Back-projection (BP) is widely used to study large earthquakes but its derived images are array-dependent. For the same earthquake, different arrays often produce different images and it is difficult to judge which result should be trusted more. How to reconcile these images properly is crucial, but few researchers have systematically worked on this problem. We find that the BP spatial discrepancy between arrays is a result of P-wave travel time errors in each receiver array. In Meng et al., GRL, 2016, we proposed to resolve this issue using "slowness calibrations".
Standard BP utilizes teleseismic travel-time table based on 1D reference velocity model. The process of determining the later sub-sources with respect to the hypocenter is similar to that of the “master event” location technique. To account for the travel time variations due to 3D Earth structures, BP applies a timing correction inferred from the “hypocenter alignment”. The first arrival of an earthquake is assumed to come from the hypocenter location. A set of travel time errors due to 3D structures is obtained by cross-correlating the initial arrivals of the P-waves. The subsequent ruptures are tracked based on their differential travel times relative to the hypocenter. The strategy of “hypocenter correction” assumes uniform travel time errors across the entire rupture zone. Therefore, it is often only accurate within close proximities to the hypocenter. The errors increase when the rupture front propagates away from the hypocenter. To account for the travel time errors at distant source locations, we apply an additional correction of slowness (ray parameter). Here, the slowness refers to the spatial derivatives of travel times with respect to source locations for a given station. An additional correction of the slowness improves the accuracy of the differential travel time between the hypocenter and a distant sub-source. The correction term of slowness can be effectively calibrated using locations of aftershocks, assuming the catalog locations are accurate. For a given aftershock, its differential travel-time relative to the hypocenter is compared to the travel-time predicted by the 1D reference model. The remaining travel-time difference is divided by the mainshock–aftershock distance and mapped into the slowness correction term. The slowness correction effectively mitigates the spatial bias due to structure effect. The BP with slowness calibration of the 2015 M7.8 Nepal-Gorhka earthquake is shown in the figure below (Meng et al., GRL, 2016). The top and bottom two panels compare the high-frequency radiators of the aftershocks and mainshock imaged by three different arrays, respectively. It can be seen that after the calibration, both of the aftershock and mainshock BP achieves significantly improved and achieve consistency between BP of different arrays.
Figure 1. The back projections with slowness correction of the Gorhka earthquake. (top two panels) Aftershock locations inferred from back projection with catalog location before (left) and after (right) slowness correction. The stars show NEIC catalog locations of four moderate size (M5 ~ 7) aftershocks, with colors corresponding to four aftershocks. The symbols (circle, square, and diamond) denote apparent back projection locations imaged by the Australian, North America, and European arrays. (bottom two panels) The main shock back projections of different arrays before (left) and after (right) correction.