Earthquake Cluster: What Can We Learn from Waveform Similarity?

The seismograms of earthquakes, which have closely spaced hypo-centers, tend to be similar due to the similarity of the Green's functions characterizing the source-receiver paths. Based on the lambda/4 criterion, it is frequently argued that similar earthquakes may represent repeated slip of the same patch of a fault. Because of the phenomenological nature of waveform similarity, such interpretations are strongly dependent on seismic signal characteristics and on the way, the waveform similarity is defined. In this article, we use two-dimensional synthetic wave-field simulations in lateral heterogeneous media to investigate how the waveform similarity of closely spaced hypocenters changes with interevent separation. We analyze the influence of correlation window length, signal frequency bandwidth, and source-receiver geometry on the waveform similarity and discuss under which conditions the lambda/4 criterion can be applied to the synthetic data set. With the correlation window length defined as 2.8 times the travel-time difference between the S- and P-phase onsets, we find a correlation threshold value of 0.95 independent of the signal frequency bandwidth. We use the same threshold value for two field data examples that are similar to the synthetic data in frequency content and waveform complexity, and we discuss the implications of the lambda/4 criterion. For three microearthquakes occurring during a fluid-injection experiment at the German deep drilling site (Kontinentale Tiefbohrung [KTB]), the interevent separation constrained by the lambda/4 criterion is sufficient to identify these events as a sequence of repeating earthquakes in the sense that at least a fraction of the source area experienced repeated slip. For a second data example of four natural (micro-) earthquakes occurring near the island of Crete, the lambda/4 criterion does not sufficiently constrain the hypocenter location to identify these events as repeating earthquakes due to the lack of high-frequency information.