A method to allow temporal variation of velocity in travel-time tomography using microearthquakes induced during hydraulic fracturing

Abstract Hydraulic injections produce fluid-filled fractures that reduce the seismic velocity of the rock compared to intact rock. The travel times of microearthquakes induced by the injections may be used to discern changes in the rock velocities, as well as locating the microearthquakes. Determining the volumes of rock where the velocities have changed provides indirect evidence for the location of the injected fluid, and the character of the changes produced in the fractured rock. Available data are generally insufficient to resolve both the spatial and temporal changes within the rock. To extract information about temporal changes, and to obtain an improved image of the velocity structure, we chose a parameterization scheme in which the velocities of each block are allowed to change from the background velocity only after a threshold number of microearthquakes have occurred in the block. Regularizing by constraining the velocity of all the altered blocks to be similar helps stabilize the inversion. The regularization can be relaxed somewhat to allow the velocity of an altered block to be different from other altered blocks if the travel-time data are compelling. The parameterization scheme is justified since observations show that the volume of the seismically stimulated rock increases linearly with the volume of the injected fluid. We applied the method to data collected in a region of Precambrian crystalline rock that was injected with 21,600 m 3 of water. We use travel times from a total of 3886 microearthquakes that were induced by the injection. The mean RMS travel-time residual decreases about 7%. The velocity structure contains a low-velocity zone located near the injection region. Other distinct low-velocity zones are identified. The pattern of microearthquake locations found using our method appears to contain more structure than the pattern found in locations determined using a homogeneous velocity structure. Two clear low-velocity regions found near the point where water was injected into the rock are separated by a region whose velocity did not change. The region of unaltered velocity had a large number of microearthquakes.