Interevent times within aftershock sequences as a
reflection of different processes
Ramón Zúñiga
Centro de Geociencias, National Autonomous University of Mexico (UNAM), Juiriquilla, Mexico.
[email protected]
1. ABSTRACT
3. DATA
We have looked at the interevent time behavior as a
function of time for aftershock sequences from
mainshocks occurring in similar tectonic regimes but
different regions with the aim of gaining information on
the aftershock process. To this end we studied some well
defined aftershock sequences from Alaska, New Zealand
and Mexico and analyzed the distribution patterns of
interevent times (also called waiting times) in both time
and space. Several results emanate from this exercise. In
most cases, more than one coherent process can be
discerned from that acting following the main process.
2. MOTIVATION
The distribution of interevent times of aftershocks suggests that
they obey a Self Organized process (Bak et al, 2002). Numerical
models such as ETAS (Ogata, 1988) take from the idea that every
event is capable of spawning its own individual sequence of
events. Thus, the sum of all sequences might be the reason
behind the self organized or fractal behavior observed.
However, spatial variations in the P value of the Omori Law
(Wiemer and Katsumata, 1999; Enescu and Ito, 2003) may be
indicative of different regimes actuating at different times and
controlling the overall process.
Here we attempt to gain information on the aftershock process
from the temporal behavior of interevent times in order to
answer the following questions:
• Can we identify differences in the generation of aftershocks
which indicate different processes acting at different times?
•Are aftershocks self organized in a unique manner?
•Do principal processes exist which govern the generation of
aftershocks?
EVENT NZaft2 1994/6/18/3/25 Ms 6.7 Depth 4.27
For this case the average shows larger scatter
but nevertheless a second (intermediate)
trend can be discerned.
The location of events falling within
the three trends appear to migrate
inward. The background seismicity has
not taken over the overall trend.
We selected some well defined aftershock sequences from Alaska, New Zealand and
Mexico which occurred in similar tectonic situations All events are shallow continental type
even though some of them they take place close to plate boundaries.
4. TEMPORAL AND SPATIAL DISTRIBUTIONS OF INTEREVENT TIMES
For every aftershock sequence, selected from the maximum affectation distance of Kagan
(2002) we show the temporal behavior of the logarithm of interevent times (waiting times
WT) and identify apparent changes in trend. We then look at the spatial location of events
ocurring within the trends identified.
EVENT AKaft1 1995 /10/6/5/23 Ms 6.2 Depth 9.09
In order to better identify linearities in the time
trend of the logarithm of interevent times, we
plot the raw data, an equal interval interpolation,
and a running average with 20 points.
For this case two main trends can be observed, after which background seismicity
seems to take over (wt oscillate around a constant value).
Events occurring within the first trend (blue
crosses) are tightly clustered around the
mainshock while those in the second trend (green
circles) are located in a wider region.
The normalized distribution of interevent times
plotted for different magnitude cut-offs, does not
indicate any departure from a single regime.
Omori aftershock decay rate can be fitted by with
a single P value, no other trend is apparent from
the data.
Yet, only one regime is seen through the
density distribution of interevent times.
EVENT MXaft1 2001/10/8/3/39 Ms 5.4 Depth 4.0
Omori Law is well fitted by means of
one P value. No other trends are seen.
EVENT NZaft3 2001/12/7/19/27 Ms 6.2 Depth 5.0
The temporal behavior of WT for this event
are similar to those of event AKaft1, again
two main trends may be observed after
which background seismicity (longer period
oscillations around a constant value) takes
over.
Two separate clusters occurring within
regions side by side are seen in this case.
Notice that the events belonging to the
second cluster (green circles) are closer to
the mainshock and their inter-distance is
no different from those of the first cluster
and trend (blue crosses).
For this case two linear trends are apparent
in the density distribution indicating two
correlation regimes.
The aftershock decay rate can be fitted by
and Omori law with a single P value.
This event shows apparently only one trend
before the background, although the magnitude
resolution for these events is much larger than in
the other cases (Mc ~ 3.6) which may preclude
observing details in the immediate temporal
vicinity of the mainshock. Notice also that the
magnitude is smaller than other cases although
aftershock production is similar.
No pattern is distinguishable from the epicenter
locations which can be correlated to the trends in
WT and no difference can be made from
background seismicity.
The density distribution of interevent times is
similar to that of a Poissonian process, again
pointing to similarities between the sequence and
background seismicity.
An Omori relation is not clearly defined for this
sequence and no single P value can be used to
model the process.
5. CONCLUSIONS
Different processes, which can be identified through the temporal behavior of
interevent times appear to actuate within aftershock sequences and which do not
seem to obey a general principle. For most cases analyzed difference in trends
might be the result of different coherent diffusion mechanism, with other
mechanisms taking over at certain later time.
The examples show that we can not generalize by stating that the initial process is
contained within a localized region near the mainshock, nor can we relate spatially
closer clusters with shorter interevent times,