We developed a flexible finite-fault inversion method for teleseismic P waveforms to obtain a detailed rupture process of a complex multiple-fault earthquake. We estimate the distribution of potency-rate density tensors on an assumed model plane to clarify rupture evolution processes, including variations of fault geometry. We applied our method to the 23 January 2018 Gulf of Alaska earthquake by representing slip on a projected horizontal model plane at a depth of 33.6 km to fit the distribution of aftershocks occurring within one week of the mainshock. The obtained source model, which successfully explained the complex teleseismic P waveforms, shows that the 2018 earthquake ruptured a conjugate system of N-S and E-W faults. The spatiotemporal rupture evolution indicates irregular rupture behavior involving a multiple-shock sequence, which is likely associated with discontinuities in the fault geometry that originated from E-W sea-floor fracture zones and N-S platebending faults.The 23 January 2018 Gulf of Alaska earthquake (moment-magnitude M W 7.9 1 ) struck offshore Kodiak Island (55.9097°N, 149.0521°W, 10.4 km depth; Alaska Earthquake Center, AEC 1 ), in the seaward-region of the Alaska-Aleutian subduction zone. The Global Centroid Moment Tensor (GCMT) project 2, 3 reported that the 2018 Gulf of Alaska earthquake had strike-slip faulting with a large non-double-couple component (47%). Aftershock seismicity determined by the AEC 1 shows a lineation extending about 120 km N-S near the epicenter and two aftershock clusters centered about 60 km northeast and about 50 km west from the epicenter (Fig. 1). The GCMT solutions of aftershocks are dominated by strike-slip faulting, but include normal and reverse faulting (Fig. 1).Several pioneering studies that built finite-fault models based on the aftershock distribution demonstrated that the 2018 Gulf of Alaska earthquake ruptured a quasi-orthogonal multiple-fault system oriented approximately N-S and E-W 4-8 . However, it is difficult to adopt a reasonable fault model because the fault model parametrization, number of fault segments, and fault geometries differ by study, partly due to the spatial spread of the aftershock distribution (Fig. 1). Based on the static slip distribution estimated from Global Navigation Satellite System and tsunami data, major slips occurred on E-W-striking segments 5,7,8 . Finite-fault inversions estimated that the maximum slip occurred around the boundary between the crust and uppermost mantle in the N-Soriented segment 4,6 , which would have played a significant role in tsunami generation. However, it remains challenging to adequately explain the complex characteristics of the observed teleseismic body waveforms by conventional finite-fault inversion methods due to the uncertainty on the fault geometry, which lead to significant model errors.In the framework of finite-fault waveform inversion, uncertainties on the Green's function and fault geometry have been the major sources of model errors [9][10][11][12][13] . Those due to uncertai...