Download An estimate of hypocentre location accuracy in a large network

Geophys. J. Int. (1997) 129, 124-132
An estimate of hypocentre location accuracy in a large network:
possible implications for tectonic studies in Italy
Rita Di Giovambattista and Salvatore Barba
Istituto Nazionale di Geofisica, 1.' Di Vigna Murata, 605,00143 Roma, Italy. E-mail: [email protected]
Accepted 1996 October 28. Received 1996 October 9; in original form 1996 January 22
SUMMARY
Data recorded by the Italian Telemetered Seismic Network (ITSN) of the Istituto
Nazionale di Geofisica (ING) have been widely used in recent years to image slab
structures and to find evidence for active processes along the Italian Peninsula.
However, the use of seismic data for geostructural purposes may be affected by the
well-known trade-off between earthquake location and seismic-velocity parameters.
Furthermore, the confidence ellipse predicted by standard procedures may be
inadequate for the representation of the probable error of a computed localization.
This paper evaluates the probable errors on the hypocentre determinations of the
seismic events recorded by the ITSN, using a Monte Carlo method.
We compute synthetic arrival times using a 1-D velocity model appropriate as an
average for the Italian area. The hypocentres used are ail those recorded by the ITSN
during the period January 1992 to March 1994 (1972 events). Station locations are
those of the current ITSN configuration. The synthetic arrival times are perturbed with
a Gaussian distribution of errors and input to I N G s standard hypocentral location
procedure, but using crustal velocities differing by 10 per cent from those used to
generate them. Each simulation is repeated at least 30 times. Average absolute shifts of
hypocentres are assessed in grid cells of linear dimension 33 km covering the whole
Italian region.
For regions within the ITSN, shifts are typically 5-10 km in location and up to
20 km in depth. However, for offshore and coastal regions, they are much greater:
50 km or more in both location and depth (far exceeding the equivalent uncertainties
quoted by ING bulletins). Possible consequences of this are highlighted by producing
a cross-section of subcrustal hypocentres from the Adriatic to the Tyrrhenian Sea,
where the large uncertainty in depth precludes any confident interpretation of dipping
tectonic features.
Key words: earthquake location, Italy, seismicity
INTRODUCTION
The problem of earthquake location can be solved using the
generalized linear inverse theory. Input data are the arrival
times of seismic waves recorded at different stations. Arrival
times are affected by various errors including reading errors
and misidentification of the first arrivals. Therefore, the
location will also be affected by errors. Since crustal velocity
models are only roughly known, simplified models are used in
the majority of the location programs, and the choice of the
velocity structure strongly affects the accuracy of the results.
Furthermore, numerical problems related to the network
configuration can arise. When the model parameters are poorly
constrained by the data, the matrix in the normal equation
can be a nearly singular matrix and consequently its computed
124
inverse may be inaccurate. This represents the main uncertainty
for seismic events occurring along the Italian coast or in areas
with a limited number of stations due to the peculiar configuration of the Italian territory and to the distribution of the
Italian Telemetered Seismic Network (ITSN).
It is a common procedure to estimate the errors in the final
model on the basis of the model variance-covariance matrix;
the standard deviation of each parameter is given by the square
roots of the diagonal terms. The uncertainty in the epicentre
is represented by an ellipse in which the ratio of the axes is
determined by the network geometry, while the size depends
on the standard deviation of the data.
Evernden (1969) points out that the confidence ellipse
predicted by standard procedures may be inadequate in
representing the probable error of a computed location. Even
0 1997 RAS
Hypocentre location accuracy in Italy
applying different hypocentre location techniques, which sometimes produce better results, it has been shown that even with
an ellipse of small magnitude the events can be mislocated by
several kilometres (Console et ul. 1992a).
We use a procedure based on the Monte Carlo method to
evaluate the errors associated with the hypocentral coordinates
of the events recorded by the ITSN. We apply this procedure
to estimate the reliability of the hypocentre locations on the
basis of the adopted crustal velocity model, of the errors on
the arrival-time picking, and of the network configuration.
METHOD
We face different kinds of errors in locating seismic events:
systematic errors due to inaccurate station coordinates, network timing errors, or picking errors. For the ITSN data these
errors are of small magnitude and we consider them negligible
in our analysis. In fact, all the stations are telemetered in a
data centre and the time signal is provided by a GPS receiver
with an uncertainty of 1 ps. The station coordinates are
determined by a GPS receiver with an accuracy of about
150 m; the algorithm used to acquire data does not introduce
systematic picking errors. In addition, other errors can affect
the estimated hypocentral coordinates: they are caused by
inaccuracy in reading the arrival times, limited amounts of
data, inadequate station distribution, and errors in the
knowledge of the seismic-velocity structure.
To evaluate their influence on the accuracy of hypocentre
locations, we use a procedure based on the Monte Carlo
method. Introduced by Von Neumann and Ulam, the Monte
Carlo method (Brandt 1976) simulates statistical processes by
introducing random values for the parameters. In our procedure, this method is applied to simulate the problems in the
location of seismic events; assuming a specific configuration of
a network and a crustal propagation model, we use our method
to evaluate the hypocentral errors. The Monte Carlo method
has already been applied to test the performance of different
hypocentre location algorithms (Console et al. 1992b) and to
quantify the reliability of events located in some particular
areas (Billings, Sambridge & Kennett 1994).
The distribution of the errors associated with the picking of
first arrivals has been analysed by many authors. Following
Buland ( l976), the picking errors associated with impulsive
arrivals recorded in analogue form are approximately described
by a Gaussian distribution. Emergent arrivals, due to the
misidentification of first arrivals confused in seismic noise, are
characterized by reading errors that can be described by a
distribution having a mean value shifted towards positive
numbers (Anderson 1982). Tests performed on the digital data
collected by the ITSN showed that reading errors can be
adequately approximated by a Gaussian distribution with a
mean equal to zero and a standard deviation of 0.1 s.
The uncertainty in assessing hypocentral coordinates,
depending on random reading errors, is determined in the
following way. The procedure calculates the theoretical traveltimes related to each velocity model considered, starting from
the hypocentral coordinates of the events. These times are then
altered by the addition of random values having a normal
distribution with a mean value equal to zero and a standard
deviation equal to that found in the final solution obtained in
locating the events. These data are then utilized as input for the
simulation procedure. The influence of the crustal propagation
model can be tested assuming a known velocity model to
obtain the theoretical traveltimes and then relocating the
events with another model. Performing a large number of
simulations, the spreading of the relocated events can be used
to estimate the uncertainty associated with the hypocentral
coordinates.
APPLICATION TO ITALIAN SEISMICITY
The analysed data, collected by the ITSN, are digitally recorded
with a sampling rate of 50Hz (Di Mar0 & Marchetti 1994;
47"
46"
45"
44"
43"
2m
4
42"
41"
40"
39"
38"
37"
36"
I
I
I
2" 3" 4"
I
I
I
I
I
I
i I"I
I
I
I
I
I
I
I
I
5" 6" 7" 8" 9" 10" 11" 12" 13" 14" 15" 16" 1 P 18" 19" 20" 21"
Longitude
Figure 1. Italian seismicity recorded by the Italian Telemetered Seismic Network from January 1992 to March 1994.
0 1997 RAS, G J I 129, 124-132
125
126
R . Di Giovambattista and S. Barbu
Barba, Di Giovambattista & Smriglio 1995). Thus arrival-time
picks can claim a resolution of 0.02 s, but an accuracy that is
probably poorer, especially for S arrivals. This is to be compared to the empirically determined scatter of 0.1 s. All the
events recorded over a two-year period, from January 1992 to
March 1994, have been selected from the database of the
Istituto Nazionale di Geofisica. Fig. 1 shows the -2000 events
analysed in this paper.
i We intend to estimate the hypocentral errors for the overall
Italian seismicity. Fig. 2 shows a general outline of the
numerical method and its main parts. The errors on the
hypocentral coordinates are connected with the number of
stations that recorded the event, and consequently with the
magnitude of the events. Therefore, we have divided all
the seismicity into three groups whose magnitudes are 2.0-2.5
(505 events), 2.6-3.0 (1146 events) and greater than 3.0
(321 events).
The procedure generates the arrival times by assuming a
crustal model, and alters them with random values computed
as described in the previous chapter. These data are then used
as input for the location program in which another realistic
model is assumed. Table 1 shows the two velocity models
assumed.
As can be seen in Table 1 the two models used are quite
similar. The former is the most recent one computed using
ITSN data (Mele & Valensise 1987). The latter is a further
refinement of the former, from which it differs by an increase
of 10 per cent in the velocity of the first layer and a decrease
of about the same magnitude in the second layer.
In a previous study, aimed at comparing a joint hypocentre
location method with the standard location method described
in this paper (Console et al. 1992b), the influence of the crustal
model has been evaluated for two Italian areas, Val Comino
(Central Apennines) and the Adriatic Sea. For the Adriatic Sea
area the absolute mean shift and the standard deviation of the
hypocentre in the horizontal plane (If)and depth ( Z )obtained
for a variation of 5 per cent in the velocity model were
AH = (3.9 2.5) km and AZ = (5.8 +_ 3.6) km. It is important
to emphasize that the variation in the crustal model assumed
in this analysis might not represent the true variations existing
in the Italian territory, due to a variety of tectonic domains
(e.g. volcanic areas, Alps mountain range). In this sense, our
analysis quantifies a minimum error. The use of the standard
deviation obtained in the location of the experimental data
allows the simulation of a more realistic situation as the
residuals at each station and thus the standard deviation
include all the deviations from the assumed crustal model.
With regard to this problem, an increase in the thickness of
the crust from 30 to 45 km, which occurs in the transition
zone from the Padana plain to the Subalpine structures, will
cause a delay in P, arrivals of about 1.3 s (assuming model l ) ,
while a seismic ray that is 0.2 km s-' slower than the theoretical
one will be retarded by only 0.3 s every 100 km (Mele &
Valensise 1987).
A more recent analysis, based on P-arrival-time tomographic
inversion demonstrated a maximum lateral velocity of
+ 7 per cent (Alessandrini, Beranzoli & Mele 1995). The
( Start Simulation )
Monte Carlo
Simulation
pq
4
ci,
Init std dev.
For each event compute mean hypocentral
coordinates and associated standard deviations
using results produced by hypocenter location
using synthetic travel times obtained by means
of Monte Carlo simulation
Figure 2. Flowchart of the procedure applied in this study. The input
parameters are the data file (P1) and the number of simulations to be
performed (P2). I is the iteration number.
Q 1997 RAS, GJI 129, 124-132
Hypocentre location accuracy in ltaly
Table 1. Velocity models used in this study for the Italian area.
Depth (km)
P velocity (km s - l )
Model 1
11.08
29.98
Model 2
11.08
29.98
5.0
6.5
8.0
5.5
6.0
8.0
variation of 10 per cent introduced in our simulation, even
though it is a simplified model (1-D), is then supported by
tomographic results.
To locate the events we used the program IPO, routinely
used for the hypocentre locations published in the ING
bulletins (Basili, Smriglio & Valensise 1984). All the analysed
events have been divided into square grid cells whose linear
dimension is about 33 km. This grid is a compromise between
the number of events in each cell and the need for a homogeneous network coverage in each cell. For each grid cell we
computed the mean and the standard deviation of the absolute
shift of the hypocentral parameters generated by at least 30
simulations repeated for each event.
The correct application of this method requires that the
weight given to each station is determined by the value
assumed from the residuals, and does not depend on the
epicentral distance of the station. This has been checked
through a qualitative analysis, allowing us to alter the computed traveltimes randomly. Figs 3 to 8 show a synthesis of
127
the results of these tests for the two groups of events of higher
magnitude.
As is seen in these figures, there are cells in which the
standard deviations of the absolute shifts of the hypocentral
coordinates are quite high in comparison with the uncertainty
of the hypocentral coordinates obtained from the covariance
matrix published in the I N G bulletins. This problem is particularly evident for the events located offshore or along the coast.
In particular, Figs 3 to 8 show areas (the Southern Tyrrhenian
Sea, the Calabrian Arc, the Ionian sea, the Forli area in
Northern Italy, the Northern Tyrrhenian coast) in which the
standard deviation attains quite large values. Depth standard
deviation for hypocentres located in the Southern Tyrrhenian
Sea (usually deep-focus events) can exceed 200 km, the largest
instability of all of the areas considered here. For the same
events, though, the depth errors cited in the ING bulletins are
usually very small (<20 km), as shown in Fig. 9.
For those events occurring inside the grid network, the
standard deviation on the horizontal plane is about 5 km.
There are only three areas (the Italy-France border, the Central
Apennines and the Southern Apennines) that are characterized
by errors larger than 10 km. For these areas the uncertainty
of the depth estimation can reach 20 km. In Northern Italy
(Forli area), in the Tyrrhenian Sea, just in front of Elba island,
in the Calabrian Arc and in the Ionian Sea there are some
areas showing a standard deviation greater than 50 km for
events of magnitude 2.5-3.0.
The data set of the events with a magnitude greater than 3
also includes events located in the Adriatic Sea, along the
Figure 3. Estimated depth location accuracy (in km) of the epicentres of magnitude 2.6--3.0 recorded by the ITSN. The seismic stations are
represented by circles. The initial arrival times were computed for model 1 assuming crustal model 2 in the location program. The theoretical
traveltimes have been altered by means of the Monte Carlo method, adding random values having a standard deviation equal to that found in the
last iteration of the standard hypocentre location procedures. For each grid cell with a linear dimension of about 33 km we computed the standard
deviation of the shift obtained in the hypocentre coordinates for each simulation and each event.
Q 1997 RAS, GJI 129, 124-132
128
R. Di Gioziambattista and S. Barba
Figure 4. Estimated latitude location accuracy (in km) obtained using the same conditions as Fig. 3. Values of the standard deviation of the shift
higher than 50 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold.
Figure 5. Estimated longitude location accuracy (in km) obtained using the same conditions as Fig. 3. Values of the standard deviation of the shift
higher than 40 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold.
Q 1997 RAS, G J I 129, 124-132
Hypocentre location accuracy in Italy
129
Figure 6. The same as Fig. 3, but for events having magnitudes greater than 3.0. Values of the standard deviation of the shift higher than 50 km
are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold.
Figure 7. Estimated latitude location accuracy (in km) obtained using the same conditions as Fig. 3 for events having magnitudes greater than
3.0. Values of the standard deviation of the shift higher than 30 km are represented by the darkest tones on the grey-scale. The distribution of the
mean error justifies the use of this threshold.
0 1997 RAS, G J I 129, 124-132
R. Di Giovambattista and S. Barba
130
Figure 8. Estimated longitude location accuracy (in km) obtained using the same conditions as Fig. 3 for events having magnitudes greater than
3.0. Values of the standard deviation of the shift higher than 40 km are represented by the darkest tones on the grey-scale. The distribution of the
mean error justifies the use of this threshold.
1
40
1
1
Latitude(Km)
0
20
0
Longitude (Km)
20
the stations are situated west of the epicentral area and they
constrain the longitudinal coordinate of the events only poorly.
In the data set of the events with magnitude greater than
3.0, there are events located in bordering areas. In particular,
because of the national borders and the roughness of the
territory, the seismically active areas in the Alps are poorly
monitored; therefore, it is not possible to record lowermagnitude events. The seismicity occurring at the borders with
Austria and France is affected by uncertainties in the epicentral
coordinates of up to 50 km.
For some events of magnitude greater than 3.0 occurring in
the Calabrian Arc and in the Southern Tyrrhenian Sea, the
errors on the horizontal plane cover a large range (up to
150 km). This shows that the solutions can be very unstable,
because the peculiar configuration of the territory along the
Calabrian Arc leads to an alignment of the seismic network
and to a consequent poor estimation of the longitude.
All previous considerations are based on cells in which more
than three events are located, and a minimum of 30 simulations
are run for each event. This ensures that the results do not
reflect instabilities of single events, but provide meaningful
uncertainties on hypocentral coordinates for all the events
recorded by that particular network configuration.
In order to check the results obtained and to estimate
whether the discrepancies between the two propagation models
adopted are sufficient to highlight the true mislocation of the
events, we compared the hypocentral locations obtained
analysing the data collected by the ITSN with those obtained
by the IGG seismic network of the University of Genoa
(Cattaneo & Augliera 1990). It is well known that local
networks, provided that they have a good station distribution,
i,l L
0
5
15
20
tk$h (Km)
Figure9.
Number of vents versus the error on the latitude (a),
longitude (b) and depth (c) as derived from the confidence ellipses for
the events of the southern Tyrrhenian Sea (Latitude 38.5"-40";
Longitude 12"-15.5").
southern coast of Italy (Puglia) and along the coast of the
former Yugoslavia. For these events, the error in longitude is
greater than the error in latitude. These results depend on the
network configuration. This offshore seismicity is located outside the network and only the latitude can be constrained by
the stations located north and south of the epicentral area. All
0 1997 RAS, GJI 129, 124-132
Hypocentre location accuracy in Italy
131
January 1992 to March 1994 our analysis highlighted
inaccurate absolute hypocentral locations, probably due to
unfavourable station geometries. The reliability of the hypocentral coordinates of these events is of major importance for
tectonic interpretations. In fact, based on the unusually deep
earthquakes, Selvaggi & Amato ( 1992) hypothesized a subduction process acting in that zone. Table 2 shows the depths with
the estimated errors determined by Selvaggi & Amato ( 1992),
those published by the ING bulletins, and the standard deviation of the depths obtained by means of the error analysis
described in this paper by using only stations belonging to
ITSN as already specified. The two locations are obtained
using different crustal models. For this reason, the depths
cannot be compared as absolute values. From Table 2 it is
possible to infer that the uncertainty, as derived from the
confidence ellipses, can be inadequate in the representation of
can provide accurate hypocentral coordinates of the seismic
events occurring inside the network. As a consequence, the
comparison between the IGG hypocentral coordinates and
those calculated by ITSN can provide a further estimate of
the probable errors associated with the focal parameters. For
the events located in the area where the IGG network is
operating, the two hypocentre locations have mean shifts that
are in agreement with the uncertainty estimated by the procedure described in this paper.
In order to highlight the importance of a realistic evaluation
of the uncertainty of the hypocentral coordinates in areas in
which the event distribution can be crucial for tectonic
implications, we applied the procedure described in this paper
to subcrustal earthquakes that occurred in the Northern
Apennines, already relocated by Selvaggi & Amato ( 1992).
For several events that occurred in the same area from
190
I
s
-80
Q
-100
1
'I1
I
I
-120
-140
I
0
1 1 1 1 ' 1 1 ~ ' 1 1 1 1 ' 1 1 1 ~ 1 ' ~ 1 ' ~ 1 ~ ' 1 ~ ~ 1 ~ ~ 1 ~
30
60
90
120
150
180
210
240
270
300
330
360
3 0
Distance (km)
Figure 10. (a) Epicentral map of the deep earthquakes located by Selvaggi & Amato (1992) and zone of projection of the vertical section A-A';
( b ) cross-section A-A'. The error bars are computed by the Monte Carlo method described in this paper.
0 1997 RAS, GJI 129, 124-132
132
R . Di Giovambattista and S . Barba
Table 2. Depth estimation of subcrustal earthquakes as computed by
Selvaggi & Amato (1992) and the ING bulletins, and depth errors as
computed by confidence ellipses and by the procedure described in
this paper.
n
Date
Lat
Lon
ERZ
(h) (km)
Depth
Depth
Std. drv.
(h) onDepth
(Selvaggi
&hato)
(Selvaggi
&Amato)
(ING
Bull)
(this
paper)
located in Italian territory can only be poorly located. In many
cases the hypocentral errors derived from confidence ellipses
are too small and are not indicative of the real mislocation of
the events.
These results are important because the areas where our
analysis shows the greatest uncertainties are of great interest
for tectonic studies (Selvaggi & Amato 1992; Selvaggi &
Chiarabba 1995).
Our simulation provides a guideline for the use of the ITSN
seismic data for geostructural purposes in the Italian territory.
Our results support the tectonic interpretations based on the
ING bulletins in the areas covered well by the ITSN network.
I!
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02.21
42N5623
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63 1
1.70
69
4
2
881015
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5.79
27.3
5
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881015
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44N28.70
10E57.23
498
5.26
26
29
4
881218
1227
44N02.28
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241
39
3
ACKNOWLEDGMENTS
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12
We thank Dr D. Console and Dr J. Pujol for helpful comments
that improved the manuscript and Dr A. Amato for discussions
on earthquake location of subcrustal events. The authors wish
to thank Gideon Smith and an anonymous reviewer for their
constructive critical comments, and the Editor, Dr Roger
Clark, for his useful advice and suggestions.
8
900206
02.49
43N37.19
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REFERENCES
10
901027
1325
44N05.74 10655.64
56.2
1.90
55
4
11
901203
18:12
43N28.78
12E40.39
63.2
1.99
69
I2
12
911209
14:39
44N29.05
10628.04
68.3
5.21
96
7
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the real error. In some cases (e.g. event number 3 ) the standard
deviation in the depth estimation is in agreement with the
difference between the depth estimated by Selvaggi & Amato
(1992) and the ING bulletins, and it is larger than the error
derived from the confidence ellipses. Fig. 10(b) shows a crosssection of the hypocentres listed in Table 2 of Selvaggi &
Amato (1992), recorded after 1987. The error bars in the
depths are those obtained from our analysis. The results
obtained, whilst still confirming that the depths of these events
are larger than those usually observed in other Italian areas,
point out that the large uncertainty associated with the depth
estimation does not allow conclusive interpretations of possible
trends delineating a dipping wedge from the Adriatic to the
Tyrrhenian Sea, as can be derived from Fig. 2( b) in Selvaggi
& Amato (1992).
CONCLUSIONS
We used a Monte Carlo simulation to estimate the errors
associated with the hypocentral coordinates of the events
recorded by a network. We quantified the influence of reading
errors, uneven station distribution and limited information
about the velocity structure.
The results show that for events occurring inside the network
grid the hypocentral coordinates are estimated with a good
accuracy. In our simulation the probable error on the epicentral
coordinates is lower than 5 km and is generally larger than
the estimates of the standard routines. Moreover, the seismic
events occurring offshore and in some of the seismogenic areas
0 1997 RAS, GJI 129, 124-132