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Constraining precise faulting geometry for shallow, shallowly dipping thrust earthquakes is a common challenge. Plate boundary megathrust faults near the trench and decollement faults beneath volcanic islands and nappes may dip only a few degrees. Long-period point source moment tensor waveform inversions provide limited resolution of shallow fault dip angle. The possibility of splay faulting requires precise dip estimation. High sensitivity to dip is provided by long-period Love wave amplitude azimuthal radiation patterns, which undergo rapid change from four lobed to two lobed as dip decreases from 10 degrees to 0 degrees. Modeling variability in Love wave nodal amplitudes allows the dip to be determined to within a few degrees. This is demonstrated for the 25 October 2010 Mentawai (M-WW 7.8) tsunami earthquake, which ruptured the 2.0-5.0 degrees dipping megathrust beneath the shallow sedimentary wedge offshore of Indonesia, and the 4 May 2018 Hawaii Island (M-WW 6.9) thrust earthquake, which ruptured the 2.5-7.5 degrees dipping decollement under the island flank.

Plain Language Summary Earthquakes that involve thrust faulting at shallow depth occur commonly, and determining the fault dip angle is important for interpreting the nature of such events. Routine seismic wave analysis procedures for determining the faulting geometry for shallow thrust events often do not provide precise resolution of dip, leaving ambiguity in the assessment of the tectonic nature of the event. Spectral analysis of long-period radiation patterns for Love waves provides good sensitivity to fault dip angle for large shallow, shallowly dipping thrust events. Analysis of long-period surface waves for two shallow thrust events, a large near-trench subduction zone tsunami earthquake and the other a large earthquake at the base of the island mass of Hawaii, demonstrates that fault dip can be resolved to within a few degrees based on the sensitivity of Love wave radiation patterns to dip angle. Improved resolution of dip angle provides better confidence in the tectonic interpretation and improves seismic moment and slip estimation.