Back-projection (BP) is a cornerstone method for imaging earthquake ruptures, particularly effective at teleseismic distances for deciphering large earthquake kinematics. Its superior resolution is attributed to the ability to resolve high-frequency (>1 Hz) seismic signals, where waveforms immediately following the first coherent arrivals are composed of waves scattered by small-scale seismic velocity heterogeneities. This scattering leads to waveform incoherence between neighboring stations, a phenomenon not captured by synthetic tests of BP using Green’s functions (GF) derived from oversimplified 1D or smooth 3D velocity models. Addressing this gap, we introduce a novel approach to generate synthetic Incoherent Green’s Functions (IGF) that include scattered waves, accurately mimicking the observed inter-station waveform coherence decay spatially and temporally. Our methodology employs a waveform simulator that adheres to ray theory for the travel times of scattered waves, aggregating them as incident plane waves to simulate the high-frequency scattered wavefield across a seismic array. Contrary to conventional views that scattered waves degrade BP imaging quality by reducing array coherence, our synthetic tests reveal that IGFs are indispensable for accurately imaging extensive ruptures. Specifically, the rapid decay of IGF coherence prevents early rupture segments from overshadowing subsequent ones, a critical flaw when using coherent GFs. By leveraging IGFs, we delve into previously unexplored aspects of BP imaging’s resolvability, sensitivity, fidelity, and uncertainty. Our investigation not only highlights and explains the commonly observed “tailing” and “shadowing” artefacts but also proposes a robust framework for identifying different rupture stages and quantifying their uncertainties, thereby significantly enhancing BP imaging accuracy.

Standard Back-Projections (BPs) use P phase recordings at large aperture arrays within teleseismic distances (30°-90°) to image earthquake sources. However, the majority of sizable arrays are in the northern hemisphere, leaving many southern hemisphere earthquakes beyond the teleseismic range. We extend the BP method by utilizing seismic waves traveling through the Earth’s core, expanding our capability to image earthquakes worldwide. Our core phase BPs incorporate PKIKP (150°-180°) and PKP (145°-175°) phases. We evaluate their theoretical resolutions using 1-D and 2-D array response functions and test uncertainties by adding white noise to coherent waveforms. Tests show that core phase BPs achieve resolutions and uncertainties comparable to P phase BP. We validate the method using a synthetic model of a unilateral rupture (Mw 7.45, 2 km/s) and demonstrate accurate recovery of rupture direction, length, and speed. Applying core phase BPs to the 2010 Mw 8.8 Chile and 2015 Mw 7.1 southeast Indian Ridge earthquakes, we compare our results with published BPs and/or slip models, confirming the feasibility and reliability of core phase BPs. We then apply core phase BPs to five understudied earthquakes in the southwest Pacific region, providing insights into these pelagic earthquakes. Core phase BPs play a crucial role in scenarios where teleseismic arrays are unavailable, and have weaker array-dependent effect and better performance in bilateral rupture imaging. Finally, we discuss the limitations of core phase BPs and outline potential avenues for future research.

We explore the potential of the adjoint-state tsunami inversion method for rapid and accurate near-field tsunami source characterization using S-net, an array of ocean bottom pressure gauges. Compared to earthquake-based methods, this method can obtain more accurate predictions for the initial water elevation of the tsunami source, including potential secondary sources, leading to accurate water height and wave run-up predictions. Unlike finite-fault tsunami source inversions, the adjoint method achieves high-resolution results without requiring densely gridded Green’s functions, reducing computation time. However, optimal results require a dense instrument network with sufficient azimuthal coverage. S-net meets these requirements and reduces data collection time, facilitating the inversion and timely issuance of tsunami warnings. Since the method has not yet been applied to dense, near-field data, we test it on synthetic waveforms of the 2011 Mw 9.0 Tohoku earthquake and tsunami, including triggered secondary sources. The results indicate that with a static source model without noise, using the first 5 minutes of the waveforms yields a favorable performance with an average accuracy score of 93%, and the largest error of predicted wave amplitudes ranges between -5.6 to 1.9 meters. Using the first 20 mins, secondary sources were clearly resolved. We also demonstrate the method’s applicability using S-net recordings of the 2016 Mw 6.9 Fukushima earthquake. The findings suggest that lower-magnitude events require a longer waveform duration for accurate adjoint inversion. Moreover, the estimated stress drop obtained from inverting our obtained tsunami source, assuming uniform slip, aligns with estimations from recent studies.