Dike‐induced earthquakes: Theoretical considerations

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Abstract
Earthquakes of magnitude 1 and greater seem to be ubiquitous features of dike propagation, but their origin is not well understood. We examine the elastic stress field surrounding propagating fluid‐filled cracks, with an emphasis on assessing the ambient stress required to produce earthquakes with linear dimensions of ∼100 m near dikes with linear dimensions of a few kilometers. An important feature of the solutions is the dike “tip cavity,” a low‐pressure region where magma cannot penetrate and where the stress field differs most from the classical near‐tip stress field. Two regions are considered: near the dike tip but away from the tip cavity and near the tip cavity. The stress state most conducive to failure occurs near the tip cavity when the cavity pressure is maintained by influx of host rock pore fluids rather than by exsolution of magmatic volatiles. Even in this case, however, shear fracture of previously intact rock seems unlikely. Thus most dike‐induced seismicity with a frequency content typical of “tectonic” earthquakes should be interpreted as resulting from slip along suitably aligned existing fractures. Production of magnitude 1 earthquakes appears to require either large ambient differential stresses or low ambient confining pressures; in the latter case, the effective normal stress on prospective faults may be low enough for slip to be aseismic. We conclude that the distribution of (recorded) dike‐induced seismicity reflects the distribution of ambient stresses that are near to failure and does not necessarily reflect the extent of the dike. This result is consistent with recent images of the seismicity associated with the 1983 dike intrusion at Kilauea.