Least-squares interferometric migration of microseismic source location with a deblurring filter

Microseismic source locations play an important role in monitoring hydraulic fracturing in unconventional oil and gas exploration. Waveform-based source location methods can reliably and automatically image source locations without phase identification. A widely used and representative waveform-based method is interferometric migration (IM), which can eliminate the excitation-time term and image the source location in space by using correlograms of pairwise receivers. IM can avoid the trade-off between the inversions of excitation time and source location, but provides low-resolution source location images with strong migration artifacts. To improve the spatial resolution, we first propose a least-squares interferometric migration (LSIM). LSIM iteratively minimizes the correlogram residuals using the conjugate gradient method. It provides a significant improvement in the spatial resolution compared to the conventional IM, but requires a large number of iterations and high computational costs. To overcome this drawback, we propose an efficient least-squares interferometric migration with a deblurring filter (DLSIM) for high-resolution microseismic source locations. We introduce the Hessian matrix into the microseismic source location problem and approximate the inverse Hessian with a relatively inexpensive deblurring filter. The deblurring filter is applied to the updated gradient matrix in the conjugate gradient algorithm. It could significantly accelerate the convergence rate of the least-squares inversion and meanwhile provide a high spatial resolution. We use synthetic and real hydraulic fracturing data to demonstrate the robustness and effectiveness of DLSIM. Data noise, velocity error and wavelet error are considered in the synthetic tests to simulate actual situations. The inverted results show that DLSIM achieves high-resolution source location images after 5-10 iterations that are equivalent to those of LSIM after approximately 50 iterations. Therefore, DLSIM can dramatically reduce the computational cost owing to its fewer number of iterations compared with LSIM.