However, the time information is usually unavailable, e.g. for microseismic events that happen during hydraulic fracturing. To deal with this situation, most existing algorithms need to perform scanning and picking over a group of potential start times (Maxwell, 2014; Fink, 2006). An alternative cross-correlation time-reversal imaging (CTRI) condition states that a true seismic source can be indicated by the coincidence of all the wavefields in both space and time. This condition can be expressed as (Sun et al., 2015; Nakata and Beroza, 2016)
The key difference between equations 1 and 2 is two-fold. One difference lies in image resolution. Summing over all the receiver wavefields will result in an image that contains non-zeros across the wave propatation paths, while multiplication will lead to non-zeros corresponding only to the focuses. The other difference lies in computational cost. The summation indicated in equation 1 is implicit, and in practice that entire data volume can be back-propagated at once. However, the multiplication in equation 2 has to be carried out explicitly, leading to an times increase in computational cost. In order to leverage the efficiency of TRI, but to retain the high-resolution of CTRI, a hybrid cross-correlation time-reversal imaging (HCTRI) condition was proposed by Sun et al. (2015):