Rapid Estimation of Earthquake Source and Ground-Motion Parameters
for Earthquake Early Warning Using Data from a Single Three-
Component Broadband or Strong-Motion Sensor
by M. Böse, T. Heaton, and E. Hauksson
Abstract
We propose a new algorithm to rapidly determine earthquake source and
ground-motion parameters for earthquake early warning (
EEW
). This algorithm uses
the acceleration, velocity, and displacement waveforms of a single three-component
broadband (BB) or strong-motion (SM) sensor to perform real-time earthquake/noise
discrimination and near/far source classification. When an earthquake is detected, the
algorithm estimates the moment magnitude
M
, epicentral distance
Δ
, and peak
ground velocity (
PGV
) at the site of observation. The algorithm was constructed
by using an artificial neural network (
ANN
) approach. Our training and test datasets
consist of 2431 three-component SM and BB records of 161 crustal earthquakes in
California, Japan, and Taiwan with
3
:
1
≤
M
≤
7
:
6
at
Δ
≤
115
km. First estimates be-
come available at
t
0
0
:
25
s after the
P
pick and are regularly updated. We find that
displacement and velocity waveforms are most relevant for the estimation of
M
and
PGV
, while acceleration is important for earthquake/noise discrimination. Including
site corrections reduces the errors up to 10%. The estimates improve by an additional
10% if we use both the vertical and horizontal components of recorded ground
motions. The uncertainties of the predicted parameters decrease with increasing time
window length
t
0
; larger magnitude events show a slower decay of these uncertainties
than small earthquakes. We compare our approach with the
τ
c
algorithm and find that
our prediction errors are around 60% smaller. However, in general there is a limitation
to the prediction accuracy an
EEW
system can provide if based on single-sensor
observations.
Introduction
Earthquake early warning (
EEW
) techniques have im-
proved significantly over the last decade, including both
technological advances in real-time seismology and the de-
velopment of algorithms for the rapid detection of possibly
damaging earthquakes a few seconds to some tens of seconds
before strong shaking occurs (
Allen
et al.
, 2009
). These al-
gorithms require the seismic waveforms either from a single
seismic sensor (the so-called on-site warning systems; e.g.,
Wu and Kanamori, 2005
;
Kanamori, 2005
;
Zollo
et al.
,
2006
;
Böse
et al.
, 2007
) or from a seismic network or subnet-
work (the so-called regional warning systems; e.g.,
Wu and
Teng, 2002
;
Allen and Kanamori, 2003
;
Cua and Heaton,
2007
). On-site and regional warning approaches deliver es-
timates of source and ground-motion parameters with differ-
ent speed and accuracy (e.g.,
Kanamori, 2005
).
Recently,
Böse (2006)
and
Böse
et al.
(2008)
developed
an algorithm for
EEW
called PreSEIS that is based on arti-
ficial neural networks (
ANN
s). Artificial neural networks
have several important features that make them attractive
tools for
EEW
. They allow for nonlinear mapping between
the seismic waveforms recorded at one or more seismic sen-
sors and the predicted source and ground-motion parameters
at a user site. They do not require explicit formulations of
relations, because they are completely data-driven and learn
from examples or experience (similar to the human brain).
They exhibit a high tolerance against noisy data, which is
a common problem in real-time seismology, and they are
computationally efficient, that is, very fast, which makes
them applicable to real-time procedures such as
EEW
(
Böse
et al.
, 2008
).
PreSEIS fills the gap between on-site and regional warn-
ing methods. To estimate the source and ground-motion
parameters of an ongoing earthquake, PreSEIS uses the seis-
mic waveforms from multiple sensors in a seismic network
without requiring that the seismic
P
wave has reached all of
them yet. Nontriggered sensors provide important informa-
tion about the source location by limiting the space of pos-
sible solutions (
Horiuchi
et al.
, 2005
;
Böse
et al.
, 2008
). The
738
Bulletin of the Seismological Society of America, Vol. 102, No. 2, pp. 738
–
750, April 2012, doi: 10.1785/0120110152
continuous update of estimates allows the application of Pre-
SEIS to large earthquakes with complex rupture evolution in
which the largest slip along the fault does not necessarily
occur close to the hypocenter, which is the point of rupture
nucleation. PreSEIS is thus largely unaffected by whether or
not the evolution of earthquake ruptures is predetermined at
the beginning of the rupture process (e.g.,
Olson and Allen,
2005
;
Rydelek and Horiuchi, 2006
;
Rydelek
et al.
, 2007
;
Yamada and Ide, 2008
).
PreSEIS was tested in several seismic-active regions
around the world, including Istanbul (
Böse
et al.
, 2008
),
southern California (
Köhler
et al.
, 2009
), Japan (
Köhler,
2010
), and Germany (
Hilbring
et al.
, 2010
). The datasets
used included (1) stochastic simulated strong-motion (SM)
records, (2) sets of purely observed SM records, and (3) joint
datasets of observed and simulated SM and broadband (BB)
records. The results of all these studies demonstrated that
ANN
s are well suited for
EEW
(
Leach and Dowla, 1996)
.
Furthermore, they showed that the uncertainties in the pre-
dicted source and ground-motion parameters decrease with
increasing length of the time window used, which causes
a trade-off between the reliability of warnings and the re-
maining warning time until strong shaking occurs (
Böse
et al.
, 2008
). These studies also revealed two major short-
comings of the PreSEIS algorithm. First,
ANN
s require large
datasets for the training. Second, the PreSEIS algorithm is
network-dependent, that is, once the
ANN
s have been trained
for a particular seismic network or subnetwork, single sen-
sors cannot be easily added or removed. While there are
various methods to handle the problem of not-reporting sta-
tions at the time of an earthquake, for example, by the inter-
polation of values at neighboring stations, the robustness of
this approach decreases if applied to less dense seismic
networks.
To overcome these limitations, we propose the new
PreSEIS On-site algorithm, which is solely based on single-
sensor observations. For the training and testing of the
algorithm, we use datasets of observed waveforms including
BB and SM records from different tectonic regions (Califor-
nia, Japan, and Taiwan). We use these performance measures
to make general conclusions about the expected uncertainties
of estimates by an
EEW
algorithm, which uses the informa-
tion from a limited time window of the
P
wave. We also com-
pare our approach with the
τ
c
algorithm for
EEW
(
Kanamori,
2005
) and show that the prediction errors of PreSEIS On-site
are around 60% smaller. However, in general there is a lim-
itation to the prediction accuracy an
EEW
system can provide
if based on single-sensor observations.
Method
Based on the observed waveforms at a single BB or SM
sensor, PreSEIS On-site provides a rapid earthquake/noise
discrimination, a near/far source classification, and estimates
the moment magnitude
M
, the epicentral distance
Δ
, and the
peak ground velocity (
PGV
) at the site of observation. All
estimates are updated with progressing time
t
0
as more
information about the earthquake becomes available. The
principal approach is illustrated in Figure
1
.
PreSEIS On-site uses the seismic acceleration, velocity,
and displacement waveform time series,
u
t
,
_
u
t
, and
u
t
,
recorded at a single three-component SM or BB sensor, ob-
tained from the integration and differentiation of the recorded
time series, respectively. The time series are parameterized
by integrating the absolute amplitudes on component
i
i
f
EW; NS; UD
g
over the time interval between the pick of
the seismic
P
wave and a given time
t
0
:
IAA
i
≡
log
10
1
Z
t
0
0
j
u
i
t
j
dt
;
(1)
IAV
i
≡
log
10
1
Z
t
0
0
j
_
u
i
t
j
dt
;
(2)
and
IAD
i
≡
log
10
1
Z
t
0
0
j
u
i
t
j
dt
:
(3)
Taking the logarithmic values in equations
(1)
to
(3)
is
important, because seismic amplitudes span several orders of
magnitude and follow logarithmic distributions (e.g.,
Yamada
et al.
, 2009
). We add 1 to obtain positive values of
IAA
i
,
IAV
i
, and
IAD
i
. Equations
(1)
to
(3)
describe the
envelope of the underlying waveform time series in a sim-
plistic way.
Because the local soil conditions at the recording sites
can lead to significant changes of the seismic wave ampli-
tudes, and thus
IAA
i
,
IAV
i
, and
IAD
i
, it is important to con-
sider these effects in our algorithm. We use the National
Earthquake Hazard Reduction Program (
NEHRP; 1994
)
V
S
30
site classification, that is, the average shear-wave velo-
city taken over the top 30 meters, as a simple proxy of local
site conditions (Fig.
1
). The
V
S
30
value at a given station is a
further input parameter to the
ANN
s. The
ANN
s have to find
out themselves the relationship between this value and the
changes of magnitudes, etcetera.
The discrimination between earthquakes and ambient
noise (nonseismic events), as well as the near/far source clas-
sification, are essential parts of PreSEIS On-site. The latter is
particularly needed for the real-time estimation of fault rup-
ture length during large earthquakes (
M>
6
:
5
; e.g.,
Yamada
et al.
, 2007
). We define the following classification: an out-
put of
1
is assigned if the pick was produced by noise; an
output of
1
is assigned if the detected event is an earth-
quake with epicentral distance of
Δ
km
≤
15
M
; an output
of 0 is assigned if the detected event is an earthquake with
Δ
km
≤
15
M
. The definition of this magnitude-dependent
distance range is fairly arbitrary. It is driven by the observa-
tion that large-magnitude events can cause damaging ground
shaking over larger areas than small earthquakes. While only
the discrete values
1
, 0, and
1
are assigned to the data for
ANN
learning, the output from the
ANN
s can be any rational
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
739
number. For instance, 0.5 indicates that the event is probably
an earthquake, and it is likely that
Δ
≈
15
M
.
As was the case for the former PreSEIS algorithm (
Böse,
2006
;
Böse
et al.
, 2008
), PreSEIS On-site uses two-layer-
feed-forward (
TLFF
) neural networks for the mapping
between the ground-motion observations and output param-
eters (Fig.
1
, Appendix
A
). We train the
ANN
s for different
time window lengths
t
0
, ranging in intervals of 0.25 s from
t
0
0
:
25
to
t
0
10
:
0
s after the
P
pick. Each timestep has
its own
TLFF
network (
Böse
et al.
, 2008
). Because we cannot
rule out that the training of the
ANN
s was insufficient (the
optimization algorithm got stuck in a local minimum and
the solution is not optimum), we construct so-called commit-
tees of
ANN
s (Fig.
1b
;
Bishop, 1995
). All
TLFF
networks of
one committee are trained with slightly different datasets,
and the training starts with slightly different (randomly de-
termined) weight initiations. In this paper we use committees
of 10
TLFF
s. The median over the outputs of all 10
TLFF
networks defines the output of the PreSEIS On-site algorithm
at a given time
t
0
(Fig.
1b
).
Figure
1.
Principal approach of PreSEIS On-site. (a) The algorithm uses the logarithmic values of the integrated absolute amplitudes of
acceleration, velocity, and displacement waveform time series,
u
t
,
_
u
t
, and
u
t
, at a single sensor, as well as
V
S
30
site characterization.
Outputs are (1) a simple earthquake/noise discrimination and near/far source classification, and estimates of (2) the moment magnitude
M
,
(3) the epicentral distance
Δ
, and (4) the
PGV
. All estimates are updated with progressing time
t
0
. (b) PreSEIS On-site uses two-layer-feed-
forward (
TLFF
) neural networks composed of simple processing units arranged in input layers, hidden layers, and output layers that are
connected to each other by a network of weighted links. Ten
TLFF
networks, which form a so-called committee, are trained on the same task
(e.g., the prediction of
M
) using slightly different training datasets and weight initializations at the beginning of the training procedure; the
median value taken over the outputs of all 10
TLFF
networks defines the output of PreSEIS On-site.
740
M. Böse, T. Heaton, and E. Hauksson
Data and Preprocessing
In this study we use a joint dataset of three-component
BB and SM waveforms recorded by (1) the California Inte-
grated Seismic Network (
CISN
), (2) the Japanese K-NET,
and (3) the Taiwanese Strong-Motion Network (
TSMIP
).
The datasets include the free-field records of small to large
crustal earthquakes with different focal mechanisms and at
different distances and soil conditions, as well as waveform
time series of ambient noise.
Because
EEW
is most important for earthquakes causing
significant levels of ground shaking, which primarily de-
pends on magnitude
M
and distance
Δ
(aside from the local
site conditions and the details of source radiation and wave
propagation), we consider only records with
Δ
km
≤
15
M
.
With this threshold, our database consists of 2431 three-
component records of around 161 crustal earthquakes with
3
:
1
≤
M
≤
7
:
6
and epicentral distances of up to 115 km
(Fig.
2
; Appendix
B
). In addition to the earthquake event
data, we download continuous time series of ambient noise
recorded at several
CISN
BB and SM stations. These data are
used to train another
ANN
for the automatic discrimination of
earthquakes and noise. If desired, the noise discrimination
could be specific for a given station site, but we want to treat
the problem more generally here.
For each record, we remove the trend and baseline and
apply a gain correction. To obtain
u
t
,
_
u
t
, and
u
t
,we
integrate and differentiate the data as appropriate. We apply
a third-order causal Butterworth highpass filter with a corner
frequency at 0.075 Hz to remove long-period artifacts due to
integration. The
P
-wave onset is automatically picked from
the vertical velocity record (
Allen, 1978
). Then we use equa-
tions
(1)
to
(3)
to determine
IAA
i
,
IAV
i
, and
IAD
i
. The time
windows for integration start from the
P
-pick and range in
intervals of 0.25 s from
t
0
0
:
25
to
t
0
10
:
0
s.
Results
It is important for
EEW
to parameterize the recorded
waveforms in a way that enables robust estimation of earth-
quake source and ground-motion parameters at a given time
after rupture nucleation. Before analyzing the performance
of PreSEIS On-site in more detail, we determine the time
series (acceleration, velocity, or displacement) and compo-
nents (horizontal or vertical) of the seismic data, or the com-
binations of these, that ensure the best mapping.
Displacement, Velocity, and/or Acceleration?
We train PreSEIS On-site with 90% of the available data
(i.e., 2188 three-component records) adopting the earlier dis-
cussed training procedure for the
ANN
s (Appendix
A
). The
training dataset is randomly selected, and we train a commit-
tee of 10
ANN
s for the prediction of each output parameter.
We repeat this procedure seven times, each time with differ-
ent input information derived from the waveforms in the
training dataset. We use the logarithmic values of the inte-
grated absolute amplitudes of the acceleration, velocity,
and displacement time series,
IAA
i
,
IAV
i
, and
IAD
i
(see
equations
(1)
to
(3)
), and consider the following seven cases:
usage of (1)
IAD
i
with
V
S
30
; (2)
IAV
i
with
V
S
30
; (3)
IAA
i
with
V
S
30
; (4)
IAV
UD
and
IAD
UD
with
V
S
30
; (5)
IAV
i
and
IAD
i
with
V
S
30
; (6)
IAA
i
,
IAV
i
, and
IAD
i
without
V
S
30
;
and (7)
IAA
i
,
IAV
i
, and
IAD
i
with
V
S
30
. Aside from case (4),
we use all three components of ground motions
i
f
EW; NS; UD
g
.
Independent from the input data chosen, the uncertain-
ties of the predicted parameters (defined by the standard de-
viation
σ
of the Gaussian error distribution of observed and
predicted output values for all 2431 records) decrease with
increasing time
t
0
; that is, the longer we wait, the more reli-
able the estimates (Fig.
3
). Later we show that the errors also
depend on magnitude. The largest error reduction is observed
within the first 2 to 3 s following the
P
-wave detection.
Usually, the errors are largest if only
IAA
i
or
IAV
i
or
IAD
i
is used, while the best results are obtained when using
a combination of the three. Including site corrections reduces
the errors up to 10%. The estimates improve by an additional
∼
10%
if we use both the vertical and horizontal components.
The importance of each time series differs from output to
output parameter (Fig.
3
). While
u
t
and
_
u
t
are most re-
levant for the estimation of
M
and
PGV
,
u
t
is more impor-
tant for the earthquake/noise discrimination.
The percentage of misclassified events (false triggers)
drops from 7% after
t
0
0
:
25
s to 2.5% after
t
0
2
sif
Figure
2.
Histograms and distributions of magnitudes
M
and
epicentral distances
Δ
of 2431 three-component BB and SM
records of 161 crustal earthquakes from California, Japan, and
Taiwan as used in this study. Because early warning is most impor-
tant for earthquakes causing significant levels of ground shaking,
we consider earthquakes with
Δ
km
≤
15
M
only.
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
741
we use three-component acceleration, velocity, and displace-
ment data with
V
S
30
values (Fig.
3a
). A larger time window
does lead to a further small reduction of misclassified
events (
∼
1
:
5%
).
For magnitude we determine a decrease in the uncertain-
ties from around 0.7 units after
t
0
0
:
25
s to 0.53 units after
t
0
2
s and 0.5 units after
t
0
3
s if we use
IAA
i
,
IAV
i
, and
IAD
i
with
V
S
30
(Fig.
3b
). A larger time window allows for a
further reduction of these uncertainties. The uncertainties are
only slightly smaller than if acceleration
IAA
i
is excluded.
There is almost no change in the uncertainty of epicen-
tral distance
Δ
estimates with increasing
t
0
. For example, if
we use
IAA
i
,
IAV
i
, and
IAD
i
with
V
S
30
, the uncertainty of
Δ
varies only slightly with values between 16 and 19 km
(Fig.
3c
). The distance estimates during the first
t
0
3
s
seem to be mainly based on the information derived from
the acceleration waveform time series. After
t
0
3
s, veloc-
ity and displacement start gaining in importance.
A rapid decrease in the uncertainties with increasing
t
0
is
also observed for
PGV
. The uncertainties are smallest for the
combination of
IAA
i
,
IAV
i
, and
IAD
i
with
V
S
30
(Fig.
3d
).
The errors in log(
PGV
) decrease from
∼
0
:
55
after
t
0
0
:
25
sto
0
:
4
cm
=
s after
t
0
2
s and
0
:
35
cm
=
s after
t
0
3
s. Acceleration
IAA
i
is the least important time series
for this prediction, while displacement provides the most es-
sential information about
PGV
up to
t
0
3
s and is replaced
by velocity for larger time windows.
Magnitude and Time Dependency
of Prediction Errors
We have seen that PreSEIS On-site performs best
if we combine three-component acceleration, velocity, and
displacement data,
IAA
i
,
IAV
i
, and
IAD
i
, with
V
S
30
site fac-
tors (Fig.
3
). In the following we analyze the prediction
Figure
3.
Smoothed errors in earthquake/noise classification and in estimated magnitude
M
, distance
Δ
, and peak ground velocity (
PGV
)
as a function of time
t
0
after the
P
-wave detection for different types of input information used. The best results are obtained when using
three-component acceleration, velocity, and displacement data,
IAA
i
,
IAV
i
, and
IAD
i
,
i
f
EW; NS; UD
g
(equations
1
to
3
) with
V
S
30
site
corrections. High-frequency acceleration data are most important for classification; mid- and low-frequency velocity and displacement data
play a dominant role for predicting the other parameters. Site corrections help improving the estimates by up to 10%, the usage of information
derived from the horizontal components by an additional
∼
10%
. We show in Figure
4
that the errors also depend on
M
.
742
M. Böse, T. Heaton, and E. Hauksson
errors for this case in more detail. We focus on analyzing the
magnitude errors
M
err
M
obs
M
pred
.
There are apparent trends of over- and underestimation
of earthquake magnitudes (Fig.
4a
). Magnitudes for small
earthquakes with
M<
5
:
0
tend to be overestimated, while
magnitudes for large earthquakes are underestimated. The
errors decrease exponentially with increasing time window
length
t
0
; the larger the earthquake, the slower is the decay;
that is, large events require more time to be recognized than
small events.
To rule out that the magnitude and time dependencies of
prediction errors in Figure
4a
are biased by the training data
or the training method of the
ANN
s, we repeat the training
and testing of PreSEIS On-site several times using (1) differ-
ent training datasets, (2) distinct error measures for optimi-
zation (mean absolute and sum squared errors), (3) different
numbers of hidden neurons (Fig.
1b
), and (4) consistent ap-
plication of the same distance range of
Δ
≤
100
km to all
events, rather than adopting a magnitude-dependent thresh-
old of
Δ
km
≤
15
M
.
The only factor that strongly affects the magnitude
–
time
dependency of errors is the magnitude-frequency distribution
of events in the dataset. While our original dataset contains
events with almost uniform magnitude distribution (Fig.
2
),
earthquakes are commonly observed to follow power-law
distributions, such as described by the Gutenberg
–
Richter
relation (
Gutenberg and Richter, 1944
)
log
M
N
∝
β
M:
(4)
We use equation
(4)
to define a simple weighting func-
tion for the events in our original dataset and increase the
number of events of a given magnitude in the set accordingly
before restarting the training procedure of the
ANN
s. To save
computational time, we restrict this approach to events
with
M
≥
4
:
0
.
The smallest errors for the uniformly distributed dataset
are observed for events with
∼
M
5
:
0
(Fig.
4a
), and for the
Gutenberg
–
Richter distributed set for events with
∼
M
4
:
0
(Fig.
4b
). This observation is not surprising because
∼
M
5
:
0
and
M
4.0 are the mean magnitudes of the two sets; we
expect the best performance at these magnitudes after the
optimization of the
ANN
s. Further, the magnitude
–
time
dependencies of the prediction errors in Figure
4a,b
are
basically the same. Thus, the magnitude
–
time behavior of the
prediction errors is not significantly affected by the compo-
sition of the dataset.
Broadband (BB) versus Strong-Motion (SM) Data
In general,
EEW
systems are based on BB or SM instru-
mentation. In this study, we use a dataset comprising the
records of both sensor types and find clear differences in
the performance of PreSEIS On-Site (Fig.
5
). The standard
deviations
σ
of the (Gaussian) error distributions in magni-
tude predictions are generally smaller for the BB than for the
SM data, that is, the errors are smaller (Fig.
5a,b
). The longer
the time window
t
0
of the
P
-waveform data used, the more
accurate are the predictions. The smallest errors for BB are
observed for earthquakes with
M
≤
5
:
5
, while for SM the
errors are smallest for
4
:
5
≤
M
≤
6
:
5
. Note, however, that
the BB and SM data in our set cover different magnitude
ranges. Most BB records are from earthquakes with
3
:
1
≤
M
≤
6
:
0
, while most SM records are from events with
Figure
4.
Magnitude prediction errors as a function of time
t
0
and magnitude
M
for (a) a uniformly distributed dataset, and (b) a dataset
distributed according to the Gutenberg
–
Richter power-law statistics; black lines show the mean values for
M
4.0 to
M
8.0. The results for
M
8.0 are obtained from extrapolation. The main difference between (a) and (b) is a shift of the prediction errors to smaller and larger values,
respectively; the magnitude
–
time dependence of the errors, however, remains almost the same. A small earthquake can be faster recognized
than a large event.
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
743
4
:
0
≤
M
≤
7
:
0
(Fig.
5c,d
). Further, the dataset contains al-
most no records with clipped waveform amplitudes typically
observed for BB sensors during large and close earthquakes.
We therefore suspect that the better performance of the BB
sensors for large-magnitude earthquakes in Figure
5
is some
artifact caused by the limitation of the BB dataset.
Figure
5
suggests that BB sensors tend to perform better
(due to the higher signal-to-noise ratio) during small- to
moderate-sized earthquakes (
M<
6
) that occur more fre-
quently, but usually do not cause significant damage. In con-
trast, because of their low gain, SM sensors outperform the
BB sensors during very strong shaking.
Examples
In Figure
6
we analyze the performance of PreSEIS
On-site, including the classification and the estimation of
M
,
PGV
, and
Δ
within the first
t
0
10
s after the
P
-wave
detection for three example earthquakes from the test dataset;
that is, these data were not used for the training of the
ANN
s:
the 2010
M
4.1 Redlands (N34.00°/W117.18°/
Z
9
km)
and 2010
M
5.4 Collins Valley earthquakes (N33.42°/
W116.45°/
Z
14
km) in southern California, and the
2008
M
6.9 Miyagi earthquake (N39.03°/E140.88°/
Z
8
km) in Japan. For each of the three earthquakes,
we randomly pick two stations at distinct epicentral distances
Δ
. Note that station IWT010 is very close to the city of
Ō
sh
ū
,
Iwate Prefecture, which experienced damaging shaking dur-
ing the
M
6.9 Miyagi earthquake.
There is a good agreement between the estimated (solid)
and observed (dashed) source and ground-motion parameters
for the three analyzed events (Fig.
6
). In all six cases, reason-
ably well predicted parameters are available between 2.5 and
around 10 s before
PGV
is observed. The strongest shaking in
Figure
5.
Comparison of magnitude prediction errors (standard deviation
σ
of error distributions) for (a) broadband (BB) and (b) strong-
motion (SM) records as a function of magnitude
M
and time
t
0
(top). The errors for the BB data are generally smaller than for SM; note,
however, that most BB records are (c)
3
:
1
≤
M
≤
6
:
0
, while (d)
4
:
0
≤
M
≤
7
:
0
for the SM data. The longer
t
0
, the smaller are the errors. The
smallest errors for BB are observed for the smallest earthquakes (
M
≤
5
:
5
), while for SM the errors are smallest for
4
:
5
≤
M
≤
6
:
5
.
744
M. Böse, T. Heaton, and E. Hauksson
these examples was observed at station IWT010. PreSEIS
On-site recognized around 2 s after
P
-wave detection that
PGV
at this site would exceed
10
cm
=
s, offering a warning
time of around 6 s prior to very strong shaking. Parameters
estimated from data at stations at larger epicentral distances
Δ
usually require more time for convergence, in particular if
the events have large magnitudes. We also expect longer
warning times for these events, so that a warning could still
be issued before strong shaking at most user sites occurs.
Discussion
PreSEIS On-site uses three-component acceleration,
velocity, and displacement waveforms of a single BB or SM
sensor to rapidly estimate earthquake source and ground-
motion parameters for
EEW
. The trade-off between magni-
tudes and distances can be solved this way, because
u
t
,
_
u
t
, and
u
t
show distinct dependencies on
M
and
Δ
(see also
Yamada
et al.
, 2009
). The three time series char-
acterize different frequency bands of seismic ground mo-
tions:
u
t
is most sensitive to high frequencies (
>
3
Hz),
u
t
is most sensitive to low frequencies (
<
1
Hz), and
_
u
t
is most sensitive to the midfrequency range (1 to 3 Hz).
We expect that as an alternative to integrating and differen-
tiating the recorded time series, we could use filters and con-
sider different frequency bands, but such effort is beyond the
scope of this study. Using integrated and differentiated time
series has the advantage that the frequency spectra are simply
weighted with
ω
or
ω
2
, respectively, that is, our approach is
scale-free, while (other) filtering approaches introduce one or
more cutoff frequencies.
The majority of algorithms that have been proposed for
EEW
need to be calibrated to the seismic data of a particular
area of interest, taking into account the regional differences
in the seismic wave propagation and sometimes the earth-
quake source (e.g.,
Wu and Kanamori, 2005
;
Wu
et al.
,
2007
;
Cua
et al.
, 2009
;
Brown
et al.
, 2011
). This procedure
is problematic, because an adequate database containing the
records of both moderate and large earthquakes over a wide
range of source-to-site distances is unavailable for most seis-
mic-active regions around the world, leading to large data
gaps and thus uncertainties in the algorithms. Some authors
have suggested filling these gaps with simulated waveforms
(e.g.,
Böse
et al.
, 2008
;
Zollo
et al.
, 2009
;
Oth, Böse,
et al.
,
Figure
6.
Demonstration of PreSEIS On-site for three earthquakes from the test dataset: (a) the 2010
M
4.1 Redlands and (b) the 2010
M
5.4 Collins Valley earthquakes in southern California, and (c) the 2008
M
6.9 Miyagi earthquake in Japan. For each earthquake, we show
the results at two stations at distinct epicentral distances
Δ
. From top to bottom the panels show the corresponding seismic records and results
for classification (output should be
1
because
Δ
km
≤
15
M
), magnitude
M
, peak ground velocity (
PGV
), and distance
Δ
. There is usually
a good agreement between the estimates (solid lines) and the observed parameters (dashed lines) between 2.5 and around 10 s before
PGV
is
observed. The initial magnitude estimates at
t
0
0
:
25
s are almost the same for all three earthquakes, indicating that this time window is
insufficient to resolve the size of the ongoing earthquakes.
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
745
2010
) or developing
EEW
systems based on theoretical con-
siderations (
Böse and Heaton, 2010
), but it is questionable
how reliable these algorithms will perform during a real
major earthquake. Our approach of using global datasets
of broadband (BB) and strong-motion (SM) records of small
to major earthquakes and searching for the common charac-
teristics of these events may be more reliable.
The magnitude-frequency distribution of events in the
training dataset has impact on the absolute prediction er-
rors of PreSEIS On-site, but the relative magnitude
–
time
dependency of these errors remains almost unaffected
(Fig.
4
). This is an important observation implying that
ANN
s
learn to some extent the
a priori
probabilities of the occur-
rence of earthquakes of different magnitudes from the train-
ing data. Alternatively, we may use a uniformly distributed
dataset for the training and apply the
a priori
probabilities
(such as the Gutenberg
–
Richter power-law statistics) after-
ward. By doing so, we can realize a fully Bayesian approach,
similar to the virtual seismologist (VS) algorithm for
EEW
(
Cua and Heaton, 2007
). This method considers both the
likelihood function (that describes how likely it is to observe
a certain output, e.g.,
M
, for a given input, e.g.,
IAA
i
,
IAV
i
,
and
IAD
i
), and the
a priori
probabilities (that are a measure
for the frequency of the occurrence of a certain output, e.g.,
M
) to determine probabilistic estimates.
SM sensors have two major advantages over BB sensors
for
EEW
: (1) wave amplitudes stay on scale, that is, they are
not clipped during strongest seismic shaking typically ob-
served during large earthquakes (
M>
6
:
5
), which are most
damaging; (2) SM sensors are usually less costly than BB
instruments. On the other hand, the dynamic range of SM
sensors is more limited. Strong-motion instruments are not
as sensitive to ground motions as BB sensors that provide
data for small and moderate earthquakes at moderate dis-
tances. These events usually do not cause structural damage
(aside from the possible failure of weakened structures dur-
ing aftershocks;
Bakun
et al.
(1994)
), but they occur more
frequently than large earthquakes and can be used to opti-
mize real-time
EEW
algorithms.
Furthermore, SM sensors are accelerometers; that is, to
obtain information on displacement, which is important to
calculate the static offset during an earthquake, the recorded
acceleration time series needs to be double-integrated. Dou-
ble integration, however, often results in significant long-
period errors caused by very small linear baseline trends
(e.g., caused by a small tilt of the sensor or thermal drift),
which are difficult to isolate and remove from current strong-
motion records (e.g.,
Clinton and Heaton, 2002
). This can
seriously distort the resultant displacement series (e.g.,
Boore, 2001
).
Our results suggest that the magnitudes of large earth-
quakes require more time to be determined than magnitudes
of small events (Fig.
4
). Because
ANN
s have a great degree of
flexibility and usually provide models with a very good or
maybe even the best possible reproduction of the desired in-
put-output mapping (at least for the training dataset), we sus-
pect that these findings are not limited to PreSEIS On-site,
but provide important insight into the predictability of earth-
quake ruptures in general.
The uncertainty in the magnitude prediction of large
earthquakes decays slower with time than for small earth-
quakes because of their longer rupture durations. The sys-
tematic trends in the errors (Fig.
4
) possibly reflect the
ambiguity of the seismic data, which do not allow for a clear
discrimination of small and large events at the very beginning
of the rupture process.
Kanamori (2005)
suggests to set
t
0
3
s, which corresponds to the typical rupture duration
of an
M
6to
M
6.5 earthquake, that is, within 3 s we should
Figure
7.
(a) Comparison of the results obtained from PreSEIS On-site and the
τ
c
algorithm. (b) Similar trends in the error distributions
for both algorithms indicate some general nature of the predictability of earthquake ruptures and magnitudes using a limited time window of
seismic data (compare with Figs.
3
and
5
). The errors in the
τ
c
algorithm are around 60% higher than in PreSEIS On-site.
746
M. Böse, T. Heaton, and E. Hauksson
be capable of deciding whether a detected earthquake is
smaller or larger than
M
6.5.
Comparison with the
τ
c
Algorithm
The input parameters of PreSEIS On-site in equations
(1)
to
(3)
show striking similarities with the period parameter
τ
c
,
which was proposed by
Kanamori (2005)
for on-site early
warning as an extension of a method developed by
Naka-
mura (1988)
and
Allen and Kanamori (2003)
. The
τ
c
algo-
rithm allows for a quick estimation of magnitude
M
of an
earthquake based on the (assumed) log-linear relationship
M
a
log
τ
c
b;
(5)
where the coefficients
a
and
b
are specific for the earth-
quakes in a given region (e.g.,
Wu
et al.
, 2007
). The
τ
c
pa-
rameter is defined by
τ
c
2
π
r
p
with
r
R
t
0
0
_
u
2
UD
t
dt
R
t
0
0
u
2
UD
t
dt
;
(6)
where
t
0
is usually set to 3 s. Using Parsevel
’
s theorem,
Ka-
namori (2005)
showed that
r
≈
4
π
2
R
∞
0
f
2
j
^
u
f
j
2
df
R
∞
0
j
^
u
f
j
2
df
4
π
2
h
f
2
i
,
where
^
u
f
is the frequency spectrum of
u
t
, and
h
f
2
i
is
the average of
f
2
weighted by
j
^
u
f
j
2
. The
τ
c
parameter
is thus a measure of the effective period of ground shaking
(
Kanamori, 2005
).
The comparison of equations
(1)
to
(3)
with equation
(6)
reveals similarities between
τ
c
and the PreSEIS On-site in-
put. The main differences are that (1) the
τ
c
algorithm uses
the squared amplitudes of
u
t
and
_
u
t
, while PreSEIS On-
site uses absolute values (PreSEIS On-site using squared am-
plitudes was also tested, but no significant changes in the
algorithm performance were detected); (2) PreSEIS On-site
uses
u
t
in addition to
_
u
t
and
u
t
; (3) PreSEIS On-site
uses three-component data; (4) PreSEIS On-site considers
seismic site effects; (5) PreSEIS On-site does not assume
a log-linear relationship of the seismic observations and
M
(equation
5
), but is completely data-driven; and (6) Pre-
SEIS On-site does not restrict the time window of integration
to
t
0
3
s, but starts at
t
0
0
:
25
s after the earthquake
detection and then continuously updates its predictions
every 0.25 s.
To compare the performance of the two algorithms, we
determine the
τ
c
–
M
relationship for the same dataset as used
for the training and testing of PreSEIS On-site with
t
0
0
:
25
to 10.0 s. For each earthquake we determine
the median
τ
c
value taken over the values at all recording
stations (BB and SM sensors) and determine at each time
window
t
0
the coefficients
a
and
b
in equation
(5)
from
least-squares regression. The standard deviations
σ
of the ob-
tained error distributions are shown in Figure
7a
. Again the
uncertainties in the predicted magnitudes decay with increas-
ing
t
0
, but are
∼
60%
higher than for PreSEIS On-site (see
also Fig.
3
). We apply a filter criterion (
Böse
et al.
, 2009
)
to identify and remove records whose data quality might
be insufficient for the
τ
c
algorithm. After that, the errors re-
duce significantly (Fig.
7a
, gray dashed line), but are still
more than 15% higher than for PreSEIS On-site.
Similar to Figure
5
we determine the standard deviations
σ
of the residuals for all events up to a certain upper mag-
nitude threshold (Fig.
7b
). Again we find that the magnitudes
of large earthquakes require more time to stabilize than mag-
nitudes of small events. The uncertainties in Figures
5
and
7a
cannot be directly compared with each other, because
Figure
7b
refers to the event median. Taking the event med-
ian is required to stabilize the predictions by the
τ
c
algorithm
(see, e.g.,
Allen and Kanamori, 2003
). Typically, the param-
eters
a
and
b
in equation
(5)
are optimized for the earth-
quakes in a specific region and over a smaller distance range
(e.g.,
Wu and Kanamori, 2005
;
Wu
et al.
, 2007
;
Böse,
Hauksson, Solanki, Kanamori, and Heaton, 2009
) than was
done in this study. The observed magnitude errors of the
τ
c
algorithm are thus usually smaller than shown in Figure
7
.
Conclusions and Outlook
We developed and tested a new algorithm for earthquake
early warning (
EEW
) that uses three-component broadband
(BB) or strong-motion (SM) waveforms recorded at a single
sensor. Based on artificial neural networks (
ANN
s), PreSEIS
On-site classifies earthquake/noise and near/far source
events, as well as estimates the moment magnitude
M
, epi-
central distance
Δ
, and the peak ground velocity (
PGV
) at the
site of observation. First estimates become available at
t
0
0
:
25
s after the
P
pick and are regularly updated. The mag-
nitude-distance trade-off is solved from usage of information
derived from the acceleration, velocity, and displacement
waveform time series,
u
t
,
_
u
t
, and
u
t
, that show distinct
dependencies on
M
and
Δ
. We find that
u
t
and
_
u
t
are
most relevant for the estimation of
M
and
PGV
, while
u
t
is important for the earthquake/noise discrimination.
PreSEIS On-site overcomes the limitations of the former
(network-based) PreSEIS algorithm (
Böse
et al.
, 2008
)by
being faster and network-independent. The algorithm has
been tested successfully with a large dataset of recorded
waveforms from different tectonic settings (California,
Japan, and Taiwan). PreSEIS On-site does not replace the
original PreSEIS algorithm that clearly has important
features arising from the usage of multiple sensors. The im-
plementation of PreSEIS On-site, however, is more straight-
forward, and the code is directly applicable (Appendix
A
).
At each time
t
0
after
P
-wave detection, PreSEIS On-site
uses the current (logarithmic) values of the integrated abso-
lute amplitudes of the acceleration, velocity, and displace-
ment waveforms,
IAA
i
,
IAV
i
and
IAD
i
i
f
EW; NS;
UD
g
. Taking the logarithm of these values has a smoothing
effect for larger amplitudes, including the seismic
S
wave
(see, e.g., Fig.
6
, top graphs). The temporal evolution of
IAA
i
,
IAV
i
, and
IAD
i
could give additional information
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
747
and help improving predictions. This shall be explored in
future studies.
This study was based on a joint dataset of BB and SM
records of 161 crustal earthquakes from California, Japan,
and Taiwan with
3
:
1
≤
M
≤
7
:
6
at epicentral distances of
up to 115 km. The initial uncertainties of
M
0
:
7
and
log
PGV
0
:
55
for this dataset decrease with progressing
time, revealing a trade-off between the reliability of warnings
and remaining warning time. We found systematic trends in
the prediction errors, such that the parameters for small earth-
quakes tend to be overestimated, while large events tend to
be underestimated. These trends are more profound at the
beginning of the rupture process and seem to be caused
by the ambiguity of the waveform data from small and large
earthquake at rupture initiation. We compared our approach
with the
τ
c
algorithm (
Kanamori, 2005
) and found that the
prediction errors of PreSEIS On-site are around 60% smaller.
However, in general there is a limitation to the prediction
accuracy an
EEW
system can provide if based on single-
sensor observations.
We tested PreSEIS On-site also for subduction-zone
events in Japan in the same magnitude range
3
:
1
≤
M
≤
7
:
6
and found that our approach is not limited to crustal
earthquakes (results are not shown here). However, very
large subduction-zone earthquakes that are often accompa-
nied by devastating tsunamis, such as the 2011
M
9.0 Toho-
ku earthquake in Japan, the 2010
M
8.8 Maule (Chile)
earthquake, or the 2004
M
9.2 Sumatra
–
Andaman earth-
quake, pose a huge challenge to
EEW
. Due to long rupture
durations of one or more minutes, these events clearly re-
quire updating procedures for magnitude estimations longer
than 10 s as we used for crustal earthquakes in this study.
Earthquakes with
M
8.0 and larger might need some special
treatment for
EEW
and will likely require the inclusion of
other types of data, such as from a real-time Global Position-
ing System (e.g.,
Crowell
et al.
, 2009
;
Böse and Heaton,
2010
;
Hammond
et al.
, 2011
).
Data and Resources
Broadband and strong-motion records used in this study
were downloaded from (1)
CISN
, operated by the California
Institute of Technology (Caltech),
USGS
Pasadena/Menlo
Park, California Geological Survey, and UC Berkeley;
(2) K-NET, operated by the Japanese National Research In-
stitute for Earth Science and Disaster Prevention (
NIED
); and
(3)
TSMIP,
operated by the Chinese Weather Bureau. The data
for the 1999 Chi-Chi earthquake and its aftershocks were
downloaded from the
COSMOS
Virtual Datacenter (
www
.cosmos
‑
eq.org/
, last accessed October 2011). The moment
magnitudes
M
from the Global Centroid Moment Tensor Cat-
alog (
www.globalcmt.org/CMTsearch.html
, last accessed
October 2011) were used to create a consistent dataset rather
than using the JMA magnitude
M
JMA
. The K-NET web site
provided borehole data and shear-wavevelocities used for soil
classification (
www.k-net.bosai.go.jp/
, last accessed Octo-
ber 2011). The National Center for Research on Earthquake
Engineering and the Chinese Weather Bureau (
http://
geo.ncree.org.tw
, last accessed October 2011) provided the
V
S
30
values. PreSEIS On-site can be obtained upon request.
Acknowledgments
This work is funded through contract G09AC00258 from USGS/
ANSS to the California Institute of Technology (Caltech). This is contribu-
tion #10058 of the Seismological Laboratory, Geological and Planetary
Sciences at Caltech. We would like to thank William H. Bakun and an anon-
ymous reviewer for their helpful comments.
References
Allen, R. V. (1978). Automatic earthquake recognition and timing from sin-
gle traces,
Bull. Seismol. Soc. Am.
68,
1521
–
1532.
Allen, R. M., and H. Kanamori (2003). The potential for earthquake early
warning in Southern California,
Science
300,
786
–
789.
Allen, R. M., P. Gasparini, O. Kamigaichi, and M. Böse (2009). The status of
earthquake early warning around the world: An introductory overview,
Seismol. Res. Lett.
80,
no. 5, 682
–
693, doi
10.1785/gssrl.80.5.682
.
Bakun, W. H., F. G. Fischer, E. G. Jensen, and J. VanSchaak (1994). Early
warning system for aftershocks,
Bull. Seismol. Soc. Am.
84,
no. 2,
359
–
365.
Bishop, C. (1995).
Neural Networks for Pattern Recognition
Oxford,
Clarendon Press, 482 pp.
Böse, M. (2006). Earthquake early warning for Istanbul using artificial neural
networks,
Ph.D. Thesis
, 181 pp., Karlsruhe University, Germany,
http://
www.ubka.uni
‑
karlsruhe.de/cgi
‑
bin/psview?document=2006/physik/
6
, last accessed October 2011.
Böse, M., and T. H. Heaton (2010). Probabilistic prediction of rupture
length, slip and seismic ground motions for an ongoing rupture: Im-
plications for early warning for large earthquakes,
Geophys. J. Int.
183,
no. 2, 1014
–
1030, doi
10.1111/j.1365-246X.2010.04774.x
.
Böse, M., E. Hauksson, K. Solanki, H. Kanamori, Y.-M. Wu, and T. H.
Heaton (2009). A new trigger criterion for improved real-time perfor-
mance of on-site earthquake early warning in southern California,
Bull.
Seismol. Soc. Am.
99,
no. 2-A 897
–
905, doi
10.1785/0120080034
.
Böse, M., E. Hauksson, K. Solanki, H. Kanamori, and T. H. Heaton (2009).
Real-time testing of the on-site warning algorithm in southern
California and its performance during the July 29 2008
M
w
5.4 Chino
Hills earthquake,
Geophys. Res. Lett.
36,
L00B03, doi
10.1029/
2008GL036366
.
Böse, M., C. Ionescu, and F. Wenzel (2007). Earthquake early warning for
Bucharest, Romania: Novel and revised scaling relations,
Geophys.
Res. Lett.
34,
L07302, doi
10.1029/2007GL029396
.
Böse, M., F. Wenzel, and M. Erdik (2008). PreSEIS: A neural network based
approach to earthquake early warning for finite faults,
Bull. Seismol.
Soc. Am.
98,
no. 1, 366
–
382, doi
10.1785/0120070002
.
Boore, D. M. (2001). Effect of baseline corrections on displacements and
response spectra for several recordings of the 1999 Chi-Chi, Taiwan,
earthquake,
Bull. Seismol. Soc. Am.
91,
no. 1, 199
–
211.
Brown, H. M., R. M. Allen, M. Hellweg, O. Khainovski, D. Neuhauser, and
A. Souf (2011). Development of the ElarmS methodology for earth-
quake early warning: Realtime application in California and offline
testing in Japan,
Soil Dynam. Earthquake Eng.
31,
188
–
200, doi
10.1016/j.soildyn.2010.03.008
.
Clinton, J. F., and T. H. Heaton (2002). Potential advantages of a strong-
motion velocity meter over a strong-motion accelerometer,
Seismol.
Res. Lett.
73,
no. 3, 332
–
342.
Crowell, B. W., Y. Bock, and M. B. Squibb (2009). Demonstration of
earthquake early warning using total displacement waveforms from
real-time GPS networks,
Seismol. Res. Lett.
80,
no. 5, 772
–
782, doi
10.1785/gssrl.80.5.772
.
748
M. Böse, T. Heaton, and E. Hauksson
Cua, G., and T. Heaton (2007). The Virtual Seismologist (VS) method: A
Bayesian approach to earthquake early warning, in
Earthquake Early
Warning Systems
, P. Gasparini, G. Manfredi, and J. Zschau (Editors),
Springer, New York, 85
–
132.
Cua, G., M. Fischer, T. Heaton, and S. Wiemer (2009). Real-time perfor-
mance of the Virtual Seismologist earthquake early warning algorithm
in Southern California,
Seismol. Res. Lett.
80,
no. 5, 740
–
747, doi
10.1785/gssrl.80.5.740
.
Gutenberg, R., and C. F. Richter (1944). Frequency of earthquakes in
California,
Bull. Seismol. Soc. Am.
34,
185
–
188.
Hammond, W. C., B. A. Brooks, R. Bürgmann, T. Heaton, M. Jackson, A. R.
Lowry, and S. Anandakrishnan (2011). Scientific value of real-time
Global Positioning System data,
Eos Trans. AGU
92,
no. 15, 125
–
132.
Hilbring, D., T. Titzschkau, A. Buchmann, G. Bonn, F. Wenzel, and E.
Hohnecker (2010). Earthquake early warning for transport lines,
Nat. Hazards
, doi
10.1007/s11069-010-9609-3
.
Horiuchi, S., H. Negishi, K. Abe, A. Kamimura, and Y. Fujinawa (2005). An
automatic processing system for broadcasting earthquake alarms,
Bull.
Seismol. Soc. Am.
95,
no. 2, 708
–
718.
Kanamori, H. (2005). Real-time seismology and earthquake damage mitiga-
tion,
Annu. Rev. Earth Planet. Sci.
33,
195
–
214, doi
10.1146/annurev
.earth.33.092203.122626
.
Köhler, N. (2010). Real-time information from seismic networks,
Ph.D. The-
sis
, 150 pp., Karlsruhe Institute of Technology, Germany,
http://digbib
.ubka.uni
‑
karlsruhe.de/volltexte/1000015555
, last accessed Octo-
ber 2011.
Köhler, N., G. Cua, F. Wenzel, and M. Böse (2009). Rapid source parameter
estimations of Southern California earthquakes using PreSEIS,
Seis-
mol. Res. Lett.
80,
no. 5, 748
–
754, doi
10.1785/gssrl.80.5.748
.
Leach, R., and F. Dowla (1996). Earthquake early warning system
using real-time signal processing, in
IEEE Workshop on Neural
Networks for Signal Processing
, , Keihanna, Kyoto, Japan, 4
–
6 Sep-
tember 1996.
Levenberg, K. (1944). A method for the solution of certain non-linear pro-
blems in least squares,
Q. J. Appl. Math.
2,
164
–
168.
Nakamura, Y. (1988). On the urgent earthquake detection and alarm sys-
tem (UrEDAS),
Proc. of the 9th World Conference on Earthquake
Engineering
, Tokyo
–
Kyoto, Japan.
National Earthquake Hazards Reduction Program (1994). Recommended
provisions for seismic regulations for new buildings,
Federal Emer-
gency Management Agency Rept. FEMA 222A
, Washington, D.C.,
290 pp.
Olson, E. L., and R. M. Allen (2005). The deterministic nature of earthquake
rupture,
Nature
438,
212
–
215.
Oth, A., D. Bindi, S. Parolai, and D. Di Giacomo (2010). Earthquake scaling
characteristics and the scale-(in)dependence of seismic energy-to-
moment ratio: Insights from KiK-net data in Japan,
Geophys. Res. Lett.
37,
L19304, doi
10.1029/2010GL044572
.
Oth, A., M. Böse, F. Wenzel, N. Köhler, and M. Erdik (2010). Evaluation
and optimization of seismic networks and algorithms for earthquake
early warning
—
The case of Istanbul (Turkey),
J. Geophys. Res.
115,
B10311, doi
10.1029/2010JB007447
.
Rumelhart, D., G. Hinton, and R. Williams (1986).
Parallel distributed pro-
cessing: Explorations in the microstructure of cognition
,vol.
1,
MIT
Press, Cambridge, 564 pp.
Rydelek, P., and S. Horiuchi (2006). Earth science: Is the earthquake rupture
deterministic?
Nature
442,
doi
10.1038/nature04963
.
Rydelek, P., C. Wu, and S. Horiuchi (2007). Comment on
“
Earthquake mag-
nitude estimation from peak amplitudes of very early seismic signals
on strong motion records
”
by Aldo Zollo, Maria Lancieri, and Stefan
Nielsen,
Geophys. Res. Lett.
34,
L20302, doi
10.1029/2007GL029387
.
Wald, D. J., V. Quitoriano, T. H. Heaton, H. Kanamori, C. W. Scrivner, and
C. B. Worden (1999). TriNet ShakeMaps: rapid generation of instru-
mental ground motion and intensity maps for earthquakes in Southern
California,
Earthquake Spectra
15,
537
–
556.
Wills, C. J., M. D. Petersen, W. A. Bryant, M. S. Reichle, G. J. Saucedo, S.
S. Tan, G. C. Taylor, and J. A. Treiman (2000). A site conditions map
for California based on geology and shear wave velocity,
Bull. Seismol.
Soc. Am.
90,
no. 6b, 187
–
208.
Wu, Y.-M., and H. Kanamori (2005). Experiment on an on-site early warn-
ing method for the Taiwan early warning system,
Bull. Seismol. Soc.
Am.
95,
347
–
353.
Wu, Y.-M., and T. L. Teng (2002). A virtual sub-network approach to earth-
quake early warning,
Bull. Seismol. Soc. Am.
92,
2008
–
2018.
Wu, Y.-M., H. Kanamori, R. M. Allen, and E. Hauksson (2007). Determina-
tion of earthquake early warning parameters,
τ
c
and
P
d
, for southern
California,
Geophys. J. Int.
170,
711
–
717, doi
10.1111/j.1365-
246X.2007.03430.x
.
Yamada, T., and S. Ide (2008). Limitation of the predominant-period esti-
mator for earthquake early warning and the initial rupture of earth-
quakes,
Bull. Seismol. Soc. Am.
98,
no. 6, 2739
–
2745, doi
10.1785/
0120080144
.
Yamada, M., T. Heaton, and J. Beck (2007). Real-time estimation of fault
rupture extent using near-source versus far-source classification,
Bull.
Seismol. Soc. Am.
97,
no. 6, 1890
–
1910, doi
10.1785/0120060243
.
Yamada, M., A. H. Olsen, and T. H. Heaton (2009). Statistical features of
short-period and long-period near-source ground motions,
Bull. Seis-
mol. Soc. Am.
99,
no. 6, 3264
–
3274, doi
10.1785/0120090067
.
Zollo, A., G. Iannacone, M. Lancieri, L. Cantore, V. Convertito, A. Emolo,
G. Festa, F. Gallovi
č
, M. Vassallo, C. Martino, C. Satriano, and P.
Gasparini (2009). Earthquake early warning system in southern Italy:
Methodologies and performance evaluation,
Geophys. Res. Lett.
36,
L00B07, doi
10.1029/2008GL036689
.
Zollo, A., M. Lancieri, and S. Nielsen (2006). Earthquake magnitude esti-
mation from peak amplitudes of very early seismic signals on strong
motion records,
Geophys. Res. Lett.
33,
L23312, doi
10.1029/
2006GL027795
.
Appendix A
Two-Layer-Feed-Forward Neural Networks
Two-layer-feed-forward (
TLFF
) neural networks are
composed of simple processing units (called neurons), which
are arranged in input layers, hidden layers, and output layers,
respectively. The neurons of different layers are connected to
each other and exchange information (Fig.
1b
). The impor-
tance of the links between different neurons is controlled
by weight parameters that are determined during the training
of the
ANN
s using a set of example patterns (e.g.,
Bishop, 1995
).
The output
y
of a
TLFF
neural network is calculated
from the input vector
x
and the weights in the input and hid-
den layers,
w
1
ji
and
w
2
j
:
y
X
J
j
0
w
2
j
g
X
I
i
0
w
1
ji
x
i
;
(A1)
with
x
0
1
. To encompass nonlinear behavior of the
network, we apply the logistic activation function
g
arg
1
=
1
exp
arg
.
For each output parameter
y
(
M
,
Δ
, and
PGV
and clas-
sification), we build one
TLFF
network with
I
10
input,
J
15
hidden, and
K
1
output units, which gives us a
total of 181 network weights. The training occurs from a
set of example patterns with known input and output values.
We adopt the Levenberg optimization method (
Levenberg,
Rapid Estimation of Earthquake Source and Ground-Motion Parameters for Earthquake Early Warning
749
1944
) combined with a back-propagation algorithm (e.g.,
Rumelhart
et al.
, 1986
) for iteratively updating the network
weights to decrease the mean absolute errors between
the observed and desired outputs:
M
err
M
obs
M
pred
,
log
Δ
err
log
Δ
obs
log
Δ
pred
, and log
PGV
err
log
PGV
obs
log
PGV
pred
. To avoid the overfitting of
the
ANN
s to the training dataset (at the expense of the desired
generalization capability for new data), we use an indepen-
dent validation dataset (which is used neither for training nor
for testing) and stop the iterative weight update, once the er-
rors for these data start increasing. The training of each
TLFF
network usually requires less than 50 iterations, which takes
roughly 1 s on a common PC (see
Böse, 2006
and
Böse
et al.
,
2008
for more details).
Appendix B
Dataset
The
CISN
dataset comprises 703 three-component BB
and 677 three-component SM records of 107 crustal earth-
quakes with
3
:
1
≤
M
≤
7
:
1
at epicentral distances of 1.2 to
105 km that occurred in northern and southern California
between 1990 and 2010. The set includes, for example,
the 1994
M
6.7 Northridge and the 1999
M
7.1 Hector Mine
earthquakes. We employ the
V
S
30
values at the
CISN
stations
taken from
Wills
et al.
(2000)
that are also used in the
Californian ShakeMaps (
Wald
et al.
, 1999
).
The K-NET dataset comprises 938 three-component SM
records of 48 earthquakes with
4
:
8
≤
M
≤
7
:
3
at epicentral
distances of 3.7 to 110 km, including, for example, the 2003
M
7.3 Tokachi
–
Oki and the 2008
M
6.9 Iwate
–
Miyagi earth-
quakes. To obtain a consistent dataset, we replaced the
JMA
magnitude
M
JMA
with the moment magnitudes
M
from the
Global Centroid Moment Tensor Catalog (see
Data and Re-
sources
) if available; for smaller events, we assumed that
M
≈
M
JMA
(
Oth, Bindi,
et al.
, 2010
). For the soil classifica-
tion at the K-NET station sites we used close-by borehole
data and averaged the shear-wave velocities down to their
full depth (see
Data and Resources
). Because most boreholes
have depths of 20 m only, we assumed that
V
S
30
≈
V
S
20
.
The Taiwanese dataset includes 113 three-component
SM records of 6 earthquakes with
5
:
0
≤
M
≤
7
:
6
at epicen-
tral distances of 5.2 km to 115 km. The set comprises records
of the 1999
M
7.6 Chi-Chi earthquake and its five strongest
aftershocks. The data were downloaded from the
COSMOS
database (see
Data and Resources
).
V
S
30
values were ob-
tained from the National Center for Research on Earthquake
Engineering and the Chinese Weather Bureau (see
Data and
Resources
).
Seismological Laboratory
California Institute of Technology
1200 E. California Blvd.
Mail Code 252
–
21
Pasadena, California 91125
mboese@caltech.edu
hauksson@caltech.edu
heaton@caltech.edu
Manuscript received 18 May 2011
750
M. Böse, T. Heaton, and E. Hauksson