Reverse time migration for microseismic sources using combinational autocorrelation imaging condition

SUMMARY Reverse time migration based on geometric mean or cross-correlation is a powerful passive-source imaging technique that can produce high-resolution source images even under low signal-to-noise ratio conditions. When the velocity model is inaccurate, a hybrid method combining geometric-mean and arithmetic-mean reverse time migration is typically used to reduce sensitivity to model errors. Conventional hybrid methods usually employ a grouping strategy, in which receivers are divided into groups and multiplicative operations are performed between these groups. However, this strategy essentially utilizes only a subset of receiver combinations, which may compromise imaging quality when the number of receivers is insufficient. To overcome this limitation, a novel combinational autocorrelation reverse time migration imaging condition is proposed. Our method forms multiple combinations of receivers and conducts zero-lag autocorrelation on the extrapolated wavefields of these combinations. The cross terms generated by the autocorrelation operation correspond to all possible receiver combinations. Finally, these autocorrelation results are linearly stacked in order to eliminate interference terms while preserving the cross terms. By including more receiver combinations, the proposed method can provide improved imaging performance. Furthermore, due to the adoption of the autocorrelation algorithm, the new method achieves minimal memory usage among methods based on reverse time migration, which makes it especially suitable for 3-D problems. Acoustic numerical simulations verify the effectiveness and advantages of the new method in both 2-D and 3-D scenarios. Additionally, the mathematical relationship between our method and conventional methods is discussed, clarifying the applicable scope of the new method.