FIRST RESULTS ON THE DIRECTION STATISTICS OF PAIRS OF EPICENTERS OF NEIGHBOR EARTHQUAKES ON KAMCHATKA

Small earthquakes, often treated as “background seismicity”, are not distributed in space-time in a random manner. Often, space-time clustering is studied, that manifests itself as aftershock sequences and swarms. These phenomena can be described as a deviation (increase) of probability of short interevent distances and times as compared to the reference “pure random” or Poisson case; this tendency manifests itself in statistics of distances between epicenters. In the present work, we study the statistics of directions for vectors connecting pairs of epicenters of such small earthquakes which are close in space-time. Components of such pairs will be called “neighbors”, and the mentioned vectors will be called “link vectors”. A study of this kind is of interest from a number of viewpoints, such as: discovering new properties of statistical structure of observed fields of epicenters; establishing interactions between earthquake sources of small earthquakes, revealing geometrical properties of the pattern of active faults of a low rank. We will show that directions of link vectors clearly deviate from isotropy, and have instead non-uniform, often spiked, distribution of directions.

Pairs of neighbors are extracted from the catalogue of small (M_L=3.5–5.0) shallow earthquakes of the Kamchatka subduction zone. То define neighbors, bounds are set on the distance (10–60 km) and relative delay (0.5 day) between members of a pair. Before pair extraction, the work catalog was decimated to reduce space-time event density within dense clusters. With the catalog of pairs at hand, we constructed distributions of azimuths of link vectors (rose diagrams of directions). In Fig. 3 one can see example histograms and corresponding rose diagrams for two 10-year periods (see Table 1 for definitions and labels of the periods); processing was done using two variants of maximum delay: 0.5 and 5 days. Angles (modified azimuths, n) in all histograms and rose-diagrams are counted off from the direction with azimuth of 37° that represents the strike of the island arc. Before constructing rose diagrams, the modified azimuths were reduced to the [0° 180°] range by subtracting 180° when needed. One can see that with the stricter limit of 0.5 days, histograms and rose diagrams show more expressed deviations from the uniform (isotropic) distribution of angles. For both variants of the maximum delay, the along-arc oriented pairs manifest themselves (at n about 0° and 180°). At the less strict limit of 5 days, this orientation begins to dominate. Although this tendency formally means a break of isotropy, it is not of particular interest because it results from the fact that a large fraction of epicenters occupy a relatively narrow strip, well seen on Fig. 1; therefore the observed 0–180° preferred direction has no connection to epicenter distribution within narrow space-time neighborhoods that we intend to analyze.

To suppress the contribution of this interfering direction, a special normalization of angle histograms was performed. We additionally calculated similar histograms for larger delays, 100 to 150 days, marked T, considering these as representing pure effect of geometry of the epicenter field, and used them for normalization, performed in the following way. Values of the initial or raw (R) histograms are divided (point by point) by corresponding values of T-histograms. In this way the normalized (N) histograms are obtained, considered as most representative of preferred directions of neighbor pairs. To make the results more convincing, we performed statistical testing of the hypothesis “N-histogram differs from a constant”; actually, the equivalent hypothesis “the R-histogram differs from the T-histogram” was tested. The Pearson’s c² criterion was used. The significance value, Q, is indicated on plots, in most cases it is below 0.1 %. Such are the processing procedures employed; then the analysis of data was performed.

N-histograms have been determined for three circles of the 150-km radius shown on Fig. 1, and for five ten-year periods. For the corresponding R-, T- and N-histograms and rose diagrams see Fig 5, 4 and 6. One can see a clear and mostly significant deviation from isotropy; instead, narrow petals are seen in many cases. To see in the original map view how these petals are formed see Figs 7 and 8.

The following conclusions can be derived from this material. (1) The observed distributions of pair azimuths deviate significantly from the uniform law; in many cases, this deviation manifests itself as narrow petals. (2) In two out of three rose diagrams of N kind, there is an expressed petal oriented across the island arc, and along the maximum compression axis. Its formation is difficult to explain from the geomechanical viewpoint. (4) There is evident difference between the rose diagrams for the two southern circles SK and SP, located in the main part of the island arc, and that for the circle KG located near to the junction of Kurile-Kamchatka and Aleutian arc. (5) Clear temporal variations of rose diagrams are seen; these can reflect short-term evolution of parameters of seismotectonic deformation (of “seismic flow of rock masses” in terms by B.V. Kostrov [Kostrov, 1974, 1975]). We believe that the observed picture can be explained through propagation of pulses of aseismic slip along secondary faults. Such pulses are accompanied by small earthquakes; in this way, a pattern of oriented epicenter pairs arises, akin to the notion of migration of epicenters. The location of oriented pairs is tied to several hypothetic systems of subparallel (en-echelon) faults; each such system is manifested as an individual petal of a rose diagram. This interpretation is illustrated by Figs 7 and 8 where one can see in map view how a separate petal of a rose diagram is related to a set of subparallel links that formed it. The main result of the study is the design and testing of a new technique of investigation of hidden anisotropy of the field of epicenters, and detection of time variations of the revealed features. The technique has a potential for monitoring the stress regimen of the lithosphere.

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