTs using the circular layout than with other layouts, if the number of sensors in the experiment is fixed. This contradicts a common opinion that networks, which cover the target area, work equally well irrespective of their layout.