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Tectonophysics 400
Robust and exploratory analysis of active mesoscale tectonic
zones in Japan utilizing the nationwide GPS array
Yuzo ToyaT, Minoru Kasahara
Institute of Seismology and Volcanology, Hokkaido University, N10W8 Sapporo, Hokkaido 060-0810, Japan
Received 5 April 2004; accepted 3 February 2005
Available online 29 March 2005
Abstract
A monitoring GPS array recently developed in Japan can yield nationwide maps of active inland tectonic zones (ATZs) on a
mesoscale, approximately 70 to several hundred kilometers in lateral extent. But it has been difficult to characterize ATZs in
Japan, as they are in fact operational on multiple scales and our efforts are often hindered by various irregularities in the data.
The key to overcoming these problems would be to gain an insight into the available data before any precise kinematic
modeling is performed with indefinite assumptions. In this study, horizontal velocity fields, deduced from the nationwide GPS
array, were treated with a set of techniques in robust smoothing and exploratory data analysis that brought out exceptionally
powerful mesoscale ATZs, and made them easier to characterize. The resolved ATZs were then retrospectively monitored to
study their regional and temporal variations, using a set of approx. 840 observation stations, about 30 km apart, for a 4-year
series of fixed observation time-intervals, 810 days each. The smoothing operation involved three steps: (1) imputation of the
velocity fields for the purpose of anti-aliasing, (2) robust smoothing of the velocity fields with the median operative, and (3)
visualization of deformation-rate distributions in several coordinate independent parameters, and post-filtering. The geometrical
resolvability of mesoscale ATZs was confirmed by calibrating the smoothing scheme against synthetic tectonic boundary
models before it was applied to the case study in Japan. ATZs in Japan, which are essentially visible as systematic deviations in
the velocity fields on the International Terrestrial Reference Frame (ITRF) and as strain rate anomalies, were highlighted sharply
along some known tectonic zones, chains of active volcanoes, and areas above low seismic velocity anomalies in the crust and
upper mantle, all of which generally paralleled the offshore trench axes. The geometrical agreements among the mapped ATZs
and the physical anomalies in the crust are presumably due to their common structural weakness on the mesoscale. In the four
main islands of Japan, all but 30–40% of the strain rate anomalies persisted during the entire 6 years of the case study period,
while the rest sporadically appeared or disappeared in a period from several months to a few years. The transient shifts in the
deformation rates were remarkably synchronous with some nearby major tectonic episodes: large earthquakes and slow events.
Differential plate coupling strengths along the subduction zones can also be inferred from the persistent pattern of rotational
strain rate anomalies forming clockwise and counterclockwise pairs along the Pacific. Our empirical observations suggest that
the first-order features of interseismic crustal deformations in Japan can be characterized as collateral processes behaving in
0040-1951/$ - s
doi:10.1016/j.tec
T CorrespondiE-mail addr
(2005) 27–53
ee front matter D 2005 Elsevier B.V. All rights reserved.
to.2005.02.003
ng author. Tel.: +81 11 706 2643; fax: +81 11 746 7404.
ess: ytoya@eos.hokudai.ac.jp (Y. Toya).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5328
response to fluctuations of the tectonic stresses on multiple scales, likely influenced by changes of plate coupling strengths on
the contiguous subduction faults.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Active tectonic zones; Crustal deformation; Earthquake; GPS; Japan; Strain rate changes
1. Introduction
Tectonic boundaries are complex (e.g., King,
1983) just as much as hierarchically distributed
tectonic blocks (e.g., Turcotte, 1992). Particularly
as Japan is situated at the confluence of several
major tectonic plates (see the insert in Fig. 1, upper-
left), tectonic block segmentation (e.g., Mogi, 1985;
Tada, 1986) might be prevalent in the area. Between
pairs of major tectonic blocks, there are confined
zones of active tectonics up to a few hundred
kilometers wide (McKenzie and Jackson, 1983) that
often host large inland earthquakes (e.g., Jackson et
al., 1997; Sagiya et al., 2000). A good example of
this is the Niigata–Kobe Tectonic Line (NKTL), a
zone of concentrated deformation that was recently
identified using the nationwide GPS array in Japan
(Sagiya et al., 2000). Still, the geometrical resolution
of the suggested zone is indeterminate, and the
nature of development or the temporal variation of
deformation rates on such zones remains to be
explored. Elucidating the geometry and the charac-
teristics of deformation along dactive tectonic zonesT(Wallace, 1986) would help improve not only the
design of the monitoring GPS networks, but also
tectonic models (e.g., a block-and-fault model,
Hashimoto and Jackson, 1993) hence the under-
standing of crustal surface deformations associated
with both intra- and inter-plate tectonics.
The investigation of full-range tectonic processes is
very challenging, despite the recent realization of
nationwide continuous GPS monitoring for crustal
deformation in Japan. The behavior of the crustal
surface is influenced by various scale sources (in
space, time, and magnitude): intra- and inter-plate
interactions (e.g., Whittaker et al., 1992; Wang and
Suyehiro, 1999; Dragert et al., 2001), readjustments of
the crust near large seismic events (e.g., Heki et al.,
1997; Pollitz et al., 1998; Segall et al., 2000), tides
(e.g., Hatanaka et al., 2001; Kasahara, 2002), volcanic
and geothermal activity (e.g., Mogi, 1958), etc.
Arranging the monitoring GPS network in a hier-
archical manner preferentially along active tectonic
zones might be ideal, but it is impractical; most active
tectonic zones have yet to be fully characterized.
In addition, local or short-term details of crustal
surface deformations are often obscured by the
intricate physical makeup and local processes along
active tectonic zones, e.g., by transrotational shearing
(e.g., Kanaori et al., 1992; Dickinson, 1997) and by
various transient events that do not directly reflect
gradual and regional plate tectonics (Nur et al., 1989).
Measurement errors in our data are also troublesome
(e.g., Kato et al., 1998; Hatanaka et al., 2003).
A practical approach to analyzing complex crustal
deformation would be to focus on crustal deformation
on one particular scale range at a time, with the
premise that crustal deformation is a scale dependent
phenomenon that might be seen to be operating in a
more or less tangible unit of scale range. Such an
approach would allow a comparison of the dynamics
of a dlevel (scale range)T of our interest with that of theimmediate higher and lower levels in the presumable
nearly decomposable hierarchies of crustal structures
and processes (cf., Hierarchy Theory; e.g., Simon,
1962; Sollins et al. (1983) in O’Neill, 1988).
Here we are searching for inland tectonic zones in
Japan that can be seen to be active on the mesoscale in
the intermediate-term, and stretching the bounds of
possibility to observe them at the maximum attainable
resolution from the present nationwide GPS array.
dMesoscaleT in this study refers to a dimensionapproximately twice the local mean GPS station
separation distance and greater (approx. 70 to hundred
kilometers). Systematic shifts in the ITRF velocity
fields and two-dimensional instantaneous strain rate
anomalies are regarded as active tectonic zones
(ATZs) in this study. A set of robust and exploratory
analyses of the continuous GPS array enables us to
accommodate various irregularities in the data, to
identify the sharp geometry of ATZs on the mesoscale
nationwide, and to help decompose the multiscale
(b) Deceleration of upheaval(b) Deceleration of upheaval at Sakurajima V at Sakurajima Volcanoolcano
-202
W E
W E
W E
Station ID 960719Station ID 960719Station ID 960719
0
S N
S N
S N
0 200200200 400400400 600600600 800800800-2-2-202
D U
D U
D U
Time (days)ime (days)Time (days)
(cm)(cm)(cm)
-2-2-2
2
(Linear trend removed)(Linear trend removed)(Linear trend removed)w.r.r.t. WGS84.t. WGS84w.r.t. WGS84
Usu VUsu Volcanoolcano Mar Mar.2000 eruption.2000 eruption
Miyakejima VMiyakejima Volcanoolcano Jun.2000 eruption Jun.2000 eruption
(a) Ongoing T(a) Ongoing Tokai-Kanto okai-Kanto Slow Event Slow Event
PA
NANA/OH/OH
EU/AREU/AR
PHPH
Reference StationReference StationStations with MAD > MAD limitStations with MAD > MAD limit
3333oN
3030oN
128128oE 132132oE
3232oN
30'30'
3131oN
130130oE 131131oE
3232oN
131131oE
Fig. 1. Deformation velocity and acceleration fields (Example: 1998/7/18–2000/10/5). (a) Ongoing trend of Tokai-Kanto slow event. (b)
Deceleration of an upheaval at the Sakurajima Volcano. The upper-left insert shows major/micro tectonic plates: Eurasia (EU)/Amur (AR),
North American (NA)/Ohotsk (OH), Pacific (PA), and Philippine Sea (PH) plates.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 29
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5330
intermediate-term processes, each of which may be
individually related to a governing tectonic process.
2. Method
Careful data quality analysis of GPS array (station
position data) in time and space makes possible the
refinement of deformation field data on the target
observational scale ranges: intermediate-term (~sev-
eral months to several years) and mesoscale, respec-
tively. Together it is important to realize that the
observable scale ranges of crustal deformation by the
existing GPS array are limited by the Nyquist
sampling criteria at the lower ends (twice a unit
sampling rate in time, provided that no higher
frequency periodic signals are present in the data,
and twice the local maximum station separation
distance, given no higher frequency undulation of
the deformation fields), and by the maximum ranges
of the data at the higher ends (the entire duration of
the case study period, and the whole length or width
of the Japan archipelago). In the same way, the
observation station arrangement plays a crucial role in
defining the local geometrical resolvability of ATZs
by the existing GPS array, given no high frequency
undulation of the deformation fields.
A temporal data quality analysis is performed at
first, to eliminate short-term noise, such as impulse
noise, additive seasonal variations and prominent
transient event noise, essentially to supply only
intermediate-term deformation rate signals to the
subsequent spatial data analysis. The deformation
fields as deduced from the intermediate-term signals
are then refined to reveal only mesoscale signals by
the application of robust smoothing and exploratory
spatial data analysis. The keys here are to recognize
the hidden structures and the exact type(s) of noise
present in the deformation field data and to apply a
suitable set of methods in handling them. As a
result of the temporal and spatial data quality
analyses, a reasonably uniform measure of deforma-
tion rates is achieved nationwide on the target scale
ranges. Using such a uniform measure of deforma-
tion rates nationwide, the continuous monitoring of
deformation rate changes, and the identification/
characterization of ATZs become feasible; they help
reveal where or which of the known tectonic (or
seismic) zones might be currently dactiveT on themesoscale.
2.1. Data
The nationwide permanent GPS network, the GPS
Earth Observation NETwork (GEONET), has been
operated by the Geographical Survey Institute of
Japan (GSI) since 1993 (Tada et al., 1997). Approx-
imately 6 years of continuous GPS station position
data on the ITRF97 (1997/6/25–2003/9/25 (UT)) were
obtained from the GSI web-site (http://www.gsi.
go.jp). The database was recently updated upon
significant reduction in systematic errors and
improvement in the database homogeneity as a whole
(Hatanaka, 2003; Hatanaka et al., 2003). Still, system-
atic errors (notably seasonal variations) exist in the
data, and their mechanisms are not entirely under-
stood. For example, regional-scale seasonal variations
in the data are known to be well correlated with the
seasonality of large subduction earthquakes near
Japan (Murakami and Miyazaki, 2001), the snow
loading cycle (Heki, 2001), etc., whereas the ampli-
tudes of such signals are commensurate with those of
baseline measurement errors in the array (Hatanaka,
2003). Sudden elastic strain signals are also trouble-
some in a study of interseismic deformation (e.g.,
Jackson et al., 1997). In view of the above concerns,
we attempted to eliminate prominent seasonal and
short-term noise from the data. The culled data sets
(presumably free of systematic errors and noise) are
then applied in the mapping of active tectonic zones.
2.2. Temporal data quality analyses
2.2.1. Removal of seasonal variations in temporal data
First, continuous daily recordings of horizontal
station positions are selected based on the criteria
listed in Table 1, and filtered with a five-point moving
median to reduce impulse noise in the time series. The
time series are then treated for removal of additive
seasonal variations. To do this, each time series is
carefully modeled with an equation consisting of three
terms: seasonality (annual and semiannual compo-
nents (e.g., Heki et al., 1997; Sagiya et al., 2000)),
drift (a second-order polynomial), a sudden disturb-
ance or an offset at time ts (a Heaviside function),
besides the residuals. The timing of offset ts is
http://www.gsi.go.jp
Table 1
Criteria for selecting continuous data
1. Data sets (stations) must belong to the permanent observation
network. No temporary campaign data are included.
2. Duration of data at a station must be longer than 2 years, in
order to estimate realistic or accurate seasonal patterns. For
this particular study, sampling time interval (dSWINT) is fixedfor 810 days (cf., Section 2.2.2).
3. The total number of observation days (dTNODT) in a dailystation position data set must be larger than 0.75 SWIN. If either
the data set for the East–West or North–South component of
horizontal deformation rates at a station does not meet this
criterion, the data for the station are not used for further
analyses.
4. There must be more than 2/9 TNOD for each successive SWIN/3
interval. Those unavoidable temporal gaps in the records are
linearly interpolated. This criterion together with the dMAD-limit(introduced in Section 2.2.2)T was effective in most cases to selectgenerally continuous data sets.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 31
simultaneously determined while minimizing the
least-squares error to the model, by sliding ts along
the time-axis (with 1% increment of the whole
duration to reduce the computation time). When the
optimal fit is found, only the seasonal components are
subtracted from the filtered original time-series.
The second-order polynomial is considered for the
drift component of the aforementioned least squares
fitting (instead of a frequently used linear model). It is
employed to account for the effects from sizable
intermediate-term deformation rate changes, such as
ones observed near the Sakurajima Volcano and the
ongoing Tokai-Kanto slow event (e.g., ddeformationaccelerationsT, Fig. 1). At the same time, a Heavisidefunction is introduced in the model to help prevent the
creation of artificial sinusoids at a large sudden offset
in the data. However, the Heaviside function alone is
not sufficient to model various types of transient
events. Therefore, short-term irregularities, inclusive
of earthquake related displacements, are handled in a
different manner.
2.2.2. Systematic removal of short-term irregularities
Next, prominent short-term irregularities are sys-
tematically identified and removed. A dvelocityTestimate of crustal deformation is a practical expres-
sion for the mean deformation-rate for a given
observation period, or a linear fit to an observed time
series. Similarly, the second derivative of a second-
order polynomial fit to the time series can be regarded
as an daccelerationT of a possible nonlinear process fora well-modeled duration. Both approximations lack fit
when large noise or transient signals are present in the
data. Accordingly, the significance of irregularities is
evaluated based on the goodness of fit measures of
our approximations to the data.
The mean absolute deviation (MAD) is used to
measure the departure of observations from a poly-
nomial model, per component. MAD=(A|ri�r*|)/n,where ri is the residual displacement at time i (i=1, 2,
3, . . . , n), and r* is the sample median of the residualsafter the seasonality removal. The 96th percentile
(approximate upper limit of the bnormal rangeQ) of thegood-fit MAD population for the case study data was
selected as the MAD-limit: 0.25 cm for the velocities
(Fig. 2a) and 0.2 cm for the accelerations. A MAD
limit was defined so as to select only those data sets
(or stations) that fit well with our models. Those
stations with outlying MAD values above the limit
were found clustered around concurrent transient
events such as earthquakes and volcanic eruptions.
The rejected stations above the limit are marked with
square-and-cross symbols in the velocity field map,
e.g., Fig. 1. Also, the observational time-interval is
kept unchanged for the case studies to keep the
measure of irregularities unbiased (810 days each [cf.,
Table 1]). The longer the observation period, the less
significant a transient event appears.
The behavior of deformation-rate parameters:
velocity and acceleration, at a transient event was
evaluated using synthetic time series (e.g., Fig. 2b–e).
As the models demonstrated, the MAD limit, e.g., for
velocities (Fig. 2b, c, and e), worked effectively in
suppressing the maximum step height of elastic
signals (or its equivalent) in our data at ~1 cm per
component, inclusive of the residual error amplitudes
after the median filtering of the original time series.
The models also suggested that some slow events
could still be hidden in our data (Fig. 2e). A
comparison of the spatial distributions of MAD
between a linear model (a velocity field) and a
nonlinear model (e.g., an acceleration field) would
alternatively help locate such slow events, with
preferred nonlinear fits. Although it was almost
outside our case study period, the Bungo Channel
slow event (Hirose et al., 1999) could be identified in
this manner with a longer sampling time-window.
Nevertheless, we handle the effects from slow events
Synthetic ModelsCase Study Data
0 0.2 >0.4
MAD-limit for velocity = 0.25
Fre
q. (
NS
)
Fre
q. (
EW
)
MAD
poor fit
good fit
poor fit
good fit
App
aren
t v
eloc
ity
(
cm/y
r)
Ste
p h
eigh
t (
cm)
App
aren
t a
ccel
erat
ion
(cm
/yr
)2
Maximum
Duration of event (DE=various)
Sampling time-interval (SWIN=810days)
Time
(b)
(c)
(d)
Ste
p he
ight
(cm
)
Duration of event (days)200 400 600 800
1
2
3
4
5
Maximum apparent velocity (cm/yr) Corresponding maximum MAD (cm)
3
2
1
1
0.8
0.6
0.4
0.2
0.25
MAD limit
(e)
TP
(a)
Fig. 2. bLeftN (a) Histograms of MADs concerning the horizontal velocity estimates (East–West and North–South components) using the case
study data. Data with MADs greater than the MAD-limit (0.25 cm for velocities; cf., Section 2.2.2) are removed from the analysis. bRightN
Behavior of deformation rate parameters at transient events on synthetic time series. (b) Synthetic displacement records of hypothetical transient
events with a given offset-height and various durations (three time series, overlaid). (c) Corresponding apparent velocity responses around the
hypothetical transient events shown in (b). (d) Apparent acceleration responses around the hypothetical transient events shown in (b). A time
series record would be disturbed by a transient event for a duration dTPT=dSWINT+dDET, where dSWINT stands for the fixed sampling time-interval and dDET stands for the duration of a transient (slow) event. (e) A summary graph showing the maximum apparent velocities and thecorresponding maximum mean absolute deviations (MAD) (shown in contours) of synthetic time series as shown in (b). All models are
evaluated using a fixed size sampling time-interval, 810 days each.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5332
and other subduction-related phenomena differently in
this study (discussed in Sections 2.3.3 and 2.3.4).
2.3. Spatial data analyses
Once the data become largely free of prominent
short-term noise, the focus is shifted to the inves-
Fig. 3. (a) Median, several EDA tools, and outliers. Outlier can be visu
histogram of absolute velocity vector lengths, for example (left figure). This
dextreme outlierT, which is greater than 3 IQR from the 75th percentileSchematic illustrations of the flow of robust smoothing process, using a de
the upper row of the illustrations, shown are the three steps of the smoothi
bStep IIN regularization of the observation grid and median filtering,
independent parameters, and post-filtering. Velocity fields are depicted in
dHNODCT indicates a nested imputation operation, described in the texoperation are: the minimum surface area, the maximum length of the si
sampling-window radius vs. nodal-point density after the imputation oper
point density is generally uniform when the sampling-window radius R is a
range of F1 sigma around an estimated point density for a given R. A mapplot the graph on the left. The reason for the preferred uniform point densit
separated by a distance of about 30 km and that they are anchored durin
robust smoothing scheme and a fixed-point smoothing operation (moving m
the true parameter distribution (a sine curve). Given specific ranges of (orig
the introduced scheme can provide a nearly even overall measure of
underestimate parameter values at local maxima and minima. (e) The ITR
Japan; cf., Fig. 4a) for 1998/7/18–2000/10/5. The original velocity field (bl
for comparison. Microscale irregularities of the original velocity field were
marked by a square symbol, and the areas labeled dAT (sketched in shade
tigation of spatial characteristics of the intermediate-
term deformation fields. The temporal data quality
analysis discussed in the previous section helped
identify and remove short-term noise, whereas some
spatial noise still remained in the data (e.g., Fig. 3a).
Through the application of robust smoothing and
exploratory data analysis (EDA), various properties of
ally identified in the ITRF velocity field (right figure), and in the
particular example of spatial impulse noise in the velocity field is an
line in the histogram. IQR stands for the interquartile range. (b)
formation field example with a narrow simple shear boundary. From
ng process: bStep IN imputation of the vector field for anti-aliasing,
and bStep IIIN representation of deformation rates in coordinate
map views and in profiles. The illustrations are not drawn to scale.
t (Section 2.3.2). Specific constraints applied during the HNODC
des and the proportion of the imputation triangles. (c) A graph of
ation (cf., Step I, b). The graph on the left illustrates that the nodal-
bout 35 km for the case study data. A vertical error bar indicates the
of Japan with circles on the right shows the sampling areas used to
y around R=35 km is likely that the original observation stations are
g the imputation operation. (d) Comparison between the introduced
edian) using simple one-dimensional models. The top graph shows
inal) observation station separation distances and signal wavelengths,
the target parameter distribution. However, our scheme tends to
F velocity fields from a small region in the case study area (central
ack arrows) and the smoothed velocity field (grey arrows) are shown
efficiently filtered out. (The location of the Matsushiro swarm area is
) indicate the general locations of tectonic boundaries.)
R
RAOutlierFreq.
25th percentile
Median
75th percentile
IQR*
>1.5 IQRaway fromthe 75th pct.
"Outliers"~ Upper hinge
~ Lower hinge
Histogram
Boxplot
Hinges
e.g.) Absolute vector length
R = Rigid blockA = Tectonic boundary
ED
A to
ols
(* IQR = Interquartile range)ITRF velocity field
Impulse noise
=
ATZ ATZHNODC
Step I: Imputation of the vector field for anti-aliasing
Step II: Regularization of the grid and 2-D median filtering
Step III: Representation of deformation rates in coordinate independent parameters, and post-filtering
Query point
Vel
ocity
fiel
dV
eloc
ity p
rofil
eV
eloc
ity fi
eld
Vel
ocity
pro
file
Vel
ocity
fiel
d
Hexagonal grid for pseudo strain rate calculation
Triangular grid from Step II, used for CMD and VLMD estimation
‘Impulse noise’
‘Edge’
y = MEDIAN ( x1...n
)A
Filter window, and CMD or VLMD estimation window
x1
x2 xn
x3
(The minimum grid spacing is reflected in thecoordinate independent parameter statistics.)
A
(a)
(b)
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 33
0100km
R = 35 kmR = 80 km
R = 35 km
20 40 60 800.02
0.03
0.04
0.05
0.06
Radius of sampling (km)
Den
sity
of p
oint
s (k
m-2
)
Map distance
Fixed-point operation
Introduced scheme
Par
am.
valu
eP
aram
. va
lue
Par
am.
valu
e True param. variation
Original GPS stations
Imputed station positions
Predicted trend
Velocities on original GPS stations
Smoothed velocity field on a triangular grid
Station 970816 w.r.t. WGS84Station 970816 w.r.t. WGS84(JUL18, 1998 ~ OCT5, 2000(JUL18, 1998 ~ OCT5, 2000
0 400400 800800Time (days)Time (days)
4
2
0
0
-5-5
-10-10
20
-2-2-4-4
5
3
MU
D (
cm)
UD
(cm
)N
S (
cm)
NS
(cm
)E
W (
cm)
EW
(cm
) Vel.= 2 cm/yrMAD = 0.1 cm
Vel.= -4 cm/yrMAD = 0.2 cm
Vel.= -1 cm/yrMAD = 0.4 cm
EQs within 50 km of the station
Spatial impulse noiseSpatial impulse noisewith clean temporal datawith clean temporal data
(c)
(d)
(e) A
Fig. 3 (continued).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5334
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 35
the deformation fields become increasingly clear. Our
data generally appear to hold the following structures
within them: dDataT=dsmooth background (brigidQtectonic blocks)T+dmesoscale edges (active tectoniczones)T+dmicroscale or impulse noises (disturbedstations, isolated tectonic features and measurement
errors)T.EDA is an approach or philosophy of how to
examine the data rather than a set of analysis
techniques (NIST, 2002). The essence of EDA can
be perceived by contrasting it to classical data
analysis. In a classical (or confirmatory) data analysis,
a researcher would first select a deterministic or
probabilistic model, which consists of a set of
assumptions for a given data set. Some quantitative
expressions for the assumed model are then calcu-
lated, ultimately to develop a hypothesis about the
data (but strictly based on the model). Accordingly,
choosing a bgoodQ set of assumptions or a ’model’ isvital for an accurate interpretation of the data. EDA,
on the other hand, focuses on ddataT properties first,and looks for hidden data structures by utilizing
synoptical tools such as scatter plots, histograms, box-
plots, or any other graphical aid that might help
visualize important features in data that might other-
wise be missed out in a simplified deterministic model
of a classical data analysis. As a result of EDA, a
feasible model may be suggested by the data (NIST,
2002). The main aim of a data analysis is to
understand the given data, and the precision of an
analysis result only has true significance when it is
also accurate (Tukey, 1977).
2.3.1. Robust and exploratory spatial data analyses
Intermediate-term velocity fields in Japan are
generally homogeneous and highly directional, except
near active tectonic zones and scattered impulse noise.
At least this is a data structure that can be immediately
recognized in the ITRF velocity fields (e.g., Fig. 3a).
The velocity fields on a geocentric reference frame are
unique in the sense that they are free of the additional
and extraneous ambiguities of locally selected refer-
ence station(s). If there were no local crustal move-
ments, the mesoscale velocity fields would appear
dflatT (at least locally) and all vectors would have anearly equal length pointing in the same direction (or
all zero vectors). For example, a test for uniformity
(against a unimodal alternative of directional data;
Mardia and Jupp, 2000) could be applied to report the
highly concentrated nature of the velocity vector
azimuths. The more concentrated the vector azimuths
concerning a certain mean preferred orientation, the
more rigid a local tectonic block would be, provided
all vectors were non-zeros and had equal lengths. In
order to describe the detailed tectonic features at our
target scale of observation, however, it is not feasible
to use such classical statistical analyses. The data sets
were too sparse for the majority of our study area.
Here instead, robust smoothing and EDA are per-
formed to delineate mesoscale anomalies in the
velocity fields, with added assumptions about the
homogeneity, continuity, and the highly directional
nature of micro- to meso-scale velocity fields. Like-
wise, the mesoscale velocity fields are smoothed with
the median operative as described below.
2.3.2. Robust smoothing of the velocity fields
The median is the 50th percentile of ordered
sample statistics. It gives a more robust estimate of
central location (in statistics) than the sample mean,
and is resistant to extreme values or doutliersT(Barnett and Lewis, 1984) in data. A drobustTestimator would be insensitive to deviations from
assumptions about a given probabilistic model or
distribution (Huber, 1979). Meanwhile, our data (the
velocity fields) did occasionally contain outliers
(e.g., Fig. 3a). dAccommodationT but not manualremoval of such outliers is preferred (Barnett and
Lewis, 1984) where it is practicable. In order to
reduce (microscale) impulse noise but to preserve
(mesoscale) edges in an image (the deformation
fields), the use of a linear shift-varying filter (e.g.,
Kalman filter) or a nonlinear filter (e.g., median
filter) is a necessity (Huang, 1981). (This is because
signals in two-dimensional images are always
positive quantities and do not follow the dnormalstatisticsT (Frieden, 1979).) Therefore, taking fulladvantage of the median’s resistant attribute, the
velocity fields are smoothed in three steps: (I)
median imputation (filling in for missing values),
an anti-aliasing measure for the subsequent filtering
operations, (II) drobust smoothingT (Huber, 1979) bymedian filtering, and (III) visualization of the
deformation fields in several alternative and conven-
tional forms of coordinate independent parameters,
and post-filtering. Fig. 3b illustrates the overall flow
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5336
of the smoothing process. Most dmicroscale noisesTare polished away in steps (II) and (III), while
dmesoscale edgesT are embossed in the dsmoothbackgroundT.
In step (I), the velocity fields with microscale voids
are filled in by a nested median imputation scheme,
illustrated in the upper row of Fig. 3b. The scheme
may be described as a hierarchical neighborhood
operation with the median operative applied over
constrained Delaunay triangles where the centroid of
each triangle is the query point to be filled in
(HNODC). The goal of this operation is to completely
fill the case study area with nodal points as uniformly
as possible (Fig. 3c), as an anti-aliasing measure for
the subsequent smoothing operations. The triangles’
proportions and surface areas are constrained to
induce repulsion among the nodal points. Repulsion
of these points makes their distribution much more
regular than otherwise (Okabe et al., 1992). At the
same time, the sample median vector-components in
the dmarginal orderingT (Barnett, 1976) of thebivariate samples (generally independent x- and y-
vector components) from its vertices are assigned to
the query point at each triangle center. This median
vector calculation, provisionally selected for its
simplicity, gives reasonable median vector estimates,
when the circular mean deviation of the sample vector
azimuths is smaller than 458, i.e., when they aresamples from a highly directional velocity field. Some
of the locally disturbed stations are also separated out
in the process.
In step (II), two-dimensional median filtering,
robust smoothing is applied on the imputed velocity
fields from step (I). This operation is effective not
only to remove impulse noise (isolated microscale
irregularities) but also to preserve the sharp edges of
the robust signals in the velocity fields (active
mesoscale tectonic zones). Justusson (1981) issued a
detailed discussion on the statistical properties of a
median filter. The sampling grid is simultaneously
regularized in a triangular grid (dStep IIT in Fig. 3b).Each new grid node is assigned with a set of the
sample medians in the marginal ordering of x- and y-
velocity vector components: Vuv=MEDIAN [BuC],B={the nodal points in the study area from step (I)},
and C={N nodal points inside a circular sampling
window radius (SWR) of 35 km}. (The word
bsampleQ is used to mean ’batch’ hereafter, since the
observations of data after step (I) are no longer
statistically independent.) As a result, the isolated
noise with a surface area smaller than half of the
sampling window (pSWR2)/2 km2 is removed. (Theedge values within an SWR from the perimeter of the
study area are slightly extrapolated outward to abate
probable edge effects.) More precisely, a new value on
the regularized grid represents the majority (or NN/2)
of the member in set C (of N nodal point values).
However, the local nearest-neighbor distances
among the original GPS stations (LNND) enclosing
an imputation triangle varied regionally from 3.8 to 70
km in our data. The Hokkaido region was particularly
thin as for station coverage, so the LNND values were
generally large. The frequency distribution of the
LNND for the whole study area is unimodal,
positively skewed and has the median and the third
quartile of 25 km and 33 km, respectively. The
problem of irregular station coverage was tolerably
overcome by the anti-aliasing treatment of the velocity
fields performed in step (I). After the robust smooth-
ing in step (II), the nationwide distribution of
deformation rates was uniformly rendered at a
resolution close to the maximum attainable from the
existing GPS array (e.g., Fig. 3d). Visual inspections
of the actual velocity fields suggested that selecting
the SWR of 35 km was reasonable for signals in our
study area, as would be reevaluated later in a
confirmatory study (Section 2.3.4). The results, e.g.,
Fig. 3e, suffice for our exploratory objective.
The median operations would leave a plateau
where spatial parameter distributions were nearly
constant. Such a plateau defines the extent of a drigidTtectonic block, and its sharp edges portray active
tectonic zones. Along a wide active tectonic zone
(N2SWR), the terracing of parameter variations,
byproducts of the median operations, is anticipated.
Still, the byproducts would have dimensions inher-
ently smaller than 1 SWR and larger than the
minimum size of the sampling grid-distance defined
in step (II). So, now the idea is to filter out those
artefacts in that range.
In step (III), the smoothed velocity fields from step
(II) are first transformed into several coordinate
independent parameters. Then, additional median
filtering with the same-size smoothing window as in
step (II) is applied on each spatial parameter
distribution to remove the artefacts from the previous
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 37
step. Changing the shape of a filtering window (e.g.,
circular or rectangular) or of the sampling grid (e.g.,
triangular or square) did not substantially change the
final case study results. The robust signals were
coherent regardless.
2.3.3. Systematic identification of active tectonic
zones
Anomalies in the spatial distribution of deforma-
tion rates were expected in two general conditions: (i)
proximity to disturbed stations and isolated micro-
scale irregularities, and (ii) proximity to active
tectonic zones. The condition (i) was easily noticed
as impulses or scattered noises in the fields, when it
did not coincide with the condition (ii). The noise (or
outliers) in condition (i) was efficiently removed (or
daccommodatedT; Barnett and Lewis, 1984) by therobust smoothing. Conversely, the condition (ii) was
made prominent partly by mapping the spatial
distribution of circular median deviation (CMD) for
the smoothed ITRF velocity fields. CMD=MEDIAN
(|p�|p�|hj�h*|||), where hj is the jth vector azimuth( j=1, 2, 3, . . . , n) in a sample from the smoothingwindow of step (III), h* is the sample median, and theoperands (inside the parenthesis) are the ordered
statistics of the minimum angular distances between
the median and sampled vector azimuths (p. 19,
Mardia and Jupp, 2000). Also, another useful param-
eter was the vector-length median absolute deviation
(VLMD) for the same velocity fields. VLMD=ME-
DIAN (|Lk�L*|), where Lk is the kth vector length(k=1, 2, 3, . . . , n) in a sample from the smoothingwindow of step (III) and L* is the sample median.
CMD and VLMD are median deviations of the
principal velocity vector components: azimuths and
lengths. Both CMD and VLMD discussed here are
specific to the ITRF velocity fields and are independ-
ent of the orientation of the geographical coordinates.
A comparison between CMD or VLMD distributions
with the original velocity fields help us realize that the
apparent bdeviationsQ do in fact represent dsystematicshiftsT in the velocity fields, or mesoscale structuralboundaries. Fig. 4 shows their spatial distributions.
The histograms on the color-scale bars in Figs. 4a
and b represent the frequency distributions of CMD
and VLMD for the whole case study area. The
overall shape of the frequency distributions is
apparently dabsolutely outlier-proneT (Green, 1976).
We realize, however, that despite the continuous
appearance of the overall frequency distribution,
there must be a nonrandom data structure within it;
the geographical regions corresponding to the pop-
ulations near the lower end of the overall frequency
distribution should represent originally claimed
drigidT tectonic blocks (R), and the other geograph-ical regions corresponding to the populations with
longer tails under the overall frequency distribution
should portray active tectonic zones (A). A perfectly
drigidT tectonic block (R) and an active tectonic zone(A) are theoretically ddisjoint.T Accordingly, theoverall frequency distribution might be interpreted
as a dcontaminated distributionT (Barnett and Lewis,1984): cja(1�k) R+kA that observations cj ofdeformation rate in a sample ( j=1,2, . . . ,n) wouldarise from a mixture of R and A , where
0bkb1(k=contamination fraction), dRT=the popula-tion for all drigidT tectonic blocks, dAT=the contam-inants or the populations of active mesoscale tectonic
zones.
Nonetheless, the active tectonic zone signals (A) in
the actual field data might include both signals: ones
that originate from inland tectonic processes and ones
that are directly from contiguous subduction zone
processes with some overlaps in between. They are
practically inseparable; they have very similar wave-
lengths, except that the latter would be noticeable
along the Pacific coast in Japan. Particularly, the
geometry of mapped active tectonic zones with
parameter values above the 75th percentile of their
frequency distribution or the dupper hingeT (Tukey,1977) coincides well with some known tectonic
features in the study area (Fig. 4). Accordingly,
deformation rate anomalies with parameter values
above the upper hinge are specifically referred as
dATZsT thereafter. The background map in Fig. 4cillustrates a percentile summary of CMD and VLMD
distributions, named dMD2T, highlighting the geo-graphical areas with CMD or VLMD parameter
values greater than their 75th percentiles. In that the
mesoscale anomalies were very powerful and con-
centrated in confined areas, slightly shifting the center
of the color-scale (either hue or value of the color) in
Fig. 4 did not significantly change the overall
appearance of the resolved ATZ distribution.
CMD and VLMD distributions (or MD2) hint at
the locations of ATZs. Now, two-dimensional instan-
Fig. 4. Maps of (a) circular median deviation (CMD) and (b) vector-length median deviation (VLMD) of the ITRF velocity fields in Japan.
Parameter values depicted in the maps are the means of the two 810-day periods before and after the 2000 W. Tottori earthquake. The histogram
and box-plot for each parameter are shown on the corresponding color-scale bar. The base of an arrow pointing to the right on the color scale
indicates the upper-hinge value for the given parameter. A diamond-shaped box over the CMD map indicates the region of the velocity field
shown in Fig. 3e. (c) Tectonic map of Japan, over a map of MD2 or a percentile summary of the CMD and VLMD distributions (cf., Section
2.3.3). Symbols denote active volcanoes (in red triangles), Setouchi Inland Sea (in black cross stripes), and the major tectonic zones (in solid and
dashed lines), which include: the Kuril Trench (KT), the Japan Trench (JT), the Sagami Trough (SaT), the Suruga Trench (SuT), the Nankai
Trough (NT), the Median Tectonic Line (MTL), the Tsuruga Bay–Ise Bay Tectonic Line (TITL), the Itoigawa–Shizuoka Tectonic Line (ISTL),
the Honjo–Matsushima Tectonic Line (HMTL) (Tada, 1986), the Niigata–Kobe Tectonic Line (NKTL) (Sagiya et al., 2000) in grey shade, and
the Oga–Ojika Seismic Zone (OSZ) (Mogi, 1985).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5338
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 39
taneous strain rates are mapped to resolve the
characteristics of intermediate-term deformations
along individual ATZs. The smoothed velocity fields
from step (II) are spatially differentiated to give
coordinate independent strain rates: dilatation, max-
imum-shear, and rotation (Terada and Miyabe, 1929;
Tsuboi, 1930). All of these strain and rotation rate
distributions together describe the trend of small
strains associated with an individual ATZ. Their
absolute quantities, however, are inexact (often under-
estimated, cf., Fig. 3d) along ATZs and thus they are
named dpseudo strain ratesT.
2.3.4. Evaluation of the geometrical resolution of
ATZs
Before applying the introduced ATZ-mapping tool
to the actual field data, its geometrical resolvability is
confirmed by calibrating it against synthetic tectonic
boundary models: (a) simple-shear and (b) pure-shear
(or a pair of irrotational zones) models, e.g., Fig. 5.
No dilatational strain is expected along a simple-shear
boundary, and no rotation is expected along an
irrotational zone. The color-scales of pseudo strain
Fig. 5. Calibration of the introduced ATZ-mapping tool against synthetic tec
pure-shear (a pair of irrotational boundaries) model. Dilatation (D)=(Bu(R)=[(Bu/Bx�Bv/By)2+(Bu/By+Bv/Bx)2)]0.5. No dilatational strain is expecan irrotational boundary. Three types of errors are shown as examples: a de
On the right, two calibration test results for our study area are shown usin
rate maps are set so as to satisfy the above require-
ments in several synthetic models, and to highlight the
mapped areas with absolute parameter values above
the upper hinge of their frequency distributions using
the case study data (cf., Fig. 4). Long-wavelength
deformation signals and some small measurement
errors (after step (II)) are suppressed below the upper
hinge limit. In that most ATZ anomalies were power-
ful on the mesoscale, the general appearance of the
resultant maps was not substantially changed by the
slight tuning of the color scale around the upper hinge
in the case study data.
It is possible to tune the overall intensity of the
ATZ signals. For instance, a large proportion of the
gap error, dGT in Fig. 5b, is avoided by adjusting themean nodal point density in step (I) (cf., Figs. 3b and
c), and the sampling grid spacing in step (II). In any
case, deflection errors, dLT in Fig. 5b, however, areinevitable within F1 SWR. Also, the widths of theATZs are adequately resolved when they are greater
than 2 SWR, and evenly recovered when they are
greater than twice the maximum LNND in our study
area. Testing the mapping tool against multiple
tonic boundary models: (a) wide simple-shear model and (b) narrow
/Bx+Bv/By). Rotation (x)=0.5*(Bu/By�Bv/Bx). Maximum shearted along a simple-shear boundary, and no rotation is expected along
flection error (L), a gap error or a loss of detail (G), and noises (NO).
g the models of types (a) and (b).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5340
synthetic models such as those shown in Fig. 5 helps
confirm that any powerful wide ATZs (N2 SWR) and
non-clustered and non-oscillating narrow ATZs (b2
SWR) are tolerably recovered by the introduced
scheme from the present GPS array. Visual inspec-
tions of the actual velocity fields in our study area
suggested that the deformation rate anomalies were
neither critically clustered nor oscillating at scales
immediately below the mesoscale.
The introduced scheme has an advantage over
other fixed-point smoothing operations, e.g., a mov-
ing median without anti-aliasing treatment on the data.
Our method is more efficient than the others
mentioned in illustrating the spatial parameter varia-
tions evenly over the irregularly distributed observa-
tion stations in our study area. This property is
Fig. 6. Comparison between the dilatational strain rate distribution maps o
method employed in Sagiya et al. (2000) (c, d, and e). (a) Dilatational p
geometrical resolvability test on irrotational boundaries (cf., Section 2.3.4)
rate map of Japan, from Sagiya et al., 2000 (reproduced, with permission, f
(c) using the least-squares inversion method on the data for 1997/1/1–1999
data quality analysis (cf., Section 2.2). dST-limitT or standard deviation limirregularities. The ST-limit is set to 0.33 cm (=1.3�0.25 cm) considering2003) and that the MAD-limit for velocities is set to 0.25 cm for the case st
test on irrotational boundaries (Section 2.3.4) using the least-squares invers
observational errors (Eq. (3), p. 2309, Sagiya et al., 2000) in the synthetic
on the actual field data property. Dots on the maps denote GEONET stati
demonstrated in a set of simplified one-dimensional
models, shown in Fig. 3d. Let us suppose that the
upper graph in Fig. 3d shows the true parameter
distribution (a sine curve). Although the introduced
scheme tends to underestimate parameter values at
local maxima and minima, it can provide a nearly
even measure of target parameter distribution, given
specific ranges of signal wavelengths and the original
observation station density.
Also, our method does not employ the variance–
covariance information of the GPS data at the
moment; therefore, the results are not directly affected
by the small but inevitable systematic errors in the
variances, which can exist as error propagates in a
large-scale network (Vanicek and Krakiwsky, 1982).
Our results are predominantly affected by the true
f Japan generated by the introduced method (a, b) and ones by the
seudo strain rate map for 1997/1/1–1999/6/30. (b) The result of a
using the same observation stations as in (a). (c) Dilatational strain
rom n Birkhauser Verlag, Basel). (d) A reconstruction of the map in/6/30, as in Sagiya et al. (2000), after the application of the temporal
it is applied in place of the MAD-limit to eliminate the temporal data
that STc1.3 MAD when the distribution is bnormalQ (MathWorks,udy data (Section 2.2.2). (e) The result of a geometrical resolvability
ion scheme, applied over the same observation stations as in (d). The
data are assumed to be 0.13 cm for both x- and y-components, based
ons used in the strain rate calculations.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 41
(immeasurable) accuracy of the available station
position data, besides the measurement errors men-
tioned earlier in this section.
The improvement of the geometrical resolution of
ATZs using the new scheme is clear, compared with
the results by other methods, for example, ones by
Sagiya et al. (2000). Their dilatational strain rate map
of Japan is reproduced in Fig. 6 and compared with
our results. They used a least-squares inversion
scheme, a slightly modified version of the method
introduced in Shen et al. (1996), on the GEONET data
for January 1997–June 1999. The results by their
method appear slightly blurred. That is likely due to
the Gaussian spatial noise assumption in the least
squares method and due to their disregard of the
highly irregular observation station arrangement in the
study area. In addition, the prominent spatial noise,
impulse noise, does not have a clear relationship with
the geographical distribution of temporal white noise
amplitudes in the data. Hokkaido region in Fig. 6 was
left blank after the temporal data quality analysis
(Section 2.2); there would have been a risk of spatial
aliasing affecting our results due to thin coverage of
usable stations in the area for the specific study
period.
2.4. Analysis plans for spatio-temporal variations of
deformation rates on ATZs
The regional and temporal variations of the
deformation fields are monitored with pseudo strain
rates. Two types of analyses are considered: (1)
comparisons of the spatial parameter distributions
before and after a reference time, e.g., the time of a
large earthquake, and (2) continuous (retrospective)
monitoring of spatial parameter distributions. The
observational time window was kept unchanged for
the case study to keep the measure of deformation
rates unbiased (cf., Section 2.2.2). For a type (1)
analysis, the identical set of observation stations is
used to compare the strain rate distributions for the
two successive non-overlapping time periods (810-
day each) before and after the 2000 Western Tottori
earthquake. In case of a type (2) analysis, the
observational time-window (810-day long) is moved
along the time-axis in increments of about a month
(30 days), and the changes in parameter strengths are
systematically recorded at the end of the time-
window. All available observation stations were used
for type (2) analyses, except for data with large
irregularities that were automatically removed from
the analysis by the application of the MAD-limit (cf.,
Section 2.2.2). A series of geometrical resolvability
tests with synthetic velocity fields (cf., Section 2.3.4;
Supplementary materials) demonstrated that not using
the complete set of observation stations for different
time steps did not severely affect the analysis results.
The mean of the upper hinge values of a given
parameter distribution for 810-day observation peri-
ods before and after the 2000 W. Tottori earthquake
was selected as the reference of the parameter
strengths.
3. Style of deformation along active tectonic zones
Mesoscale tectonic zones on the four main islands
of Japan were outlined in the maps of CMD, VLMD,
and MD2 (Fig. 4), and the characteristics of current
concentrated deformation were illustrated in the
pseudo strain rate maps (Fig. 7). Both types of
anomalies appeared to overlap geographically.
Although the definition of ATZs was rather qualita-
tive, the signals were as powerful as can be visualized
as the systematic shifts in the ITRF velocity fields and
as coherent strain rate anomalies. The ATZs were
preferentially located along some known tectonic
zones, chains of active volcanoes and low seismic
velocity anomalies in the crust and upper mantle. The
majority (60–70%) of the mapped ATZs was con-
tinuously active for the whole 6-year case study
period, while the remainder continued to operate
sporadically.
3.1. Dilatation
The Japanese islands are under compression from
the subduction of the Pacific and Philippine Sea plates
(e.g., Kato et al., 1998). Near trench-parallel belts of
areal contractional (negative dilatational) strain rate
anomalies were noticed for almost the entire length of
the island arc (Fig. 7a). The strain rate anomalies were
persistent for the whole case study period in the
Shikoku Island, along a belt from near Matsushiro to
Niigata, and along the volcanic front in Tohoku and
eastern Hokkaido.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5342
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 43
Contractional strain rates were exceptionally
prevailing on the ATZs in much of Shikoku, Kinki,
and southwestern Chubu regions before the 2000 W.
Tottori earthquake (MJMA 7.3). In the following year,
the Geiyo Earthquake (MJMA 6.7) also occurred 140
km southwest of the W. Tottori event (Fig. 4a). The
contractional strain rates at the crustal surface
relaxed about 20% after the sequence of the earth-
quakes (Fig. 7a). Meanwhile, a broad area from
Kinki to Kanto appeared to be influenced by the
accelerating Tokai-Kanto slow events (Fig. 1a) in the
sense that it would encourage relaxation of the
contraction in the affected upper plate areas. Sim-
ilarly, there was an episode of intensifying areal
contractional strain rates near the Sendai plains, a
20% increase (Fig. 7a), before the recent sequence of
large earthquakes in the vicinity: 2002/11/3 Miyagi-
Oki earthquake (M6.3), 2003/5/26 Miyagi-Oki earth-
quake (MJMA 7.1) and 2003/7/26 Northern Miyagi
earthquake (MJMA 6.4).
Positive dilatation was remarkable near the Sakura-
jima Volcano, e.g., for 1998/7/18–2000/10/5 (Fig. 7a),
and the deceleration of an upheaval was evident in the
acceleration field (Fig. 1b). An acceleration field
associated with a permanent deformation, which
would be proportional to a set of driving forces in a
nearly uniform medium, is an interesting subject to
study in detail. However, it is beyond the scope of this
paper, and will be explored elsewhere.
3.2. Shear
Fig. 7b shows the distributions of maximum shear
strain rates. Large shear strain rates were detected in
several areas: over much of Shikoku and the
southeastern Kyushu islands, near the Atotsugawa
fault, in the Matsushiro–Niigata area or the northern
Fig. 7. Pseudo strain rate maps: (a) dilatation, (b) maximum shear, and (c
(Period 1), and the bottom one is for 2000/10/6–2002/12/25 (Period 2). Th
value of a given absolute parameter frequency distribution. Temporal variat
in two selected areas: Zone 1 and Zone 2, are graphed in the inserts for (a)
illustrate the fluctuations of the sample medians of maximum shear pseudo
line illustrate the fluctuations of the corresponding IQRs. IQR stands for t
records (cf., strain rate calculation points, Fig. 3b), and the time series o
Section 2.2.2) is changing with time. Labels in the inserts for (b) denote: 20
earthquake (M1), 2003/5/26 Miyagi–Oki M7.1 earthquake (M2), and 200
denote: Shimanto metamorphic belt (Shimanto), Abukuma metamorphic t
(data sources: Japan Meteorological Agency and their affiliates (2003), an
NKTL, near the Sagami Trough, along the volcanic
front in Tohoku (Nakajima et al., 2001) and eastern
Hokkaido, and above a low seismic velocity
anomaly in the Hidaka range (Takanami, 1982;
Murai et al., 2003).
Shikoku and southern Kyushu are extensively
strained in the intermediate-term, but with very little
MN3 seismicity. Particularly, the Nankai forearc sliver
to the south of Setouchi or the Median Tectonic Line
(MTL) is in a fast right-lateral shear with respect to
the dRigidT Chugoku block (Fig. 8) and internallybrotatingQ (Fig. 7c; cf., Section 4.3). Fig. 8 showsMTL-parallel and -normal components of deformation
rates in the Shikoku Island with respect to the
Chugoku block. The apparent aseismic movement
on MTL is roughly 5 mm/year right-lateral, which
agreed with the rate estimated by others (Miyazaki
and Heki, 2001; Tabei et al., 2003). What is striking is
that both MTL-parallel and -normal deformation-rates
on the Shikoku Island decreased several millimeters
per year after the 2000 W. Tottori earthquake (upper-
right graphs in Fig. 8). This observation can be
compared to the aforementioned decrease of areal
contractional strain rates around the turn of the
century (Fig. 7a). Both components of the deforma-
tion rates along the MTL contained parts of the
trench-normal strain rate changes, because of the
obliquity of the MTL with respect to the Nankai
Trough (lower-left map in Fig. 8).
Southwestern and northeastern Japan are in colli-
sion at central Japan on a plate boundary between the
Amurian and North American plates (Miyazaki and
Heki, 2001). The rate of convergence is approxi-
mately 2 cm/year in the EW direction, derived by
estimating the relative drigidT block movements acrossan ATZ near the junction of the Itoigawa–Shizuoka
Tectonic Line (ISTL) and the NKTL (Fig. 9). This
) rotation. The upper map of each pair is for 1998/7/18–2000/10/05
e base of an arrow drawn on a color-scale indicates the upper-hinge
ions of dilatational and maximum shear pseudo strain rate parameters
and (b) on the right. Thick lines in the time series (the insert for (b))
strain rates in Zones 1 and 2, and two thin lines paralleling a thick
he interquartile range. dNT stands for the number of grid nodes withf dNT illustrate how the density of usable observation stations (cf.,00/10/06 W. Tottori earthquake (WT), 2002/11/03 Miyagi–Oki M6.3
3/7/26 Northern Miyagi M6.4 earthquake (M3). Labels on map (c)
errane (Abukuma), and Hidaka range (Hidaka). (d) Seismicity map
d Utsu (1982)).
Maximum Shear Pseudo Strain Rate
0.5
1.5
1
2x 10
-7
0
(Average of Period 1 and 2)MTL normal
MTL parallel
0 M
TL
0 M
TL
AA
NTNT
3
2
1
0
MTL normalMTL normal
Con
trac
tiona
l v
eloc
ity w
.r.t.
'A'
(
cm/y
r)
50 100 150 200 3
2
1
0
MTL parallelMTL parallel
Distance from 'A' kmW
este
rly
vel
ocity
w.r.
t. 'A
'
(cm
/yr)
decrease { Vel.(Period2) - Vel.(Period1) > 0 }increase { Vel.(Period2) - Vel.(Period1) < 0 }
MTL MTL A A
0
Deformation Rate:
a few mm/yr
MTLMTLForearcForearc SliverSliver
r
MTL
6.56.5 cm/m/y
NT
Cont. 3x10Ext.
-7Principal Strain Axes
Shikoku
(Convergence rate, Miyazaki and Heki, 2001)
/yr
/yr
Fig. 8. Crustal deformation in Shikoku region. Shown are Median Tectonic Line (MTL) parallel and normal components of the velocity fields
with respect to the drigidT Chugoku block. The group of stations in the box with cross-stripes along A–A line was considered as the fixedreference. On the right, two sets of velocity field profiles are shown. Period 1=1998/7/18–2000/10/05. Period 2=2000/10/06–2002/12/25. Two
things can be noted. (1) Small right-lateral slip along the MTL was apparent, 5 mm/year at the most. (2) There was an orderly decrease in the
deformation-rates (both MTL parallel and normal components) on the forearc in Shikoku around the turn of the century.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5344
result agrees with the estimate by others (Miyazaki
and Heki, 2001; Hirahara et al., 2003), determined by
other means. Fast creep movements along the
Atotsugawa fault on the NKTL appeared to be driven
by such a fast convergence in the area. When the
relative velocity vector was projected onto an NKTL
segment near the Atotsugawa fault with a strike of
N60E, a rapid right-lateral shear (1.6 cm/year) and a
fault-normal contraction (1.3 cm/year) were detected
for 1998/7/18–2000/10/5, for example. The median
absolute deviation for both components was ~0.35
cm/year. GSI (1997), otherwise, reported local varia-
tions of creep rates along the central portion of the
Atotsugawa fault: 1.5 cm/year for a fast moving
segment and non-creeping at a position 15 km west of
it. These estimates were based on multiple precise
distance measurements with several 1–2 km baselines
across the fault. The last large earthquake to occur in
the area was the 1858 Hietsu earthquake (M7)
(Usami, 1996).
3.3. Rotation
Rotational ATZs were noticeable along the NKTL
(clockwise) and along the Pacific. Several clockwise
and counterclockwise pairs of rotational ATZs were
perceived in areas along the Pacific: the Shimanto
metamorphic belt (southern Kyushu to Shikoku-Kii),
Tokai, Sagami, the Abukuma metamorphic terrane to
the Kitakami mountains, and the Hidaka range to the
volcanic front in eastern Hokkaido (Fig. 7c). The
direction of maximum compressive stress, as deduced
from the focal mechanisms of shallow inland earth-
quakes, is known to be the same as that of the plate
convergence (E–W) in northeastern Japan, while it is
near trench-parallel (SW–NE) (Wang and Suyehiro,
1999) and occurs at an angle of about 458 to the plateconvergence direction in southwestern Japan (McCaf-
frey, 1993). Supposing that an in-between block of a
rotational ATZ pair was compressed faster than the
surrounding areas in the fashion depicted in the insert
Fig. 9. Pseudo strain rate maps of central Japan, for 1998/7/18–2000/10/05. Shown are, from the left, dilatational (D), rotational (x), andmaximum-shear (R) components. The base of an arrow drawn on a color-scale indicates the upper-hinge value of a given absolute parameterdistribution. The spatial distributions of the dilatational and maximum shear strain rates across two anomalies are also shown in profiles. A red
line on the profiles indicates the upper hinge value for the corresponding parameter. The active faults are shown in grey lines on the maps (active
fault data source: Research Group for Active Faults of Japan, 1991).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 45
of Fig. 7c, then, the sense of rotation on the ATZ to
the right of the in-between block facing the compres-
sion direction would rotate clockwise and that of the
left would rotate in a counterclockwise direction.
Given such a configuration, it is possible to recognize
that landward crustal movements of the in-between
blocks were prevailing during the whole 6-year
observation period, except for a pair in Tokai that
indicated a seaward transient crustal movement. The
trend and timing of the crustal surface movement in
Tokai (Fig. 1a) matched that of the ongoing Tokai
slow earthquake (Ozawa et al., 2002).
4. Discussion
Our empirical observations, refined by the appli-
cations of robust smoothing and exploratory–confir-
matory analyses on the irregular data sets,
demonstrated that the primary features of the inter-
seismic crustal deformation in Japan can be described
in terms of two overlapping operative processes: (1)
the regional-and-steady mode of strain accumulation
(cumulative effect of distant tectonic forces) and (2)
the local-and-transient mode of strain accumulation
(individually linked to an imminent or concurrent
sequence of large tectonic events, both inland and
offshore).
Mesoscale intermediate-term deformation signals
(here altogether recognized as of ATZs) often
account for slow earthquakes (e.g., Hirose et al.,
1999), post-seismic deformations (e.g., Heki et al.,
1997), elastic strain accumulations and permanent
internal deformations in the upperplate areas. ATZs
accommodate interseismic deformation of various
forms: elastic strain accumulation (Jackson et al.,
1997), creep along a confined zone of crustal
weakness (e.g., GSI, 1997), and wall-block perma-
nent deformation (Sibson, 2002). Superposed upon
these localized inland crustal movements, there are
broader tectonic loading signals of various scales
from the contiguous major plate boundaries in
Japan. Widespread disagreements between regional
instantaneous geodetic strain rates (�10�7/year)
In space: MESOSCALE (70~several hundred kilometers)In time: INTERMEDIATE TERM (several months to years)
Our field of view / Observational scale range
Operational scales of interseismic crustal deformation
SPACE
long(several-100s years)
intermediate (months-several years)
short(seconds-months)
large(100s-1000s km)
medium(10s-100s km)
small(0-10s km)
Our field of view
Static stress-change
effect dominant
TIME
Regional-and-steady processLocal-and-transient process
Operative / characteristic scales of crustal deformation in our field of view:
Highly heterogeneous
mixture of effects + noise
Dynamic stress-change
effect dominant
Fig. 10. Summary diagram of the operational scales of interseismic
crustal deformation with respect to the observable range by the
existing GPS array. Our observable scale-range is limited within the
rectangular box in the center, labeled dOur Field of ViewT. Thediagram would help distinguish the regional-and-steady deforma-
tion signals (of scales around the solid circle) from local-and-
transient deformation signals (of scales around the open circle).
Local-and-transient strain rate changes are presumably caused by
stress-changes accompanying the bco-seismicQ phenomena prevail-ing on certain scale-ranges, labeled in the background. bCo-seismicQin this context might include immediate precursory deformation and
immediate post-seismic deformation (both fast and slow).
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5346
(Kato et al., 1998; Sagiya et al., 2000) and local
geologic strain rate estimates along active fault
traces (�10�8/year) (Nohara et al., 2000) are oftenattributed to such interseismic elastic strain accumu-
lation due to broad tectonic loading from the
contiguous subduction zones, where only small
portions of the differences actually contribute to
the permanent strains on many individual faults.
(Additionally, the fact that not all active microscale
or blind faults are identified in the crust might
explain a part of the large disagreements.)
Subduction effects (on both meso- and macro-
scales) should be removed from our data to correctly
assess the upperplate and intraplate deformations
(personal communication with several at IUGG,
2003). However, separating these effects presents
quite a challenge, as Japan is situated at the
confluence of several major tectonic plates. If one
were to identify and remove various subduction
effects, it would be necessary to perform the tasks
comprehensively; otherwise, it could merely create
biases in one’s interpretation of inland tectonics. The
maps of coordinate independent deformation-rate
parameters (Figs. 4 and 7) alternatively helped
identify mesoscale areas of disturbances or ATZs in
the upperplate that likely resulted from both intra- and
inter-plate tectonics. The resolved geometry and
characteristics of the ATZs might be utilized in a
tectonic model (e.g., Hashimoto and Jackson, 1993)
and could provide an improved understanding of
heterogeneous and non-isotropic mesoscale tectonic
processes in the near future.
4.1. Geometry and origin of inland ATZs
The geometrical agreements among the mapped
ATZs, chains of active volcanoes, and low seismic
velocity anomalies in the lithosphere are apparently
due to their common weakness on the mesoscale.
Moderate to large inland earthquakes (M5.7–8.0,
Db=20 km, in Japan (Zhao et al., 2000)) also tend
to occur near such preexisting weaknesses in the
crust (Zhao et al., 2000; Sagiya et al., 2000). The
weakness is believed to come from a high water
content in the shallow crust originating from the
dehydration of the subducted slabs (Nakajima et al.,
2001; Iio et al., 2002; Hyodo and Hirahara, 2003).
The presence of partial melt materials in the upper-
most mantle, e.g., beneath the volcanic front in
Tohoku (Nakajima et al., 2001), might be another
contributing factor for the relative structural weak-
ness on the mesoscale. Leaving aside the issue of
whether these weak zones constitute micro-plate
boundaries, they were apparently more sensitive to
ambient stress changes than the neighboring drigidTblocks. The apparent weakness on the mesoscale,
however, does not necessarily imply the same
quality for dmicroscaleT ATZs. Our observations arelimited to the scale-range in our field of view (Fig.
10). Similarly, the apparent behavior of crustal
surface materials whether it is ductile or brittle
critically depends on the observational scale (e.g.,
King, 1983).
A focused strain rate anomaly with its instability
apparent in a certain geometric condition of tectonic
boundaries, e.g., a triple junction on land (King,
1983; Gabrielov et al., 1996), might imply a stress
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 47
concentration. For example, the 1965–1967 Mat-
sushiro earthquake swarm area appeared to be
located near a junction of three mesoscale ATZs
(Figs. 3e and 4a). With southwestern Japan in
collision against the northeastern half (Fig. 9), the
localized stress near Matsushiro was possibly close
to its critical state in 1965 and eventually developed
into an energetic ductile deformation. The source of
locally dexcess (continuously been replenished)Tseismic energy-inputs during the swarm (Kisslinger,
1968) might have been the momentum in such a
ductile deformation. Expansive strains in the NS
direction were distinctive of the swarm episode,
which also matched well with the concurrent
moderate seismic events’ mechanisms (Kasahara
and Okada, 1966). It is likely that water eruptions
and other unusual phenomena were secondary to
such a diffuse process. In addition, the 1964 Niigata
earthquake (224 km north–north–west of Matsush-
iro) appeared to trigger the Matsushiro swarms, as
witnessed in the migrating pattern of diffused
seismicity from Niigata to Matsushiro (Mogi,
1988). In general, prominent ATZs, such as those
near Matsushiro and Akan in Fig. 4a, are suggestive
of well-developed tectonic zones, highly strained
and heterogeneous areas, where continued readjust-
ments and ductile deformation might possibly be
taking place on the mesoscale. Further investigations
of the swarm areas might be necessary to confirm
the above conjecture.
4.2. Subduction-induced strains on ATZs
Tectonic stresses in the overriding plate of a
subduction zone in the absence of back-arc spreading
are critically influenced by the locking and unlocking
of the adjacent subduction fault (Whittaker et al.,
1992), and the stresses fluctuate with time over many
earthquake cycles because of such a locking-and-
unlocking mechanism (e.g., Wang and He, 1999).
Temporal fluctuations of the stresses in turn induce
strain rate changes in the overriding plate that may be
observed by geodetic means. In our 6-year GPS
observation period, which was much shorter than the
interseismic period of a large characteristic earthquake
such as the Nankai earthquake, we still perceived at
least two apparent modes of strain accumulation along
the island arc. This is illustrated in the summary
diagram of operational scales of interseismic crustal
deformation, Fig. 10.
(1) Regional-and-steady mode (scales around a
solid circle in Fig. 10). About 60–70% of the
mapped inland ATZs or strain rate anomalies
were perceptible for the whole 6-year observa-
tion period; the overall pattern (the distribution
and the trend) of the anomalies did not
significantly change over time nationwide.
These steady strain rates presumably reflect
the gradual interseismic loading from the
adjacent subduction zones.
(2) Local-and-transient mode (scales around an
open circle in Fig. 10). The remaining part of
the anomalies occurred only for brief moments,
from several months to a few years, and affected
zones from 70 to a few hundred kilometers
wide. For example, there were two notable cases
where the transient shifts in areal contractional
and shear strain rates were remarkably synchro-
nous with the sequences of nearby major
tectonic episodes including both large earth-
quakes and slow events (Figs. 7a and b;
Sections 3.1 and 3.2).
In Shikoku and Kinki regions, the areal contrac-
tional strain rates had weakened suddenly at the turn
of the century, when the W. Tottori and Geiyo
earthquakes occurred (Figs. 7a and 8). The Tokai
slow event (Ozawa et al., 2002) (or aseismic slip on
the subduction fault) was also happening some 500
km away east of the W. Tottori epicenter. All of these
events would cause the stresses in the upper plate
areas to decrease.
In order to determine the stress changes caused by
transient aseismic slips on a subduction fault, it is
essential to have precise knowledge of the spatial
extent, magnitude, and duration of the slips. However,
it is quite difficult to estimate these items solely from
an observation of crustal surface deformation. The
most useful vertical component of strain has the
poorest resolution with GPS observations (e.g.,
Melbourne and Webb, 2003).
Optionally, there is a possibility that transient rate
changes in microseismicity (MN=3) on the subduction
fault (a lower right graph, Fig. 11) might help
determine the precise duration and extent of the
Inland Seismicity
Subduction Slab Seismicity
4
6
4
6M
M
048
12x 10
20
Cum
ulat
ive
en
ergy
rel
ease
7 x 10(mainshock)
21
1930
R=25km
R=150km
Quiescence
1940 1950 1960 1970 1980 1990 2000
R=25km
Inland Seismicity before W.Tottori Earthquake (Depth < 25km)
1998 1999 2000 2001 20020
0.2
0.4
0.6
0.8
1
Time [year]
Cum
ulat
ive
num
ber
(nor
mal
ised
)
Subduction Slab Seismicity (M>3)
WT (inland)
GY (intra-slab)
Zone E
Zone W
130 132 134 136 13831
32
3334
35
36
R=25km R=150km
Zone E (N=964)
Zone W (N=1420)
GY (Depth=51.4km)
WT (Depth=11.3km)
Fig. 11. Seismicity rate changes around the turn of the century in southwestern Japan. (1) Inland seismicity before the 2000 W. Tottori
Earthquake, within 25 km of the epicenter (top), and within 150 km of the epicenter (bottom). (2) Subduction slab seismicity. WT=W. Tottori
earthquake. GY=Geiyo earthquake. The microseismicity rate in Zone E changed at 2000 (increased out of the background level), at dWTT(further rate increase, indicative of a triggered aseismic slip), and at 2001 (decreased back to the background level). The earthquake catalogue of
the Japan Meteorological Agency and their affiliates (2003) used here was generally dhomogeneous (Habermann, 1983)T and dcomplete (e.g.,Wiemer and Zuniga, 1994)T.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5348
aseismic slip in combination with geodetic observa-
tions. A separate detailed study on this subject is
necessary. (It would also be interesting to investigate
the relationship between the non-volcanic tremors
(Obara, 2002) and slow events, as was done in the
Cascadia subduction zone (Rogers and Dragert,
2003).) Since the shear stress changes on the fault
would likely be reflected as changes in the micro-
seismicity rate, it is plausible that the plate coupling
strengths on the Tokai to Tonankai (and possibly a
part of Nankai) subduction faults had weakened
slightly during 2000 to 2001, followed by the Geiyo
earthquake in 2001 (Fig. 11). Particularly, the flow of
these tectonic events appeared in sync with the
decrease of areal contractional strain rates on the
overriding plate regions (Figs. 7a and 8). It is
conceivable that the scale of crustal deformation and
seismicity would correlate well only when their
operative scales match.
The situation in Miyagi Prefecture was similar to
the case in southwestern Japan insofar as the areal
contractional and shear strain rates were higher in the
overriding plate before the recent sequence of large
earthquakes (both inland and offshore events). The
tectonic setting in northeastern Japan is overall differ-
ent from that of southwestern Japan. The overriding
plate in northeastern Japan is under trench-normal
compression and the rate of subduction is much faster
(and the slab is colder) than that of southwestern Japan
(Wang and Suyehiro, 1999). Accordingly, the earth-
quake production rate in northeastern Japan is much
faster than that of the southwest, for example.
The strain is evidently being accumulated near
Miyagi Prefecture. The Headquarters for Earthquake
ID 950392
ID 950393
WT
Station ID: 950393; on WGS84 (annual and semi-annual additive seasonality and linear trend removed)
0 400 800 1200 1600
NS(cm)
Time (days)
-1
0
1 WT
Fig. 12. Small precursory displacements detected at a few GEONET
stations (e.g., station d950393T) near the 2000 W. Tottori earthquakeepicenter (dWTT). Station position time series at the station d950393T(North–South component) on the WGS84 reference ellipsoid is
shown. Data are for 1998/7/18–2002/12/25. Signals at the station
d950392T were also very similar to those at the station d950393T.dWTT=W. Tottori earthquake.
Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 49
Research Promotion in Japan (ERP at http://
www.jishin.go.jp) gave their forecast for the next
M7.5-class interplate Miyagi-Oki earthquake to
occur in the next 30 years at the probability of
90% or greater, as estimated from earthquake
recurrence-time studies.
Wang (1995), for example, viewed that strain
accumulation at a subduction zone might take place
on multiple spatial scales. Elastic strain energy
induced by distant tectonic forces is stored up in a
broad region in the lithosphere, while the strain is also
accumulated locally around isolated asperities on a
subduction fault. Locally accumulated strain is even-
tually released as earthquakes near asperities. Because
fast crustal shortening (inelastic permanent deforma-
tion) in the overriding plate is typically not observed,
the remaining stored strain energy must be released by
some other effective mechanism(s) conceivably on the
subduction fault (Wang, 1995). With the knowledge
of prevalent low seismic coupling factors at world-
wide subduction zones, compiled by Pacheco et al.
(1993), Wang (1995) suggested that aseismic slip
must be the predominant mechanism of strain releases
at a subduction zone, where the growth of a single
seismic slip with a rapid elastic rebound of the
overriding plate is hindered by the viscous force in
the asthenosphere. Although the viscoelasticity of the
asthenosphere may not be the sole factor in control-
ling the low seismic coupling factors at world’s
subduction zones (Hirahara, 2002), our observations
are not in conflict with Wang (1995)’s observations of
a common subduction zone environment where
aseismic slips are prevalent and multiscale strain
accumulation zones exist. If each pair of rotational
ATZs along the Pacific (Fig. 7c) is presumed to
constitute a subduction-induced strain accumulation
zone, some of the pairs would make up zones several
hundred kilometers wide. They are clearly larger than
a single historic interplate earthquake rupture in the
area. The prevalence of aseismic slips and the
existence of nested strain accumulation zones seem
to be in accord with our findings.
4.3. Limitations of the scheme
Our ATZ-mapping tool successfully delineated
sharp mesoscale tectonic boundaries; however,
dmicroscaleT features were outside our perceivable
range of scale (Fig. 10). Therefore, we were unable to
deduce the style of microscale deformations, e.g.,
along a rotational ATZ, whether they involved multi-
ple distinct block rotations or more diffused deforma-
tions within a zone of concentrated deformation. Also,
most precursory deformations of an inland earthquake
(if there were any tangible ones) on an imminent
rupture surface,
Recommended