A simple inversion algorithm to estimate a linearly increasing velocity model for microseismic monitoring

Abstract

Microseismic monitoring is used to optimise shale gas production or enhanced geothermal stimulation. The technical tools for microseismic monitoring, which is a passive seismic method, are similar to those used in earthquake detection, but differ in that the target area is much smaller than areas affected by earthquakes. Therefore, it is important to use an accurate velocity model. However, such models require conducting an additional survey, which can be both expensive and time-consuming. Many microseismic monitoring studies have used an approximated velocity model constructed from well logging data to reduce these additional costs. In this study, we used a simple approximated model in which velocity increases linearly with depth and creates an accurate velocity model, eliminating the need for an additional survey. We analytically derived formulas for seismic ray traveltime and inverted the velocity gradient using the Gauss–Newton method. Using a numerical example, we verified that the proposed algorithm accurately describes the long-wavelength trend of the true velocity model in a negligibly short time. We performed a Monte Carlo simulation to evaluate the effects of traveltime picking errors. The simulation results indicated that the proposed algorithm provides a reasonable solution under the probable uncertainty of traveltime picking. Finally, we verified that our algorithm was not sensitive to the initial velocity gradient through inversion tests using various initial values. Thus, the numerical example and analysis confirm that the proposed algorithm is efficient and robust.