Time‐dependent dike propagation from joint inversion of seismicity and deformation data

Dike intrusions both deform Earth's surface and induce propagating earthquake swarms. We develop methods to utilize both deformation and seismicity from brittle, volcano‐tectonic earthquakes to image time‐dependent dike propagation. Dieterich's (1994) seismicity‐rate theory is used to relate dike‐induced stress changes to seismicity rate and is combined with elastic Green's functions relating dike opening to deformation. Different space‐time patterns of seismicity develop if earthquakes occur at the same depth as the dike compared to above/below the dike. In the former, seismicity initiates near the dike's leading edges but shuts off as the dike tips pass and seismogenic volumes fall into stress shadows. In the latter, seismicity continues at a decaying rate after the tips pass. We focus on lateral propagation and develop a nonlinear inversion method that estimates dike length and pressure as a function of time. The method is applied to the 2007 Father's Day intrusion in Kilauea Volcano. Seismicity is concentrated at ∼3 km depth, comparable to geodetic estimates of dike depth, and decays rapidly in time. With lateral propagation only and a vertical dike‐tip line, it is difficult to fit both GPS data and the rapid down‐rift jump in seismicity, suggesting significant vertical propagation. For the events to have occurred below the dike requires a very short aftershock decay time, hence unreasonably high background stressing rate. The rapid decay is better explained if the dike extends somewhat below the seismicity. We suggest that joint inversion is useful for studying the diking process and may allow for improved short‐term eruption forecasts.