Understanding the directivity of earthquakes by generating virtual far-field seismograms conditioned on the P-ray take-off direction

Understanding earthquake rupture directivity is crucial for constraining source physics and improving seismic hazard assessment. In an ideal setting, one would analyze far-field seismograms free from subsurface scattering, travel-time uncertainties, and ambient noise, enabling direct inference of rupture directivity from the observed waveforms. In practice, however, recorded seismograms are strongly influenced by path effects, site responses, and additive noise, while station azimuthal coverage is often sparse and uneven. These limitations significantly complicate directivity analysis, particularly for 1) low-magnitude noisy events and 2) earthquakes with complex rupture processes, for which simple source–path deconvolution models are inadequate.

We employ a conditional Diffusion Transformer (DiT) to learn the dependence of far-field seismograms on the P-ray take-off direction. The DiT is trained on measured far-field seismograms from multiple earthquakes with moment magnitudes Mw ≥ 6.0. Once trained, the model generates virtual far-field seismograms conditioned on specified ray azimuth and take-off angle, while holding an empirical realization of the path effects fixed by conditioning on a reference observed seismogram. This enables controlled experiments in which variations attributable to source directivity can be examined independently of path-induced variability. In this sense, our approach closely mimics the idealized setting in which far-field seismograms vary only with source directivity and are free from complex path effects. In other words, this generative framework enables us to isolate and examine variations in the wavefield that are attributable solely to source directivity, while holding path effects constant. We demonstrate that this approach is particularly effective for earthquakes with complex multi-episode moment release. For all events considered, the generated wavefields vary smoothly with take-off direction, indicating physical consistency. Importantly, the DiT training is self-supervised, requiring neither synthetic earthquake simulations nor explicit correction for path effects. The proposed framework provides a scalable and physically consistent tool for investigating earthquake directivity and rupture complexity across a wide range of magnitudes.