Microseismic hypocenter location using nonlinear optimization
Reduced arrival times from microseismograms caused by hydraulic fracturing and recorded by borehole or surface arrays of geophones can be modeled assuming a layered-earth velocity model. These reduced times are independent of t0, the unknown clock time at which a microseismic event occurs. Ray-tracing through a layered-earth velocity model can be used to calculate arrival times from a hypocenter to the geophone arrays. Assuming that we know the velocity model, the receiver coordinates, and observed arrival times, we can use a nonlinear optimization method similar to the Levenberg-Marquardt algorithm to find the microseismic source coordinates if the array of geophones spans a sufficient solid angle relative to the source.
The location of hypocenters requires that the velocities in the layered-earth model be known. In real-world microseismic surveys, arrival times observed from a perforation shot in the treatment well are used to calibrate the velocity values. If the perforation shot location, the geophone coordinates, and layer depths are known, the model velocities can be ascertained. Synthetic arrival- time data created by ray-tracing were used in a simulation of velocity calibration. An objective function equal to the RMS misfit between synthetic observed and calculated arrival times was created. The required velocity values were found by using search schemes such as the genetic algorithm and pattern search to minimize the arrival time misfit. For this simulation, the search method performed better than the modified LM technique and the genetic algorithm.