Seismic P-wave Polarization in the Context of On-site Early Warning System

Abstract

Design of an on-site seismic early warning system for critical facilities, based on P-wave detection, requires a knowledge of local seismicity, analysis of strong-motion records, and local geological settings. The scope of current paper is to present an efficient and reliable methodology for P-wave detection for a specified region. It is tolerant to the environmental, traffic and other types of noise at the location of the critical facility. The basic idea that is exploited in the proposed algorithm is the degree of P-wave polarization, which is obtained with Karhunen-Loève transform of the orthogonal triaxial records. A system consisting of borehole sensor array that has been designed based on these ideas is described and some preliminary results are provided. This system has been already implemented to provide earthquake early warning for a tunnel on a major highway in British Columbia, Canada.

Full text

SEISMIC P-WAVE POLARIZATIO I THE COTEXT OF O-SITE EARLY
WARIG SYSTEM
Anton Zaicenco
Weir-Jones Engineering Consultants, Ltd.
2040 West 10
th
Avenue, Vancouver,
British Columbia
Canada
E-mail: anton.zaicenco@weir-jones.com
Tel: 604-732-8821, Fax: 604-732-4801
Sharlie Huffman
Bridge seismic engineer, Ministry of
Transportation, 940 Blanshard St.,
Victoria, British Columbia, V8W 3E6,
Canada
E-mail: Sharlie.Huffman@gov.bc.ca
Tel: 250-356-0761, Fax: 250-387-7735
Iain Weir-Jones
President, Weir-Jones Engineering
Consultants, Ltd. 2040 West 10
th
Avenue,
Vancouver, British Columbia
Canada
E-mail: iain.weir-jones@weir-jones.com
Tel: 604-732-8821, Fax: 604-732-4801
ABSTRACT
Design of an on-site seismic early warning system for critical facilities, based on P-wave detection, requires a knowledge of local
seismicity, analysis of strong-motion records, and local geological settings. The scope of current paper is to present an efficient and
reliable methodology for P-wave detection for a specified region. It is tolerant to the environmental, traffic and other types of noise at
the location of the critical facility.
The basic idea that is exploited in the proposed algorithm is the degree of P-wave polarization, which is obtained with Karhunen-
Loève transform of the orthogonal triaxial records. A system consisting of borehole sensor array that has been designed based on these
ideas is described and some preliminary results are provided. This system has been already implemented to provide earthquake early
warning for a tunnel on a major highway in British Columbia, Canada.
INTRODUCTION
Due to the increased interest in the earthquake early warning
systems (EEWS) 14th World Conference on Earthquake
Engineering in Beijing China had a special session on the
topic. 11 papers were presented at this session, mainly by
authors from Japan. In what follows, a review of several
papers will be presented to provide a snapshot of major topics.
Kanda et al. (2008) were interested in accurate prediction of
the seismic intensity using different source locations and site-
specific empirical method. On-site warning system has been
developed for sites with small epicentral distance in addition
to JMA system to pick P-waves and predict seismic intensity.
The prototype of the system has been validated using vibration
tests, numerical simulations, and observations. Authors
provide empirical relationships between RMS value of P-wave
velocity V
SD
, maximum velocity V
max
of 1-3 sec time series
after P-wave and measured intensity:
I = 2 log(VSD) + α (1)
I = 2 log(V
max
) + β (2)
where
α
=6.12 and
β
=5.14 for 2 seconds of P-wave. Yet,
standard deviation was found relatively large.
Yutaka Nakamura (2008) gives an overview of the P-wave
early warning systems. The author introduces the notion of
“On-Site Alarm”, which is the alarm based on the observation
at the side of the objects to be warned, and emphasizes that it
is more important that the network alarm. Such capabilities of
EEWS as estimation of azimuth, predominant frequency for
magnitude evaluation, and vertical to horizontal ratio for
discrimination between P- and S-waves are discussed.
UrEDAS system described by the author can detect
earthquakes in P-wave triggering and then estimates
magnitude, epicentral and hypocentral distance, depth and
back azimuth. Tolerance of EEWS to electrical thunder noise
and small pre-shocks has been emphasized. Author concludes
that “on-site alarm ... is useful for anywhere, even epicentral
area”.
Jun Saita et al. (2008) discuss the applications of EEWS. On-
site alarm is viewed as an extension of network alarm system
important to protect rescue teams. FREQL, Fast Response
Equipment against Quake Load, is a new generation of EEWS,
which is an all-in-one seismometer with the power unit. It is

capable of detecting P-wave from a single station and issue an
alarm in 0.2 seconds. EEWS by JMA that includes a large
number of seismometers nationwide is pseudo real-time
system because the system stores the waveform of the first 2
seconds and calculates parameters. If the system does not
converge to the acceptable results, it uses 3, 5, 7, 10 seconds
repeatedly. Therefore, the authors recommend that it is better
to have an on-site EEWS at each facility, while the network
information must be used as backup.
Masato Motosaka (2008) discusses application of EEWS
based on the nationwide earthquake observation networks in
Japan for disaster prevention in schools. Availability of
several EEWS in Japan, Mexico, Taiwan, South California
and Istanbul is mentioned. The author demonstrates the
application of EEWS to schools in Miyagi prefecture, Japan.
Li Shanyou and Song Jindong (2008) present a methodology
for predicting magnitude from the first few seconds of the P-
wave, which is important in EEWS applications. They propose
to estimate the value of magnitude from a single station as
function of amplitude P
max
, predominant period
τ
c
and
epicentral distance ∆ based on a linear regression model:
M = a log P
max
+ b log τ
c
+ c log ∆ + d (3)
The waveforms used in the study were collected from 17
earthquakes occurring between 1999 and 2006 from NSMP by
USGS. Automatic P-wave picker has been employed (Allen
(1978)) to detect the P-wave arrivals. The proposed technique
has less uncertainty in comparison with current methods based
on τ
c
or P
max
only.
Kuyuk and Motosaka (2008) identify another important
application of EEWS -- its ability to provide information to
reduce seismic response. Forecasting Fourier Amplitude
Spectrum is important for structural control systems. The
authors developed a regional warning system in Miyagi
Prefecture against Miyagi-ken offshore earthquakes and
integrated it with JMA national Japan EEWS.
Fujinawa et al. (2008) describe the EEWS built around JMA
network in cooperation with NIED. Real-time data collection
allows distributing warning to various customers. Since
October 1, 2007 the information has been put to general use
via broadcasting companies (TV, radio, mobile phones), and
contracted use by private companies using special application
instruments. Meguro (2008) discusses the problems of EEWS
based on JMA network related to proper dissemination of the
information to the public. In view of the author, the EEWS
should finally become a driving force to promote disaster
mitigation countermeasures. Regarding the technical aspects
of the EEWS, it is emphasized that accurate determination of
the magnitude from initial phase of the rupture is not possible.
There is a trade-off between available time and accuracy.
Alarm network is described by Masaki et al. (2008). It is
based on JMA EEWS and targets central area of Japan --
Mikawa area. The system is useful for earthquake disaster
reduction by performing evacuation of workers and stopping
machines before strong shaking arrival.
EARTHQUAKE EARLY WARNING BASED ON P-WAVE
DETECTION
The equation of the seismic wave propagation in the elastic
medium under assumption that Lame parameters
λ
and
µ
are
constant is:
ρü = (λ+µ)∇(∇⋅u) + µ∇×(∇×u) (4)
where
ρ
is the density of material and u is the displacement
vector. This is a 3D homogeneous vector wave equation for a
uniform, isotropic linear medium.
There are two propagation modes: P- (associated with div: ∇⋅u
and governed by a scalar wave equation) and S-waves
(associated with curl: ∇×u, and governed by vector wave
equation), which are pressure and shear waves, Fig.1.
Fig.1 Example of seismic wave propagation in the
inhomogeneous elastic medium from a point source:
numerical solution using spectral method, Zaicenco and Alkaz
(2008)
P-waves are associated with the propagation of deformations
in terms of dilatation:
∇⋅u = ∂u
1
/∂x
1
+ ∂u
2
/∂x
2
+ ∂u
3
/∂x
3
(5)
This is a scalar value and is related to trace of strain tensor
tr(ε
εε
ε), which is invariant under coordinate transformation. By
taking the divergence of Eq.(4) a wave equation for P waves is
obtained. The propagation speed of P wave is:
v
P
2
= (λ+2µ)/ρ (6)
S-waves are associated with the propagation of deformations
related to change of shape/rotation. They are described by off-
diagonal terms of antisymmetric rotation tensor:
ξ
ij
= 1/2 (∂u
i
/∂x
j
- ∂u
j
/∂x
i
) (7)
By taking the curl of Eq.(4) a wave equation for S-waves is
obtained. The propagation speed of S-wave is:
v
S
2
= µ/ρ (8)

The difference in propagation speeds given by Eqs.(6) and (7)
is usually exploited in early warning systems.
Along with speed of propagation, polarization is another key
factor allowing one to distinguish between P- and S-waves.
Since P-wave is related to change of volume, it propagates
perpendicular to the wave front, and is linearly polarized for a
homogeneous isotropic linear medium. S-wave, being related
to rotational deformations, is polarized in the plane parallel to
the wave front for a homogeneous isotropic linear medium.
An example of orthogonality in polarization of P- and S-waves
is demonstrated for 1989 Loma Prieta earthquake record in
Fig.2. Axes of polarization of 3D ground motion for both
waves are visualized with the help of ellipsoids.
(a)
(b)
(c)
Fig.2 (a) Three components of 1989 Loma Prieta
earthquake record measured by the instrument aligned parallel
to the fault, (b) time-frequency distributions, and (b) scaled
polarization ellipses and their axes for P- and S-waves
POLARIZATION ANALYSIS
The method based on polarization analysis has been used for
source location by Christoffersson et al. (1988), Ruud et al.
(1988). They applied probability estimator to the energy of a
temporal window corresponding to P-wave onset. Jackson et
al. (1991), based on several previous papers by Flinn (1965),
Montalbetti and Kanasewich (1970), Esmersoy (1974), have
achieved a polarization analysis using singular value
decomposition for a single-station triaxial recording.
When the location of the source is known, a simple rotation of
the coordinate system can be used to identify SH-, SV-wave
axes. This method has been used by Cassidy and Rogers
(1999) to study the site response spectra, which were
computed using a 15 s data window, beginning about 2 s
before S-wave arrival. The authors analyzed data from 1996
Duvall and 1997 Georgia Strait earthquakes and concluded
that strong amplification, up to 11 times, relative to the
bedrock is present at frequencies 1-3 Hz.
When the source direction is not known, polarization analysis
of the seismic wave can be done with the Karhunen-Loéve
transform (KLT). KLT is treating stochastic process as a
combination of the orthogonal functions, and the expansion
basis depends on the process itself. Polarization of the
recorded 3 orthogonal components of ground motion is
computed with discrete KLT, which is based on the
eigenvalue decomposition of the covariance matrix C:
C = TΛ
ΛΛ
ΛT
-1
(9)
Eigenvector matrix T allows to uncorrelate initial orthogonal
components. Coordinate rotation aligns transformed axis with
the directions of maximum variance. Since components with
larger variance correspond to interesting dynamics and lower
ones represent noise, signal-to-noise ratio (SNR) is critical in
such type of analysis.
TRIGGERING ALGORITHM
The EEWS system includes 2 borehole strings with 4 triaxial
sensors each. Total 8 sensors provide 24 channels of real-time
data.
The basic steps of the algorithm are as follows:
1. Band pass filter is applied. Non-recursive FIR band pass
filter is applied to each channel y
i
:
v
ij
= Σ
k
c
k
y
i-k,j
(10)
Coefficients c
k
are computed outside of the real-time
computations.
2. Cramer-Leadbetter envelope function q
ij
is computed, Fig.3.
3. Peak values of q
ij
are compared with threshold Q.
4. STA/LTA (Allen (1978)) on the envelope function produces
r
ij
. If r
ij
> R, event is detected at time t
i
* for each channel of 8
sensors, Fig.4.
5. Extract portion of signal P
k×3
that includes the first-motion
P-wave from each triaxial record, which corresponds to time
frame t
p
= [t
i
* - ∆t
1
; t
i
* + ∆t
2
].

6. Apply discrete KLT to covariance matrix of P
k×3
:
Σ
ΣΣ
Σ = Cov(P
i
) = QΛ
ΛΛ
ΛQ
T
(11)
Compute normalized variances:
w
i
= Var(Y
i
)= max(Var(Y
i
)) (5)
and decide if polarization ellipsoid is strongly stretched in one
dimension (linear polarization).
7. If q out of 8 sensors show linear polarization and peak
levels on q sensors out of 8 are greater then triggering level,
detected event is confirmed as P-wave.
(a)
(b)
Fig.3 (a) Raw and filtered data, (b) Cramer-Leadbetter
enveloped function for filtered data
Fig.4 Event location with STA/LTA ratio
EEWS SYSTEM CALIBRATION
The records of ambient noise obtained by the sensors of the
EEWS, Fig.5, indicate the presence of two dominant peaks
around 3 Hz and 12 Hz. They seem to originate from the
highway R/C structure excited by the traffic, and thick alluvial
soft soil deposits, which are characteristic for the location of
the early warning system.
(a)
(b)
Fig.5 Normalized PSD of the records of ambient noise
obtained by EEWS sensors: (a) vertical components, (b)
horizontal components
Horizontal axis calibration and system tests were performed
by applying a vertical short-duration force on the free surface,
Fig.6. The 40 J pulse was generated by hitting a metallic plate
with a 20 kg rod at a distance of 6 m from the borehole collar,
which corresponds to magnitude M
L
=-2. In spite of the fact
that the site is contaminated by traffic noise from a highway,
the signal was picked by the bottom geophones at depth ≈40m.
The soil profile at shallow depths is represented by 20 m of
loose sand at the top followed by sandy silt, in both cases
saturated. The signals with frequency around 50 Hz recorded
by the borehole sensors are provided in Fig.7.
Fig.6 In situ free surface P-wave pulse test
Fig.7 P-wave recorded by 3C sensors of the EEWS from
the pulse test
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
Frequency [Hz]
Power Spectral Den sity
4 m depth
40 m depth
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
Frequency [Hz]
Power Spec tral Density
4 m depth
40 m depth

Projections of the polarized P-wave component recorded by
four 3C sensors on the horizontal plane are shown in Fig.8.
The signal picked by the surface sensor exhibits higher
elliptical polarization due to the strong contribution of the
surface waves. The orientation of the sensors in horizontal
plane is computed from polarized components by fitting a
straight line with the equation y=kx using least-squares
method. Coefficient k for each sensor is given in Fig.8.
Fig.8 Horizontal projections of polarized P-wave
component recorded by four 3C sensors of the EEWS from the
pulse test
The ratios of vector lengths of peak amplitudes ||max (a
x,y,z
)||
for sensors at depths ≈4 m, 20 m and 40 m are,
correspondingly, ≈1:6:9, while distance to the source ratios are
≈1:2:4. Higher than 1/R attenuation is partly explained by
reflection of body wave from the interface between sandy clay
and clay at depth ≈15m, and presence of water table close to
this interface.
Knowledge of the sensor horizontal axis orientation allows to
compute the direction of the incoming seismic wave, while its
amplitude can serve as an estimate of the magnitude of the
event and its destruction capacity.
Several multi-channel 3C records available from other
locations were used to test the algorithm and confirm the
applied methodology. Records 1 through 5 contain P-waves
obtained from various sources. Results are summarized in
Table 1, and Figure 9.
Table 1 Test of EEWS algorithm using 3C records
Record
Nr
Nr. of
sensors
f
1
Hz
f
2
Hz
Nr. of
located
events
Nr. of
located P-
wave traces
1 24 100 200 24 14
2 24 100 200 24 15
3 24 100 200 24 12
4 4 100 200 2 2
5 4 4 6 4 3
(a)
(b)
(c)
(d)
(e)
Fig.9 Test multi-channel records: (a,b,c) underground
explosion, (d) calibration pulse test, (e) heavy weight drop test

Several records of the Nisqually earthquake (Feb 2001) were
kindly provided by GSC Pacific. Fig.10 shows time-histories
of the ground motion record from the station KID, and STFT
analysis of these components. These examples demonstrate
presence of higher frequency components in the P phase in
comparison with the S phase. Polarization analysis of P- and
S-phase of the record showed orthogonality of these
components and in-plane polarization of the S-wave. The
algorithm designed for the EEWS was able to identify the P-
wave from this record successfully.
(a)
(b)
Fig.10 Records of Nisqually earthquake provided by GSC
Pasific. Site KID, southern shore of North Fraser Arm: (a)
longitudinal, transversal and vertical components, (b) STFT
analysis of these components
EARTHQUAKE PARAMETERS ESTIMATION USING P-
WAVE COMPONENTS
The following describes the possible expansion of the on-site
EEWS to include earthquake parameters estimation and its
ability to predict the severity of the ground motion.
Least-squares method applied to the arrival time data is a
standard technique for a hypocentral location problem. Adding
additional information -- the azimuth and emersion angle of
the seismic ray coupled with ray-tracing technique -- allows to
calculate more accurately coordinates of the hypocenter,
Alessandrini et al. 1994. These additional parameters are
computed with the polarization analysis, which is part of the
proposed EEWS.
The maximum predominant period of the first 1-4 s of the P-
wave
τ
c
is widely used as a key parameter to estimate the
magnitude of the seismic event (Allen and Kanamori (2003),
Wu and Kanamori (2005)):
τ
c
= 2π/r
1/2
, r = ∫ u″
2
(t)dt / ∫ u
2
(t)dt (6)
where u(t) is the ground-motion displacement. Expression of
τ
c
seems to be an obvious extend of the Parseval’s theorem,
frequency-domain derivation u″=
ω
2
⋅u and an assumption that
P-wave component is a narrow-band signal.
It has been demonstrated that the peak initial displacement
amplitude, P
d
, correlates well with PGV, and its attenuation
functions are provided for southern California by Wu and
Zhao (2006). Such relationship can be used to estimate the
earthquake magnitude.
In order to expand the capabilities of the proposed EEWS the
authors consider expanding the on-site system to a regional
level and incorporating parameters
τ
c
and
P
d
into the existing
algorithm.
CONCLUSIONS
The on-site EEWS for a tunnel on a major highway in British
Columbia, Canada has been presented in the current paper.
The algorithm for detection and discrimination of P-wave is
based on the polarization analysis of band-passed triaxial
record obtained in real-time by geophone sensors installed in
two boreholes. The proposed methodology has been tested
using available data of blast records and strong-motion free-
field records. Proposals for future system expansion include
magnitude estimation and hypocentral location using
parameters
τ
c
and
P
d
.
ACKNOWLEDGEMENTS
The records of strong earthquakes were kindly provided by
Prof.Carlos Ventura, Department of Civil Engineering,
University of British Columbia, and by Dr.Andreas
Rosenberger, Geological Survey of Canada, Pacific
Geoscience Centre. Support provided by BC Ministry of
Transportation is highly appreciated.
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Frequency, Hz
10 20 30 40 50 60 70 80 90
2
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Frequency, Hz
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2
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10
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Frequency, Hz
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