Receiver functions extract crustal structure from teleseismic recordings: an earthquake on the far side of the planet sends waves through the crust beneath a seismometer, and deconvolution separates the crustal response from the source signature. The method works because earthquakes from the same direction should produce the same crustal response. In practice, they don't — each earthquake carries its own noise, its own source complexity, its own nuisance effects. And earthquakes don't arrive uniformly from all directions. Gaps in backazimuthal coverage leave blind spots in the crustal image.
Conditional diffusion models fill the gaps (arXiv:2603.20902). Trained on receiver functions conditioned on backazimuth, epicentral distance, and station coordinates, the model learns what the crustal response should look like from directions where no earthquake has been recorded. The key insight enabling this: receiver functions from earthquakes at similar backazimuths share consistent crustal signatures but differ in noise. The diffusion model learns to suppress the variable part (nuisance effects) and retain the consistent part (crustal structure).
The virtual receiver functions — generated for directions where no real earthquake exists — correlate more strongly with true crustal responses than traditional stacking methods applied to real data. The synthetic seismograms are cleaner than the real ones.
Applied to the Cascadia Subduction Zone, virtual receiver functions sharply image scattered S-waves from the dipping slab. In southern California, the inferred anisotropy parameters are spatially coherent and align with regional fault geometry.
The structural insight: the method doesn't interpolate between existing observations. It generates observations from a learned model of crustal physics, conditioned on geometry. The virtual earthquake is not an average of real earthquakes — it's what a real earthquake from that direction would produce if it existed and carried no noise. The model separates signal from nuisance by exploiting the statistical structure: the signal is consistent across events, the noise is not. What you measure constrains what you could measure.