Teleseismic back-projection has emerged as a widely-used tool for understanding the rupture histories of large earthquakes. However, its application often suffers from artifacts related to the receiver array geometry, notably the ‘swimming’ artifact. We present a teleseismic back-projection method with multiple arrays and combined P and pP waveforms. The method is suitable for defining arrays ad-hoc in order to achieve a good azimuthal distribution for most earthquakes. We present a catalog of short-period rupture histories (0.5-2.0 Hz) including all 54 earthquakes from 2010 to 2021 with M_w ≥ 7.5 and depth less than 200 km. The method provides semi-automatic estimates of rupture length, directivity, speed, and aspect ratio, which are related to the complexity of large ruptures. We determined short-period rupture length scaling relations that are in good agreement with previously published relations based on estimates of total slip. Rupture speeds were consistently in the sub-Rayleigh regime for thrust and normal earthquakes, whereas a tenth of strike-slip events propagated in the unstable supershear range. Many of the rupture histories exhibited complex behaviors such as rupture on conjugate faults, bilateral ruptures, and dynamic triggering by a P wave. For megathrust earthquakes, ruptures encircling asperities were frequently observed, with down-dip, up-dip, double encircling, and segmented patterns. Although there is a preference for short-period emissions to emanate from central and down-dip parts of the megathrust, emissions up-dip of the main asperities are more frequent than suggested by earlier results.