Transdimensional simultaneous inversion of velocity structure and event locations in downhole microseismic monitoring

In downhole microseismic monitoring, the velocity model plays a vital role in accurate mapping of the hydraulic fracturing image. For velocity model uncertainties in the number of layers or interface depths, the conventional velocity calibration method has been shown to effectively locate the perforation shots; however, it introduces nonnegligible location errors for microseismic events, especially for complex geologic formations with inclinations. To improve the event location accuracy. we have exploited the advantages of the reversible jump Markov chain Monte Carlo approach in generating different dimensions of velocity models and adopted a transdimensional Bayesian simultaneous inversion framework for obtaining the effective velocity structure and event locations simultaneously. The transdimensional inversion changes the number of layers during the inversion process and selects the optimal interface depths and velocity values to improve the event location accuracy. The confidence intervals of the simultaneous inversion event locations estimated by Bayesian inference enable us to evaluate the location uncertainties in the horizontal and vertical directions. Two synthetic examples and a field test are presented to illustrate the performance of our methodology, and the event location accuracy is shown to be higher than that obtained using the conventional methods. With less dependence on prior information, our transdimensional simultaneous inversion method can be used to obtain an effective velocity structure for facilitating highly accurate hydraulic fracturing mapping.