Introduction
One of the most challenging problems in seismology is presently the study of
preparatory processes for strong earthquakes. Seismometric data still
represent the most informative observations available to researchers who
investigate their association with signals emitted by faults before
catastrophic ruptures. In this respect, new features in seismometric records
have been discovered and studied in the recent past
. Beside seismometric recordings,
slow deformation observations and laboratory experimental simulations
contributed to give new important pre-seismic information
.
Nevertheless, the physical processes taking place on time scales ranging from
few years to few hours before the seismic rupture still remain mostly
unknown.
Geographical setting of the study area located in the Calabria
peninsula, southern Italy (see inset). Green triangles show the location of a
radon monitoring stations MMN and MMNG. Yellow circles represent the
earthquakes recorded by between December 2011 and October 2014
with epicentral distance from MMN (the older station) less than or equal to
15 km (4800 events). Focal mechanisms of the Mw 4.3 28 May 2012,
Mw 5.2 25 October 2012, Mw 3.7 4 June 2014 and
Mw 4.0 6 June 2014 earthquakes
(http://cnt.rm.ingv.it/tdmt.html) are also represented.
Evidence gathered in recent years indicates that, in specific seismotectonic
settings, fluid transport and dynamics could play an important role in
seismogenic processes
. In these
seismogenic systems, the study of transient signals associated with fluid
migration (markers) becomes particularly significant. Among all the possible
transient signals, the radioactive nature of radon makes it a potentially
extremely efficient marker to study and monitor fluid flows. Indeed,
radioactive detectors are generally quite efficient and accurate instruments,
and their implementation and installation requirements make them also
particularly competitive in terms of operating costs. A radon monitoring
station equipped with meteorological sensors presently costs almost one order
of magnitude less than a CO2 / O3 geochemical station
. The cost factor becomes particularly
important considering that the experience in operating seismometric and
geodetic observational networks taught us that, in order to achieve high
quality results, instrumentally dense networks are needed.
From the beginning of 2010 the Pollino Range area, in the southern Apennines
on the border between Calabria and Basilicata, has experienced a seismic
sequence. The seismic activity is characterized by frequent periods of
intense output with others of relative quiescence and culminated on
25 October 2012 with a Mw 5.2 mainshock .
From 2010 to the end of 2014 about 5000 events (mostly ML ≤3.0) were
recorded . The hypocenters clearly show two main clouds (see
Fig. ): a western cluster which includes most of the seismicity
(the Mw 5.2 mainshock too) and seems consistent with a normal faulting
trending NNW and dipping WSW and an eastern cluster, including the Mw 4.3
earthquake occurred on 28 May 2012 that does not clearly exhibit instead a
definite fault plane . During 2014, two other
significant events took place in the area: Mw 3.7 and Mw 4.0 earthquakes on
4 and 6 June on the western and eastern cluster, respectively. Recently
relocalized the hypocenters of the 2010–2013 swarm
revealing two main clusters, differing both in number and in magnitude
distribution of seismic events. The two different clusters of values for
magnitude and total number seem to suggest that two distinct structures of
different dimensions have been activated, as supported by the
Gutenberg–Richter law too.
In late 2011, we started a long-term experiment in the Pollino area of
Southern Italy, installing a high sensitivity, high efficiency active radon
monitoring station based on a Lucas cell
. In November 2012, a second station
was installed a few kilometres away from the first one.
Several world-wide compilations of radon emission anomalies that could be
associated with variations in the seismic activity and/or occurrence of a
single earthquake are available in the literature seefor a
review. In recent years, laboratory experiments gave
unambiguous evidence of the relation between the rock state of stress and
variations in the radon emanation properties .
It is widely accepted that meteorological parameters play an important role
in modulating soil radon emanations
. But, as
evidence grows, it becomes clearer that this relation is complex and strongly
site dependent, so it cannot be steadily assessed. Even the relative
importance among the main relevant variables (temperature, precipitation,
pressure) in modulating the radon emissions cannot be univocally determined
and it is likely to be site dependent, since different analyses led to
different results i.e.,.
MMN radon concentration in (Bq m-3)/115 min (yellow dots) and
daily average rainfall (red line) for some significant fall–winter
(a–d) and spring–summer (e, f) periods (see text for
details). Red ellipses mark heavy rain events, whilst yellow rectangles
represent radon concentration peaks.
In the following, we propose an articulate approach, taking advantage of
different investigative tools, to better assess the questions described
above. In particular, we will consider the problem both from a quantitative
phenomenological point of view and by means of suitable numerical analyses.
The presentation of our results is organized as follows: in
Sect. we describe the observational setup, the
collected radon time series and some phenomenological insights about the
impact of meteorological conditions on the detected signal. In
Sect. we analyse time series by means of different
numerical approaches: namely, in Sect. we perform a
correlation and cross-correlation analysis between radon emanation
observations and the other relevant observables (meteorological parameters
and seismic moment release) and successively we outline an approach aimed at
reducing meteorological effects in the measured radon time series; in
Sect. we investigate the potential predictive
capability of the radon signals, testing the possibility of highlighting in
advance the occurrence of the major events of the seismic sequence in the
Pollino area from the radon time series analysis. Finally, in
Sect. we discuss and summarize all our findings.
MMNG radon concentration in (Bq m-3)/115 min (yellow dots)
and daily average rainfall (red line) for some significant fall–winter
(a, b) and spring–summer (c, d) periods (see text for
details). Red ellipses mark heavy rain events, whilst yellow rectangles
represent radon concentration peaks.
MMN and MMNG sites
We installed two radon monitoring stations in the Pollino area, equipped with
prototype detectors based on a Lucas cell that continuously acquired radon
concentration data, with a sampling interval of 2 hours. Station MMN was
co-located with the homonymous seismic station belonging to the INSN, Italian
National Seismic Network, at Mormanno (39∘53′58.6′′ N
15∘59′25.5′′ E) in December 2011, at about 921 m above sea
level. Station MMNG was installed in October 2012 (just after the Mw 5.2
event) about 3.0 km east of MMN (39∘53′8.1′′ N 16∘1′33.6′′ E), at about 858 m above sea level. Both stations are shown in
Fig. with green triangles. The complete time series and
technical features characterizing the MMN and MMNG stations are reported in
the Supplement.
Station MMN shows a high variability in radon concentration, with sharp peaks
and rapidly changing values ranging from a few tens up to 2500 Bq m-3
(see Supplement Fig. S1), while MMNG station has lower
concentration values (up to 600 Bq m-3) and a trend ascribable to a
major seasonal correlation with temperature (see
Fig. S2), as laboratory tests and long-term radon
monitoring studies
would indicate.
The evidence of the impact of meteorological parameters on radon observations
and at the same time the strong site-dependent nature of the characteristics
of radon emissions introduce uncertainties into the comprehension of the
problem. These complexities suggest the problem should be approached from a
phenomenological point of view in order to supplement the indications
retrieved by means of a purely quantitative analysis. First of all, we focus
on the “sealing” effect induced by precipitation on soil radon emanation.
Such effect has already been suggested and established by several studies
i.e.,, and its impact in the MMN time series
seems particularly evident. Figure shows a collection
of selected periods from MMN time series (radon in concentration
[Bq m-3]/115 min) corresponding to major rainfall episodes. From
Fig. it is clear that, after a major precipitation
episode (red ellipses), radon concentrations drastically fall by a factor
greater than 10 up to a factor of almost 100. Precipitation, as well as all
of the meteorological parameters discussed here, is obtained as short term
(12–24 h) weather forecast by an Italian weather forecasting site
(http://www.ilmeteo.it/). Figures a, b, c and d
represent fall–winter heavy rain events, which are common in this
region , whilst
Figs. e and f show spring–summer time windows, when
shorter and less intense rain episodes occur. Despite the different magnitude
of precipitation episodes, similar reduction effects in radon emission can be
seen in fall–winter as well as in spring–summer periods. Moreover, it can be
seen that during prolonged dry periods, independently from the season, radon
concentration peaks are more pronounced (yellow rectangles). For the MMNG
station the reduction effect of rainfall on radon observations seems less
marked, but it is still present. Figures a, b,
c and d show selected
fall–winter and spring–summer periods for MMNG, respectively. In this case,
though the reduction of radon emission with precipitation is still present
(Fig. a), heavy rain events cannot be clearly
separated from radon concentration peaks, being sometimes overlaid (yellow
rectangles) (Figs. b, c and d). Anyway, overall both
stations have evidenced that radon activity was on average higher during the
summer than the winter, in according with observations by
and more recently by and . The complete
explanation of this behaviour involves complex interactions among all
environmental parameters. Nevertheless, it is likely that a partial role is
played by the inhibitory effect of the rain on radon emanation. Of course,
this effect is much smaller in dry season than in winter.
(a) 14-day moving-averaged time series of radon
concentration at MMN (black line) and of rainfall (red line). (b)
14-day moving-averaged time series of temperature (black line) and pressure
(red line). (c) 14-day moving average of cumulative seismic moment
release (black line, in logarithmic scale) and of seismic moment release (red
line). Yellow stars represent the occurrences of the main earthquakes of the
sequence.
Analysis of radon time series
In the following we try both to assess the impact of meteorological
parameters on radon signals on a quantitative basis and to outline an
original approach aimed at removing (or at least mitigate) the effects of
meteorological events on the detected time series. Our goal is to maximize the
informative power of radon emanation variations potentially related to a
variation in seismic energy release.
Even though the effects of meteorological conditions on temporal radon
time series have been investigated for the last 50 years by means of
different approaches and methodologies
, a clear assessment and a solid
interpretation has not been univocally established yet.
(a) Time series of daily moving-averaged radon concentration
at MMN (black line) and of rainfall (red line) for the period between
1 April 2012 and 31 December 2012. Yellow stars represent the occurrences of
the two main earthquakes of the sequence. (b) an enlarged view of
the first yellow rectangle of (a), from May to June 2012. Yellow
dots represent radon concentration at MMN in (Bq m-3)/115 min, while a
black line shows the daily averaged concentration. Daily averaged rainfall
levels are represented by a red line. (c) An enlarged view of the
second yellow rectangle of (a), from September to December 2012, as
in panel (b).
For the following analyses, we decided to use only radon time series from
station MMN, since it was the only one installed before the main events of
the sequence (Mw 4.3 on May 2012 and Mw 5.2 on October 2012), corresponding
to the major changes in cumulative seismic moment release rate
(Fig. c). From data collected in the time window
from April 2012 to December 2012 (Fig. a) that
includes the two major seismic events, we note that in correspondence of
these two change-points the radon emanation increased a few days before the
seismic events. Both the average amplitude and duration of such increases
appear to scale with the magnitude of the corresponding earthquakes, as
highlighted in the two yellow rectangles of
Fig. a. The apparent discontinuity in the radon
increase just after the Mw 5.2 seismic event is likely to be associated with
a major precipitation episode right after the earthquake occurrence. In fact,
the severe rain event occurred just after the Mw 5.2 earthquake has likely
interrupted the underlying radon increase characterized by a quasi-linear
trend starting from the beginning of October (therefore almost a month before
the mainshock) until the end of November 2012 with just the only exception of
the week after the 35 mm H2O peak rain episode
(Fig. c).
Figures b and c show in detail the time windows
corresponding to the two seismic events. The intensity of radon emanation
sharply increases about 24–48 h before the occurrence of both earthquakes,
reaching similar peak values (800–900 Bq m-3) and then, in the case
of the 28 May 2012 Mw 4.3, it returns to previous values after about 7 days,
while, after the mainshock of the 25 October 2012 Mw 5.2 event, observed
values continue to increase up to about 1600 Bq m-3 for more than
30 days after the earthquake (except, as described above, for the first few
days of November, when a major precipitation event flattened down radon
levels). While not quantitatively constrained yet, it is reasonable to assume
that the time needed for radon emanation to recover from the perturbed state
returning to background level is proportional to the overall energy involved
in the seismogenic processes and hence to the magnitude of the impending
earthquake.
Cross-correlation function (CC) evaluated for 2012–2013–2014
separately, between radon concentration Rn and temperature T, pressure P
and seismic moment release M0. The CC is evaluated between 14-day moving
average filtered time series. Horizontal gray lines represent 99 %
confidence threshold.
Correlation and cross-correlation analysis
In order to quantitatively assess the phenomenological evidences described
above by means of numerically objective procedures, we perform a series of
statistical evaluations on our dataset. Figure
shows the whole time series employed in the statistical analysis filtered
with a 14-day moving average. All the moving averages employed in our
computations are evaluated backwards (i.e., average at day di, employs
only the previous (di-14) days). Figure a
represents the radon concentration (black line) and rainfall (red line),
Fig. b shows temperature (black line) and pressure
(red line). Figure c shows the cumulative seismic
moment release (black line) with the seismic moment release (red line).
Since the Pearson coefficient reflects mainly a linear relationship between
variables, we estimated the correlation between variables using both the
Pearson coefficient and a non-parametric correlation
coefficient . The two approaches yield virtually identical
results, so we show here only the classical Pearson analysis. We performed
both a correlation analysis between radon and environmental parameters and a
cross-correlation analysis between radon, meteorological parameters and
seismicity. All analyses look for a linear relationship between two
variables, but the cross-correlation considers it to be a function of the time offset of
one relative to the other. Formally cross-correlation function reads
i.e.,:
CCuy(k)=1N∑t=1N-k(ut-u‾)(yt+k-y‾)k=0,1,…,(N-1)1N∑t=1-kN(ut-u‾)(yt+k-y‾)k=-1,-2,…,-(N-1),
where N is the series length, ut and yt are the two time series,
u‾ and y‾ are their sample means, and k is the lag.
Differently from Pearson linear correlation, the cross-correlation
coefficient is not normalized a priori: in order to grant compatibility with
the previous analyses, we normalized the cross-correlation coefficient here
so that it varies between -1 and 1 and set the lag range between -40 and
40 days.
We decided to exclude rainfall from this analysis since, differently from
other meteorological variables, it is intrinsically characterized by a
strongly discontinuous, spike-like behaviour being the majority of the
sampling times characterized by a null value. In fact, during the time window
of our most relevant analyses, we have null rain values ranging from 65 to
75% of the sampling intervals (to compare for instance with less than
10% of days with null seismic moment release). This makes correlation
and cross-correlation analysis inadequate approaches to evaluate the
relationship between radon concentration and rainfall.
The results regarding the correlation analysis in terms of Pearson
coefficient are summarized in Table . For all considered cases,
we report both global cumulative value (G) corresponding to the entire
acquisition window (2012–2014) and separate results for each year
(2012–2013–2014). The Pearson coefficient ρ shows a significant level
of negative correlation only between radon concentration and temperature with
values ranging from -0.6 to -0.2. The value of the Pearson coefficient
for pressure, even though coherent both in sign and in magnitude for each
time window, is nevertheless statistically compatible with zero.
Pearson correlation coefficient (ρ) between radon concentration
time series (Rn) and temperature (T), pressure (P) time series, evaluated both
as global value (G) for the entire acquisition window and as annual value for
2012, 2013, 2014 separately. Rn concentration, T and P time series are
filtered with a 14-day moving average.
ρ
G
2012
2013
2014
(Rn, T)
-0.46
-0.58
-0.20
-0.46
(Rn, P)
0.15
0.13
0.24
0.04
Within the cross-correlation analysis, whose results are shown in
Fig. , we include also the seismic moment release M0,
since for this physical variable a lagged approach is able to consider also a
causal relationship in addition to an instantaneous feedback among variables
. Figure is arranged in
nine panels: from left to right the cross-correlation between radon and
temperature, pressure and seismic moment release, respectively, are
presented, while the rows represent 2012, 2013 and 2014 time windows. No
sharp and isolated peak is observed in Fig. , indicating
that no clear cross-correlation scenario can be deduced from this analysis.
Nevertheless, we can confirm the correlation pattern described above: the
cross-correlation function between radon concentration and temperature does
not show clear preferences for a lag time, but it is almost always
characterized by negative values, while the cross-correlation between radon
and pressure time series varies in time, with value always below the 99%
confidence level. The confidence level is defined as the value of the Pearson
coefficient ρ for which the probability of obtaining a cross-correlation
greater than or equal to ρ for uncorrelated data is equal to 1
and is represented in Fig. by the
grey lines. The cross-correlation function between radon concentration and
seismic activity shows a significative positive peak during 2012 (when the
major seismic events occurred), with a maximum value of 0.5 in correspondence
of a 21 day delay forward of radon concentration (Fig. ,
panel upper right).
Cross-correlation function (CC) between radon concentration Rn and
seismic moment release M0 time series, filtered with a 14-days
moving average and evaluated in two different time windows (black line for
tw-1 and blue line for tw-2), with (dashed lines) and without (solid lines)
correction coefficients. Both the values of correction coefficients and time
windows bounds are summarized in Table .
Of course the relationship between variations of radon emanation and
seismotectonic processes would be better assessed if we would be able to
remove, or at least reduce, the bias of meteorological parameters on the
radon measured concentration. To this aim, we implement an empirical
correction procedure for temperature, pressure and precipitation variations.
Basically, given an observed radon concentration value Rnobs, taken
at time t when a temperature T, an atmospheric pressure P and a
precipitation level R have been registered, we define a corresponding
meteorological-corrected concentration Rncor as follows:
Rncor=Rnobs×CP×CR×CT,
where CP, CR and CT are positive correction factors obtained
as a simple linear interpolation from the minimum detected values of T, P
and R in a selected time window where {CP=CR=CT=1}
(that is to say there is no-correction), to the maximum detected values in
the selected time window where {CP=CPmax;CR=CRmax;CT=CTmax}. The optimal value of
CPmax, CRmax and CTmax can be obtained
by maximizing the cross-correlation function for the selected time window (of
course a time window including a significant seismic activity must be
selected). We want to note that the subscript “max” above stands for
maximum magnitude of the correction, not for maximum absolute value of the
correction parameter Ci. Indeed, if the correction factor corresponding
to the maximum value of a given meteorological parameter Ci is >1, it
means a negative correlation between radon and that parameter, the opposite
if the correction factor Ci is >1. Since it is reasonable
to consider the possible connection between radon concentration variations
and seismotectonic processes as dependent from the seismic source-observer
distance , we have implemented in the correction
procedure also the possibility of weighting for the epicentral distance
. Again, given an earthquake with seismic
moment M0obs occurred to an epicentral distance r from station
MMN, we consider a corresponding distance-weighted value M0wgt:
M0wgt=M0obsrw,
where w is a positive weighting factor (w=0 means no correction for
epicentral distance).
In Fig. we show the effects of our correction
procedure on the cross-correlation function. The extrapolation of the optimal
values for the correction parameters CPmax, CRmax,
CTmax and w was performed by means of the MINUIT
package , which implements a variable-metric method with an
inexact line search, a stable metric updating scheme and a
positive-definiteness check . The search domain for Ci
and w was limited in the range between 0.1 to 10 to avoid unphysical
solutions. This procedure has been applied with two different time windows,
both including the two main events and the active part of the sequence
(May 2012 Mw 4.3 and October 2012 Mw 5.2): the first
time window (tw-1) covers a whole year from January 2012 to January 2013,
while the second (tw-2) focuses on the most active part of the seismic
sequence from April 2012 to January 2013. As can be seen from
Fig. , the proposed correction procedure
significantly increases cross-correlation peaks for both time windows
(indicated as tw-1 corrected and tw-2 corrected). Notably, the increase is
greater for the larger time window where a lower (but still significant) peak
cross-correlation value was obtained, while the time lag of the peak remains
completely unchanged after the correction, indicating that the variation of
radon intensity seems to follow the variation in seismic moment release. In
Table the correction coefficient values maximizing the
cross-correlation peak in the two time windows tw-1 and tw-2 are reported. From the tabulated values we note the following: (i) the correction values for the
rainfall lie in both cases at the top of the searching domain
(CRmax=10 for tw-1 and CRmax=9 for tw-2); i.e.,
rainfall is strongly anti-correlated with radon emanation, confirming the
phenomenological analysis in previous Sect. ; (ii) the
correction values for the temperature are always greater than 1, confirming
that for MMN station temperature is anti-correlated with radon emanation (see
above in this same section); (iii) the correction values for the pressure
oscillate about CPmax=1, confirming the lack of a clear
correlation regime between pressure and radon emanation for this station.
Correction coefficients for temperature (CTmax), pressure
(CPmax), rainfall (CRmax) and epicentral distance (w)
maximizing the cross-correlation function (CC) in time windows tw-1
(January 2012–January 2013) and tw-2 (April 2012–January 2013).
CTmax
CPmax
CRmax
w
tw-1
2.4
4.4
10.0
1.3
tw-2
5.6
0.9
9.0
0.0
Change point analysis and detection algorithm
The problem of detecting changes in time series is well known in climate
literature: the definition and identification of discontinuous steps, or
change points, may be subjective and it also depends on the form of the trend
one expects between changes. Several methods have been implemented to solve
the change point problem both for short and long climatic time series. We
refer the readers to , in which the literature about the
change points methods is widely reviewed and discussed.
We applied to the measured radon intensity time series an algorithm developed
in the realm of Earth's climate system studies in order to calculate, by
means of a Bayesian approach, the posterior probability of multiple change
points in a generic climatic time series (Bayesian Change Point algorithm,
, BCP hereinafter). Once the algorithm has identified an
arbitrary number of change points in our time series, whose maximum is an
input parameter of the algorithm (kmax=6 in the following) , our
primary interest is to verify if the detected change points in the radon
time series are consistent with corresponding changes in cumulative seismic
moment release rate (i.e., major earthquakes).
Applying the BCP algorithm to the whole MMN time series, we obtain an
indication of most likely two change points that are potentially associable
with the two largest events of the sequence. Figure
show the 14-day moving-averaged time series of radon intensity (solid black
line) along with the change point regression model (dashed green line); the
locations of the change points are displayed as red spikes, whilst
earthquakes occurrences are displayed as yellow stars. Furthermore, the algorithm has the ability to provide an uncertainty estimate in locating a
change point: in this case the height of the two considered spikes (the
second and the third in Fig. ) indicates a probability
equal to 0.33 for the change point corresponding to the Mw 4.3 on May 2012 and a probability equal to 0.57 for the change point
corresponding to the Mw 5.2 on October 2012. The second change
point occurs on 8 May 2012, 20 days before the Mw 4.3 28 May,
while the third change point occurs on 22 October 2012, 3 days before the
Mw 5.2 25 October event.
Change point analysis applied to time series of radon concentration
at MMN. The black solid line represents the radon concentration at MMN
filtered with a 14-day moving average, while the green dashed line
represents the model predicted by the Bayesian Change Point (BCP) algorithm.
The red line represents the probability of a change point at each time.
Yellow stars represent the occurrence of the earthquakes Mw 4.3 on
28 May 2012 and Mw 5.2 on 25 October 2012.
The different time advances of the change points found by the BCP algorithm
with respect to the two associated earthquakes occur (20 days and 3 days
before, respectively) is not determinant for our investigations, since the
dynamics of radon emission is intrinsically complex, as shown also by
. Nevertheless, it could be useful
to get further insight into the relationship between radon and seismicity,
employing the same BCP algorithm on the cumulative seismic moment release
time series, in order to check the possibility of finding significant
variations in seismic moment release that are different from the trivial ones
(i.e. coincident with a major seismic event). The result is shown in
Fig. : in this case the rates changes, which are
clearly visible a priori, are all found by the algorithm with a probability
near to 1. While the 2nd and the 4th change points clearly identify the two
earthquakes, the 1st and the 3rd change points seem, instead, to identify the
beginning of a preparatory phase of the two events. The first occurs on
20 February 2012 (1st red spike in Fig. ) and the
third on 18 August 2012 (3st red spike in Fig. ).
We note that the temporal difference (about 70 days) between each of these
two change points and the change points estimated by the BCP algorithm for
the MMN time series (the two blue dashed vertical lines in
Fig. ) is comparable. In this respect, radon
concentration variations could be sensitive to the internal processes taking
place during the preparatory phase of an earthquake.
Change point analysis applied to cumulative seismic moment release.
The black solid line represents the cumulative seismic moment release
filtered with a 14-day moving average, while the green dashed line
represents the model predicted by the BCP algorithm. The red curve indicates
the probability of a change point at each time. The two blue dashed vertical
lines mark the occurrence of the second and of the third change point
represented in Fig. . Yellow stars represent the
occurrence of the earthquakes Mw 4.3 on 28 May 2012 and Mw 5.2 on
25 October 2012.
We point out the fact that a standard change point analysis uses always the
whole time series, since to identify a change point at a time ti the
algorithm processes also data at t>ti. This is a limitation because the
algorithm cannot be employed for predictive purposes. To overcome these
limitations and most of all to extend the range of our investigations, we
implemented an original detection algorithm that potentially could be used in
real time analyses. A schematic flow chart of the algorithm is shown in
Fig. . It basically works on a simple two stage
condition: (i) the radon daily average (DA) exceeding by a factor
(p1) the 2-week moving average (MA) and (ii) the moving
average (MA) successively increasing by a factor (p3) for a given
time window (p2). When both conditions are satisfied, an alarm is issued
at day (i+p2) (red font in box of Fig. ). If an
M>4.0 earthquake occurs during 40 days after the alarm has been issued,
all the thresholds to issue subsequent alarms are increased by a factor
(p4) during a time window proportional to the energy released by the event
(p5MEQ). The algorithm works only with five free parameters,
and there is no limitation to the number of alarms that could be issued and
to the time when they could be issued.
Flow chart representing the detection algorithm.
(p1, p2, p3, p4, p5) are the free five parameters described in the
text. DA and MA are the daily and the 2-week moving
average of radon time series, respectively. MEQ is the magnitude
(>4) of the earthquake occurring (if any), during 40 days after the alarm.
Figure shows the output of our detection algorithm running
on the whole MMN time series. Issued alarms are represented by red triangles,
while yellow stars mark the largest seismic events that occurred in the 40
days following the alarm. For each year, the two greatest seismic events have
been also displayed (white stars), regardless of the issuing of an alarm.
Incidentally, except for 2014, in 2012 and 2013 the two greatest seismic
events are just the seismic events that occurred in the 40 days following an
alarm. Some main observations can be pointed out here: (i) the algorithm
succeeds in forecasting the Mw 5.2 mainshock of October 2012; (ii) it
succeeds in forecasting the two main events of the whole sequence (the
Mw 5.2 of October 2012 and the Mw 4.3 of May 2012 that started the most
active part of the sequence); (iii) it succeeds in forecasting the major
events for 2012 and 2013, while it fails for 2014; (iv) it issues only one
false alarm in 3 years. We note also that the time advance of the alarms
with respect to the earthquake occurrence for the two main events of the
sequence is remarkably similar to that observed by means of change point
analysis.
Output of the detection algorithm applied to time series of radon
concentration at MMN. The red triangles represent all the issued alarms,
yellow stars represent the greatest seismic events occurred in the 40 days
following each alarm. For each year the two greatest seismic events have been
also displayed (white stars), with corresponding occurrence date and
magnitude.
Therefore, both the cross-correlation analysis and the change point analysis,
as well as the application of our detection algorithm, indicate that a
physical relation between the variation of soil radon emanation and seismic
moment release exists. While change point and detection algorithm both succeed
in finding some useful radon signal before the variation in seismic moment
release, the cross-correlation investigations seem to behold the radon
signature after the seismic moment release variation. Relying on the change
point analysis and detection algorithm, we have verified if also the
cross-correlation analysis is compatible with a radon signal preceding the
seismic moment release signal. To investigate this possibility, we have
repeated the procedure described in Sect. . In this case
we limit the search domain to positive lag values (i.e. radon signal
preceding moment release signal), in order to verify if a suitable solution
can be found also in this case. As Fig. highlights,
such a solution exists and, comparing Figs.
and , it is evident that it is only marginally less
significant with respect to the best one. Remarkably, as a confirmation of
the previous findings, the correction coefficients associated with this
solution (see Table ) are consistent with these found in
Sect. . They indicate for radon observations at MMN
station a strong anti-correlation with respect to precipitation
(CRmax=9.3 for tw-1 and CRmax=10.0 for tw-2), a
clear anti-correlation with temperature and the lack of a clear correlation
with respect to pressure variations.
The same as Fig. , but limiting the
search domain of MINUIT only to positive lag values (k) (the
corresponding correction coefficients are reported in
Table ).
The same as Table , but limiting the search domain of
MINUIT only to positive lag values (k).
CTmax
CPmax
CRmax
w
tw-1
5.6
0.9
9.3
3.0
tw-2
2.7
1.6
10.0
3.0
Conclusive remarks
We have performed a detailed analysis of the temporal variations of radon
emanations from late 2011 to 2014 in a seismically active area during a
seismic sequence that culminated at the end of 2012 with a Mw 5.2
event. We exploited several different approaches to carry out our
investigations. Namely: (i) phenomenological analysis; (ii) correlation and
cross-correlation investigations; (iii) empirical correction of the
meteorological parameters effect on radon time series and its impact on
cross-correlation; (iv) change point analysis; (v) detection algorithm.
We can split the main results of our work in two classes: (a) those
concerning the impact of meteorological parameters variation on the observed
radon time series and (b) those concerning the existence of a physical
connection between the observed radon time series and the seismic moment
release temporal variations. Converging indications coming from both classes
represent an important outcome of our work. Regarding class (a), we have
indications that, in the investigated setting, soil radon emanation is
strongly anti-correlated with precipitation and weakly anti-correlated with
temperature, while we do not get significant and univocal evidence of
correlation (positive or negative) with pressure variations. In this context,
approaches (i), (ii) and (iii) give remarkably consistent indications and we
see as particularly significant the agreement between the strength of the
correlation evidenced by (i) and (ii) and the magnitude of the corresponding
correction factor found with (iii). These results, when compared with
previous findings, confirm that the environmental impact on radon
observations is strongly site dependent. The correlation between radon
variations and temperature is, in this sense, a clear example: many works
found it positive, as several others (including ours), negative. This
observation suggests that a specific characterization is needed for each
station, when implementing an observational network (see, for example, the
dependence on the varying soil characteristics as porosity, permeability, and
pre-rain moisture state). Regarding class (b), all of our analyses univocally
indicate the existence of a non-accidental correlation between the temporal
evolution of soil radon emanation and seismic moment release. The primary
output of approach (ii) suggests that the radon signal follows the seismic
moment variation, while approaches (i), (iv) and (v) indicate that it is
possible to retrieve the radon signal also before the seismic moment
variation. Remarkably, we have found that even if approach (ii) gives as
primary result a shifted forward temporal correlation also the solution with
the radon signal preceding the seismic moment variation is acceptable at a
barely lower significance level.