Main points
 The Mogul sequence is decomposed into 2335 individual clusters.
 The cluster threshold is chosen in accordance with randomized catalog analysis
that identifies inter-event distances (in time-space-magnitude domain) that cannot
be observed on the same fault structure and with the same event intensity but
without time-space dependencies.
 The 17 largest clusters (N > 10) clearly identify the three main geologic structures
over which the Mogul sequence had developed.
 The time plot of the 17 largest clusters illustrates the switch of the activity
between the two main geologic structures.
 The analysis is not sensitive to the parameters (we see the same for other sets of
the largest clusters, etc.)
 The results seem like a good point for further discussion.
Analysis description
Data. We work here with a relocated catalog of the Mogul sequence (hypodd.reloc)
from Chritsine Ruhl (e-mail of March 10, 2014). The catalog consists of 3748 events with
magnitudes in the range [-0.5, 4.9]. The spatial location of events is shown in Fig. 1; the
time-magnitude sequence is shown in Fig. 2.
Parameters. The analysis here is done with b = 1, df = 2.6. The main qualitative results
are not sensitive to this choice.
Nearest-neighbor distance. The join distribution of rescaled components (T, R) of the
nearest-neighbor distance  is shown in Fig. 3a. The four white lines in the figure are 
=10-8, 10-7, 10-6, and 10-5 (bottom to top). Notice that the main body of the Mogul data is
located below the line  =10-5, which is usually used as a threshold that separates cluster
and background populations. Another noteworthy observation is overall “spherical”
shape of the point scatter, which is characteristic of clustered population. Hence, in a
large-scale analysis (that considers, say, the Nevada region), the entire Mogul sequence
would be identified as a single cluster.
Homogenized profile. Our goal, however, is to explore the internal structure of the
Mogul sequence. To approach this problem, we construct a homogenized profile of the
sequence; it is shown in Fig. 2b. Specifically, the figure shows the average of joint (T,R)
distributions for 50 randomized catalogs. Each randomized catalog is constructed by
independent random reshuffling of times and magnitudes of the events from the Mogul
sequence. This procedure destroys possible space-time-magnitude correlated structures in
the catalog, while keeping the original (inhomogeneous) marginal distributions of time,
space, and magnitude.
The homogenized profile has overall “diagonal” location that is characteristic of
background events. The homogenized profile suggests that events that happen at
distances smaller than 0 =10-7.5 are due to space-time dependent structures rather than
region fault structure of increased seismic activity within the Mogul sequence. We chose
this threshold for further analysis.
Clusters. We detect 2335 clusters in the catalog. The distribution of cluster sizes can be
closely approximated by a power law with the slope drop at N = 20; see Fig. 4. The
distribution is dominated by clusters of size N = 1 (singles) that comprise 88% of clusters
and 55% of all events. Map of the epicenters of the 277 families (clusters with N>1
events) is shown in Fig. 5.
Figure 6 (top) shows the epicenters of the families with more than 10 events.
There exist 17 such families; they contain 956 events that is 25.5% of the entire
sequence. The largest families depict the three main geological features in the Mogul
region.
The bottom panel of Fig. 6 shows the temporal evolution of the epicenters of the
17 largest families. We see that the sequence starts at the NW-SE fault (cyan colors) and
jumps to a NE structure after the sequence largest event (M4.9) depicted in the panel by
vertical line. Movie clusters_N10.avi further illustrates the evolution of seismicity
within the Mogul sequence by showing the location of consecutive clusters with N > 10.
The detected clusters with N > 10 clearly identify the main three geologic
structures over which the Mogul sequence had developed. (Figure 7 illustrates the
seismic activity on each of the structures during the sequence.)
Figure 1: Map of epicenters
Figure 2: Time-magnitude sequence
Figure 3: Joint distribution of the rescaled time (T) and space (R) components of the
nearest-neighbor distance η. White lines (bottom up) correspond to η =10-8, 10-7, 10-6,
and 10-5. (a) Original Mogul sequence. (b) Average of 50 randomized catalogs that use
independently reshuffled times and magnitudes of the original events.
Figure 4: Cluster size distribution. The figure shows the proportion of clusters with size
over N as a function of N.
Figure 5: Epicenters of families (clusters with more than one event). Color code and
colorbar correspond to g = (longitude + 2*latitude) and is used to distinguish between
geological features used in subsequent analysis.
Figure 6: Epicenters of families with more than 10 events (17 families, 956 events,
25.5%). Color code and colorbar correspond to g = (longitude + 2*latitude) and is used to
distinguish between geological features used in subsequent analysis. Top: geographic
map. Bottom: Time vs. g; the line depicts the occurrence time of the M4.9 event.
Figure 7: Evolution of Mogul sequence on the three main geological structures depicted
by color in the top panel. The bottom panel shows the number of events in a 1-day
window on each of the structures.
Figure 8: Characteristics of Mogul sub-clusters vs. time. Top: Magnitude, m. Middle:
Cluster size, N. Bottom: Average leaf depth, <d>.