Focusing patterns of seismicity with relocation and collapsing

Seismicity is generally concentrated on faults or in fault zones of varying, sometimes complex geometry. An earthquake catalog, compiled over time, contains useful information about this geometry, which can help understanding the tectonics of a region. Interpreting the geometrical distribution of events in a catalog is often complicated by the diffuseness of the earthquake locations. Here, we explore a number of strategies to reduce this diffuseness and hence simplify the seismicity pattern of an earthquake catalog. These strategies utilize information about event locations contained in their overall catalog distribution. They apply this distribution as an a priori constraint on relocations of the events, or as an attractor for each individual event in a collapsing scheme, and thereby focus the locations. The latter strategy is not a relocation strategy in a strict sense, although event foci are moved, because the movements are not driven by data misfit. Both strategies simplify the seismicity pattern of the catalog and may help to interpret it. A synthetic example and a real-data example from an aftershock sequence in south west Iceland are presented to demonstrate application of the strategies. Entropy is used to quantify their effect.