Viscoelastic Block Models of the North Anatolian Fault: A Unified Earthquake Cycle Representation of Pre‐ and Postseismic Geodetic Observations

Abstract

Along the North Anatolian fault (NAF), the surface deformation associated with tectonic block motions, elastic strain accumulation, and the viscoelastic response to past earthquakes has been geodetically observed over the last two decades. These observations include campaign-mode Global Positioning System (GPS) velocities from the decade prior to the 1999 Mw 7.4 İzmit earthquake and seven years of continuously recorded postseismic deformation following the seismic event. Here, we develop a 3D viscoelastic block model of the greater NAF region, including the last 2000 yrs of earthquake history across Anatolia, to simultaneously explain geodetic observations from both before and after the İzmit earthquake. With a phenomenologically motivated simple two-layer structure (schizosphere and plastosphere) and a Burgers rheology (with Maxwell viscosity log10 ηM ≈ 18:6–19:0 Pa·s and Kelvin viscosity log10 ηK ≈ 18:0–19:0 Pa·s), a block model that incorporates tectonic plate motions, interseismic elastic strain accumulation, transient viscoelastic perturbations, and internal strain can explain both the pre- and post-İzmit earthquake observations with a single unified model. Viscoelastic corrections to the interseismic GPS velocity field with the unified model reach magnitudes of ~2:9 mm=yr. Geodetically constrained slip-deficit rate estimates along the central NAF and northern strand of the NAF in the Sea of Marmara vary nonmonotonically with Maxwell viscosity and change by up to 23% (~4 mm=yr) for viscosities ranging from 10¹⁸ to 10²³ Pa·s. For the best-fit viscosity structures, central NAF slip-deficit rates reach 22 mm=yr, increasing to 28 mm=yr in the Sea of Marmara. Along the central NAF, these rates are similar to the fastest geologic slip-rate estimates. The fastest slip-deficit rate estimates along the entire fault system (~27–28 mm=yr) occur less than 50 km from Istanbul, along the northern strand of the NAF in the Sea of Marmara.

Full text

Ⓔ
Viscoelastic Block Models of the North Anatolian Fault:
A Unified Earthquake Cycle Representation of
Pre- and Postseismic Geodetic Observations
by Phoebe M. R. DeVries, Plamen G. Krastev, James F. Dolan, and Brendan J. Meade
Abstract Along the North Anatolian fault (NAF), the surface deformation associ-
ated with tectonic block motions, elastic strain accumulation, and the viscoelastic
response to past earthquakes has been geodetically observed over the last two decades.
These observations include campaign-mode Global Positioning System (GPS) veloc-
ities from the decade prior to the 1999 Mw7.4 İzmit earthquake and seven years of
continuously recorded postseismic deformation following the seismic event. Here, we
develop a 3D viscoelastic block model of the greater NAF region, including the last
2000 yrs of earthquake history across Anatolia, to simultaneously explain geodetic
observations from both before and after the İzmit earthquake. With a phenomenologi-
cally motivated simple two-layer structure (schizosphere and plastosphere) and a
Burgers rheology (with Maxwell viscosity log10 ηM≈18:6–19:0Pa·s and Kelvin
viscosity log10 ηK≈18:0–19:0Pa·s), a block model that incorporates tectonic plate
motions, interseismic elastic strain accumulation, transient viscoelastic perturbations,
and internal strain can explain both the pre- and post-İzmit earthquake observations
with a single unified model. Viscoelastic corrections to the interseismic GPS velocity
field with the unified model reach magnitudes of ∼2:9mm=yr. Geodetically con-
strained slip-deficit rate estimates along the central NAF and northern strand of the
NAF in the Sea of Marmara vary nonmonotonically with Maxwell viscosity and
change by up to 23% (∼4mm=yr) for viscosities ranging from 1018 to 1023 Pa·s. For
the best-fit viscosity structures, central NAF slip-deficit rates reach 22 mm=yr, increas-
ing to 28 mm=yr in the Sea of Marmara. Along the central NAF, these rates are similar
to the fastest geologic slip-rate estimates. The fastest slip-deficit rate estimates along the
entire fault system (∼27–28 mm=yr) occur less than 50 km from Istanbul, along the
northern strand of the NAF in the Sea of Marmara.
Electronic Supplement: Figure of sensitivity of viscoelastic block model slip-
deficit rate estimates and contour plot of mean residual improvement.
Introduction
Existing models of earthquake cycle deformation are
largely focused on either explaining postseismic geodetic ob-
servations from the first 1–10 yrs after large (Mw>6:5)earth-
quakes (e.g., Reilinger et al.,2000;Bürgmann et al.,2002;
Ergintav et al.,2002,2009;Hearn et al.,2002;Ryder et al.,
2007,2011), or explaining observations of nominally inter-
seismic deformation occurring long after (>10 yrs) an earth-
quake (e.g., Savage and Burford, 1973). To gain a more
complete understanding of the earthquake cycle, postseismic
and interseismic geodetic observations must be integrated and
explained with a unified model that can provide a physical
explanation for both rapid postseismic deformation and more
slowly varying interseismic deformation (Hetland, 2006;
Hearn et al., 2009;DeVries and Meade, 2013,Meade et al.,
2013;Yamasaki et al., 2014;Hearn and Thatcher, 2015).
Geodetic observations across strike-slip faults from both
before and after large earthquakes exist along the San Andreas
fault (SAF) at Parkfield (e.g., Bakun and Lindh, 1985), across
the Kunlun fault in Tibet (Bell et al.,2011;Zhang et al., 2004,
2009;Ryder et al., 2007,2011), and along the North Anato-
lian fault (NAF)inTurkey(Fig.1;Reilinger et al., 1997,2006;
Bürgmann et al., 2002;Ergintav et al.,2002,2009). These
BSSA Early Edition / 1
Bulletin of the Seismological Society of America, Vol. 107, No. 1, pp. –, February 2017, doi: 10.1785/0120160059

pre- and postseismic observations represent an opportunity to
constrain models of the earthquake cycle on strike-slip faults
worldwide.
The Global Positioning System (GPS) observations
across the NAF exhibit dense spatial and temporal coverage.
The easternmost and westernmost sections of the NAF were
widely recognized as seismic gaps prior to the 1999 Mw7.4
İzmit earthquake (Toksöz et al., 1979;Barka, 1992,1996;
Stein et al., 1997) and as a result, survey-mode GPS cam-
paigns were conducted in eastern Turkey and the Sea of
Marmara region in the decade before the earthquake (Rei-
linger et al., 1997,2006;Straub et al., 1997;McClusky
et al., 2000). In addition, several permanent GPS stations
were installed to continuously record deformation (Ergintav
et al., 2002). These observations together revealed a local-
ized velocity gradient with a differential velocity of
∼24 mm=yr over a 200-km-wide transect across the
western strand of the NAF in the Sea of Marmara region
prior to the 1999 earthquake (Fig. 1;Bürgmann et al., 2002;
Meade et al., 2002). Elastic block models incorporating
these pre-earthquake velocities provide fault-slip-deficit
rate constraints (sometimes termed geodetic slip-rate con-
straints) of ∼24–30 mm=yr along the NAF, with rates in-
creasing westward along the main northern strand of the
NAF in the Sea of Marmara region (Reilinger et al., 1997,
2006;McClusky et al., 2000;Meade et al., 2002).
Postseismic GPS displacements immediately following
the 1999 İzmit earthquake have been effectively explained
by aseismic afterslip down-dip of the coseismic rupture zone
with maximum slip of about 43 cm over a 75-day period
(Reilinger et al., 2000). Time-dependent analysis of GPS
position time series in the 87 days after the İzmit earthquake
suggests that maximum aseismic slip rates may have reached
2m=yr (Bürgmann et al., 2002). A weakly velocity strength-
ening (a–b0:19 MPa) frictional afterslip model has also
been used to explain the GPS displacements in the 80 days
immediately after the İzmit earthquake (Hearn et al., 2002).
Over a longer observation period from 1999 to 2003, three
logarithmic decay constants have been used to fit the dis-
placement time series observed at continuous GPS stations
(Ergintav et al., 2002,2009). Postseismic time series from
the four years immediately after the İzmit earthquake have
also been explained by a combination of frictional afterslip
during the first few months after the earthquake, and visco-
elastic deformation with a Maxwell rheology with viscosity
ηM2–5×1019 Pa·s for the remainder of this observatio-
nal interval (Hearn et al., 2009). Another study (Wang et al.,
2008) incorporates a standard linear solid rheology to explain
the İzmit postseismic observations.
To understand the NAF earthquake cycle to an even
greater extent, both the pre- and postearthquake data have to
be examined and explained simultaneously. This was first rec-
ognized after the İzmit earthquake (Hetland, 2006), and in 2D,
GPS data from both before and after the 1999 Mw7.4 İzmit
earthquake have been successfully explained with a two-layer
Burgers model with a transient (Kelvin) relaxation timescale
(τKηK=μK)of2–5 yrs and a steady (Maxwell) timescale
(τMηM=μM) of more than 400 yrs (Hetland, 2006). More
recently, models incorporating shear zones (24–40 km in
width) extending to midcrustal depths with low viscosities
(∼2×1018 Pa·s) in the shear zone and higher viscosities
(>2×1020 Pa·s) in the surrounding medium have been used
Figure 1. Interseismic Global Positioning System (GPS) velocities (Reilinger et al., 2006) and shaded relief map of Turkey. Velocities are
shown in a nominally Eurasian reference frame and are color coded by magnitude with warmer colors indicating faster velocities. The trace of
the North Anatolian fault (NAF) is shown with a thick black line. The black box over the northern strand of the NAF on the western edge of the
figure highlights the area shown in Figure 4b; the 1999 Mw7.4 İzmit earthquake ruptured the segments of the fault within the black box.
2P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

to explain GPS observations in the Sea of Marmara region
from both before the İzmit earthquake and six months of post-
seismic deformation after the event (Yamasak i et al., 2014). In
another recent study (Hearn and Thatcher, 2015), crust- to
lithosphere-scale viscous shear zones with effective viscosity-
per-unit width in the zones increasing from ηsz=w≈
1015 Pa·s=minthecrusttoηsz=w≥5×1016 Pa·s=mbe-
low the Moho were found to explain pre- and postearthquake
deformation. In these preferred models, the shear zones cut
through a strong (η>1020 Pa·s) lithosphere and a weaker
asthenosphere (η<1019 Pa·s) (Hearn and Thatcher, 2015).
The previous earthquake cycle models of the NAF
described above (Hetland, 2006;Yam asaki et al.,2014)have
taken into account repeated earthquakes on the İzmit strand of
the western NAF. Here, we develop a 3D viscoelastic block
model of the greater NAF region, taking into account the last
2000 yrs of earthquake history (e.g., Barka, 1992,1996;Am-
braseys and Jackson, 2000;Ambraseys, 2002)toassessinan
internally consistent manner whether or not both pre- and
postearthquake deformation along the NAF canbesimultane-
ously explained with a single rheological model. We also ex-
amine the sensitivity of geodetic slip-deficit rate estimates to
the assumed viscosity structure and compare these slip-deficit
rates from geodetically constrained viscoelastic block models
with Holocene slip-rate estimates along the NAF based on off-
set geomorphic features (e.g., Hubert-Ferrari et al.,2002;
Kondo et al.,2004;Kozacıet al., 2007;2009;Pucci et al.,
2008;Dolan, 2009; Uçarkuş[unpublished thesis, 2010; see
Data and Resources]; Meghraoui et al.,2012).
Viscoelastic Block Model
In classical elastic block theory (Matsu’ura et al., 1986;
McCaffrey, 2002;Meade and Hager, 2005;Meade and Love-
less, 2009), interseismic velocities vIare modeled as the sum
of the velocities due to long-term block motion vB, the veloc-
ities due to the accumulated slip deficit vSD , and the veloc-
ities due to internal strain of the blocks v_
ε:
EQ-TARGET;temp:intralink-;df1;313;419vIvB−vSD v_
ε:1
To incorporate the viscoelastic earthquake cycle effects of
past earthquakes into 3D kinematically consistent block
models (Sato and Matsu’ura, 1988;Smith and Sandwell,
2006;Johnson et al., 2007;Pollitz et al., 2008,2010;Hilley
et al., 2009;Chuang and Johnson, 2011;Hearn et al., 2013;
Tong et al., 2014), a viscoelastic correction must be taken
into account. The correction consists of two components:
(1) the viscoelastic effects of the most recent earthquake vVE
along the fault segment and (2) the mean velocity throughout
the earthquake cycle 
vVE. In a viscoelastic block model
framework, modeled interseismic velocities are composed
of five components (Fig. 2):
EQ-TARGET;temp:intralink-;df2;313;246
vIvB−vSD v_
εvVEηM;ηK;t−teq
−
vVEηM;ηK;T:2
The first term of the viscoelastic correction, the viscoelastic
effect of the most-recent earthquake, depends on the time
since the most-recent earthquake t−teq and the assumed vis-
cosities ηMand ηK. The mean earthquake cycle velocity term,
the second term in the correction, depends on the assumed
recurrence interval Tand viscosities ηMand ηK. This con-
struction ensures that over many earthquake cycles, the dis-
placements everywhere are equal to the long-term block
displacements. In classic block theory (Matsu’ura et al.,1986;
McCaffrey, 2002;Meade and Hager, 2005;Meade and
Loveless, 2009), this is referred to as kinematic consistency.
vB
t=0
vSD vVE vVE vI
t=T/ 2
t=T
-
-
-
+
+
+
-
-
-
=
=
=
Figure 2. The components of a velocity field in a viscoelastic block model framework (equation 2) at three times through the earthquake
cycle. Interseismic velocities vIare modeled as the sum of the velocities due to long-term block motion vB, the velocities due to the accumulated
slip deficit vSD, the viscoelastic effects of the most recent earthquake vVE along the fault segment, and the mean velocity throughout the earthquake
cycle velocity 
vVE. For simplicity, the velocities due to homogenous internal strain of the blocks v_εare not included in this schematic diagram.
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 3
BSSA Early Edition

Fault-slip-deficit rates constrained by an elastic block model
are kinematically consistent because they are linearly propor-
tional to differential block motions.
However, in a viscoelastic block model framework, the
concept of kinematic consistency is more complicated and
may be divided into two distinct components, which we term
type I and type II kinematic consistency. To satisfy type 1
kinematic consistency, fault-slip-deficit rates must be lin-
early proportional to differential block motions, just as in
elastic block models. Type II kinematic consistency is related
to the assumptions implicit in the viscoelastic correction term
vVEηM;ηK;t−teq−
vVEηM;ηK;Tin equation (2). To cal-
culate this viscoelastic correction, we assume a characteristic
slip sand recurrence interval Tfor the earthquake and there-
fore implicitly assume a long-term slip rate of s=T on the
fault. In order for a viscoelastic block model to satisfy type
II kinematic consistency, the final slip-deficit rate estimate
from viscoelastic block models must be equal to the long-
term slip rate s=T that we assume in the viscoelastic correc-
tions. Constructing a viscoelastic model that satisfies type II
kinematic consistency and is as consistent as possible with
the timing and estimated magnitudes of historic earthquakes
would require an iterative method, in which we would as-
sume a long-term slip rate consistent with geologic estimates
of sand Tand then incrementally iterate these values until
we approach sII and TII, the values of sand Tfor which s=T
is equivalent to the final viscoelastic block model slip-deficit
rate estimates. In a viscoelastic block model that satisfies the
conditions of both type I and type II kinematic consistency,
the assumed long-term slip rate sII=T II may or may not be
consistent with geologic constraints on sand T. The visco-
elastic block models in this article automatically satisfy type
I kinematic consistency (e.g., Meade and Loveless, 2009),
but here we choose to be as consistent as possible with geo-
logic estimates of sand Talong the NAF (Barka, 1992,1996,
1999;Ambraseys and Jackson, 2000,Ambraseys, 2002)at
the cost of type II kinematic consistency.
To show the construction of the viscoelastic block model
in more detail, we can rewrite the right side of equation (2) in
a block model framework:
EQ-TARGET;temp:intralink-;df3;55;253
vIGB−GSDΩG_
ε_
ϵvVEηM;ηK;t−teq
−
vVEηM;ηK;T:3
The matrix–vector products give the contributions of block
rotation, slip-deficit, and homogenous internal block strain to
the velocity field. Assuming that the viscoelastic contribu-
tions are functions of past earthquake activity only, we can
rewrite equation (3) as
EQ-TARGET;temp:intralink-;df4;55;145
vI−vVEηM;ηK;t−teq 
vVEηM;ηK;T
GB−GSDΩG_
ε_
ϵ:4
Generalizing this framework to incorporate the viscoelastic
effects of Neq periodic earthquakes on different fault seg-
ments requires only a summation over all of the individual
earthquakes, because the rheologies considered here are
linear:
EQ-TARGET;temp:intralink-;df5;313;697
vI−X
Neq
i1vi
VEηM;ηK;t−ti
eq−
vi
VEηM;ηK;Ti
GB−GSDΩG_
ε_
ϵ:5
This can be rewritten as
EQ-TARGET;temp:intralink-;df6;313;615vηM;ηKGB−GSDΩG_
ε_
ϵ;6
in which
EQ-TARGET;temp:intralink-;df7;313;568
vηM;ηK
vI−X
Neq
i1
vi
VEηM;ηK;t−ti
eq−
vi
VEηM;ηK;Ti:7
Equation (6) is a classic block model problem (e.g., Meade and
Loveless, 2009) with a velocity field vηM;ηKmodified to
correct for the viscoelastic effects of Neq sets of periodic earth-
quakes. With this framework, it is straightforward to construct
a viscoelastic block model incorporating the effects of many
ancient and historic earthquakes: we calculate the viscoelastic
effects from previous earthquakes PNeq
i1vi
VEηM;ηK;t −ti
eq−

vi
VEηM;ηK;Ti and then combine these viscoelastic veloc-
itieswiththeobservedinterseismicGPS velocities to calculate
vηM;ηKas
EQ-TARGET;temp:intralink-;df8;313;372
vηM;ηK
vGPS −X
Neq
i1
vi
VEηM;ηK;t−ti
eq−
vi
VEηM;ηK;Ti:8
The 3D calculations of vi
VEηM;ηK;t−ti
eqand

vi
VEηM;ηK;Tiare based on the spectral propagator matrix
approach (Sato, 1971;Sato and Matsu’ura, 1973,1988;Mat-
su’ura and Sato, 1975,1989;Fukahata and Matsu’ura, 2005,
2006;Hashima et al., 2014) to calculate strains, stresses,
velocities, and displacements at depth due to point-source
dislocations embedded within a vertically layered half-space.
The model can incorporate an arbitrary number of viscoelas-
tic layers, and earthquake sources may be in both elastic and
viscoelastic layers. The viscoelastic layers may have either
Maxwell or Burgers (transient) rheologies (e.g., Pollitz, 1992;
Chopra, 1997;Hetland, 2006;Hetland and Hager, 2006;
Meade et al.,2013).
The time-dependent viscoelastic response is calculated
using the correspondence principle, which allows any linear
viscoelastic problem to be written in the form of an elastic
problem in the Laplace domain (e.g., Nur and Mavko, 1974;
Savage and Prescott, 1978;de Hoog et al., 1982;Hetland and
Hager, 2005).
4P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

To approximate finite rupture sources, we integrate over
point sources using a 2D Legendre–Gaussian quadrature rule
(e.g., Hildebrand, 1987). The deformation due to each point
source can be simply summed with Gaussian weights to
obtain the deformation due to a finite source. The number of
earthquake sources (n2) required to accurately represent a
particular finite source is based on a heuristic scaling
ncL=d (Klöckner et al., 2013), in which dis the distance
of the closest observation point to the finite source, Lis the
length of the finite source, and cis a constant. We use c3,a
value at which the mean percentage difference in displacement
magnitude from an equivalent elastic finite source solution
(Okada, 1992)is<0:2% immediately after an earthquake
in a square area of 2L×2Laround the fault at the surface.
Here, we use an idealized two-layer rheology structure
(schizosphere and plastosphere), in which the upper elastic
layer is 15 km thick, and earthquakes rupture through
this entire layer. The lower layer is a Burgers viscoelastic
half-space with a transient Kelvin viscosity ηKand a long-
term Maxwell viscosity ηM(Fig. 3). Elastic moduli of
λμ3×1010 Pa are assumed in the elastic layer and
in the Burgers viscoelastic layer. More complicated models
incorporating three rheological layers and viscous shear
zones have been considered in the previous studies of post-
seismic deformation along the NAF (e.g., Hearn et al., 2009;
Yamasaki et al., 2014;Hearn and Thatcher, 2015). Here, the
use of a simple two-layer model is phenomenologically mo-
tivated, as we are interested in finding the simplest model that
can explain the available data. In 2D, this two-layer model can
explain the agreement between geodetic slip-deficit rates and
geologic slip-rate estimates across 15 strike-slip faults world-
wide (Meade et al., 2013).
To do these calculations in practice, we rotate each fault
segment into an oblique Mercator projection so that its strike
is parallel to the xaxis and calculate the viscoelastic effects
of the earthquakes along individual fault segments
vi
VEηM;ηK;t−ti
eq(Meade and Loveless, 2009). The mean
earthquake cycle velocities 
vi
VEηM;ηK;Tiare given by the
difference between the displacements dat the beginning and
end of the earthquake cycle divided by the duration of the
earthquake cycle Ti:
EQ-TARGET;temp:intralink-;df9;313;659 
vi
VEηM;ηK;Tidi
VEηM;ηK;Ti−di
VEηM;ηK;0
Ti
:9
The North Anatolian Fault
Geodetic Observations of Preseismic and Postseismic
Deformation
In anticipation of potential future earthquakes, survey-
mode GPS campaigns were conducted around the western
part of the NAF in the Sea of Marmara region in the decade
before the İzmit earthquake. The pre-earthquake velocity
field used here consists of 122 stations (Fig. 1;Reilinger
et al., 2006). For simplicity, we treat this campaign-mode
velocity field observed from 1988 to 1999 as representative
of the instantaneous velocity field on 1 January 1997. Addi-
tionally, a few permanent GPS stations were recording defor-
mation at the time of the İzmit earthquake (Ergintav et al.,
2009) and continued to record postseismic deformation after
the earthquake. Immediately after the earthquake, more con-
tinuous stations were deployed (Ergintav et al., 2009). A 7-yr
position time series has been published from GPS station
TUBI. This station was moving steadily prior to the earth-
quake (Fig. 4a,b; from fig. 4a of Ergintav et al., 2009). In the
weeks immediately after the earthquake, the station moved
rapidly (>100 mm=yr) to the east, but its eastward velocity
decayed to ∼10 mm=yr after two years (Fig. 4).
Because a linear interseismic trend has been subtracted
from the TUBI time series (Ergintav et al., 2002,2009)
(Fig. 4a), this time series records a postseismic perturbation
to steady interseismic motion. In other words, if we integrate
equation (2) in time, we obtain displacements
EQ-TARGET;temp:intralink-;df10;313;250
dtvBt−vSDtv_
εtZt
0
vVEηM;ηK;t−teqdt
−
vVEηM;ηK;Tt: 10
The linear terms vBt,vSDt,v_εt, and 
vVEηM;ηK;Tthave
been subtracted from the time series (Fig. 4b), so we compare
the TUBI position time series in the east direction with
dfeastg
VE tRt
0vfeastg
VE ηM;ηK;t−teq dt, the eastward displace-
ments due to only the viscoelastic perturbation term. We do
not take into account the (nonlinear) viscoelastic effects of
the historic earthquakes in Figure 5on the TUBI time series
for simplicity and because the 1999 İzmit earthquake domi-
nates the nonlinear viscoelastic signal. Across all viscosity
structures tested, the maximum east displacement due to
Layer 2
Layer 1
Elastic
Burgers
15 km
Figure 3. Model geometry cross section and rheologies used in
this study.
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 5
BSSA Early Edition

dfeastg
VE t2007from the penultimate earthquake, in 1967,
is 2.4 mm, <3% of the total displacement at TUBI.
Earthquake History along the NAF
Because the region was colonized by the Greeks in the sev-
enth century B.C.E. and was the seat of the Roman, Byzantine,
and Ottoman Empires since the fourth century C.E., the earth-
quake history along the western NAF over the past 2000 yrs is
relatively well known from written records (Ambraseys, 2002).
In the Sea of Marmara region in particular, 55 Ms≥6:8earth-
quakes have been identified since 1 B.C.E. (Ambraseys, 2002).
For the purposes of this article, we have included the effects of
the earthquakes that likely occurred along the strands included
in the block model geometry (Fig. 5;Ambraseys and Jackson,
2000;Ambraseys, 2002). The block geometry (Fig. 1)isbased
on a detailed fault map of Turkey (R. Reilinger, personal
comm., 2013). The historic earthquakes included in the visco-
elastic block models and their parameters are listed in Table 1.
The effects of the 1949, 1992, 1971, and 1966 earthquakes are
not included because they occurred to the east of our study area,
beyond the eastern extent of the 1939 rupture (Barka, 1992,
1996;Stein et al., 1997).
For segments of the NAF that have ruptured multiple
times over the past two millennia, we use the timing of the
repeated ruptures to estimate characteristic recurrence inter-
vals. There are records of earthquakes occurring near the
1999 İzmit earthquake in 68, 268, 478, 1719, and 1894 (Am-
braseys, 2002;Drab et al., 2015). Based on the more recent
events, we use a recurrence interval of T100 yrs for these
İzmit-like earthquakes. For fault segments in the Sea of Mar-
mara region without a recorded pattern of repeated ruptures,
we assume T500 yrs. The exceptions are the 1 B.C.E. and
121 C.E. earthquakes, for which we assume recurrence inter-
vals of 2050 yrs, and the 1296 and 1419 events, for which we
assume recurrence intervals of 1000 yrs, assuming that they
may reoccur soon but have not done so yet. Along the central
NAF, prior to the 1999 event, seven earthquakes of Mw>6:8
have ruptured the fault in 1939, 1942, 1943, 1944, 1951,
1957, and 1967, largely from east to west. Based on earth-
quake history along the central NAF (Barka, 1992,1996), we
use T400 yrs for these most recent earthquakes.
The average slip magnitude estimates for earthquakes
that occurred before 1939 are based on estimated surface-
wave magnitudes (Ambraseys and Jackson, 2000;Ambra-
seys, 2002). We treat these surface-wave magnitudes as
proxies for moment magnitudes and calculate average slip us-
ing a shear modulus of μ3×1010 and the fault geometry in
Figure 1. For the 1894 earthquake, we assume the moment
magnitude of the 1999 İzmit earthquake (Mw7.4; Barka, 1999;
Ambraseys, 2001). For the earthquakes from 1939 to 1967, we
calculate the average slip for each earthquake using the seismic
moments reported in previous viscoelastic studies of the NAF
(Lorenzo-Martín et al., 2006). We assume uniform slip along
the entire length of each historical rupture (Table 1).
We have also included hypothetical ancient earthquakes
at 1 B.C.E. on two segments of the two southern strands of the
NAF in the Sea of Marmara (Fig. 5; Table 1). The removal of
these hypothetical earthquakes from the models does not sub-
stantially change the conclusions in this article. However, be-
cause these fault segments are in a tectonically active region
and to our knowledge there is no evidence that they accommo-
date substantial creep or have ruptured in recent historical earth-
quakes (Ambraseys and Jackson, 2000;Ambraseys, 2002), we
assume that they have ruptured within the last few thousand
years and may now be late in the earthquake cycle.
Viscoelastic Modeling of the NAF Earthquake Cycle
Modeling the Postseismic Data from GPS Station
TUBI
We found the viscosity structure that best explains the
postseismic GPS data from TUBI, a Maxwell viscosity ηM
1018:6Pa· s and a Kelvin viscosity ηK1018:0Pa·s (Fig. 4a),
by a grid search over Maxwell and Kelvin viscosities in the
1017:0to 1023:0Pa·s range. We present residuals in terms of a
mean residual improvement (MRI) percentage over an elastic
model:
1998 2000 2002 2004 2006
0
20
40
60
80
t (yrs)
d (mm)
1999 Mw=7.4 Izmit earthquake
TUBI
(a)
(b)
Figure 4. (a) Position time series from GPS station TUBI for the
year and a half before and seven years after the 1999 Mw7.4 İzmit
earthquake (from fig. 4a of Ergintav et al., 2009). Vertical gray
dashed line indicates the time of the earthquake. The black line
shows the model that best explains the time series, a Maxwell vis-
cosity ηM1018:6Pa·s and a Kelvin viscosity ηK1018:0Pa·s,
assuming uniform slip of 2.83 m. (b) Modeled rupture extent of
the 1999 Mw7.4 İzmit earthquake and the location of TUBI.
6P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

EQ-TARGET;temp:intralink-;df11;55;450MRIηM;ηK−jrVEηM;ηKj −jrEj
jrEj×100 11
(Fig. 6a), in which rVEηM;ηKare the residuals for the vis-
coelastic models with viscoelastic parameters ηM,ηK, and rE
are the residuals for an elastic model. Models that explain the
data better than an elastic model will have a large and pos-
itive MRI; models that do not explain the data as well as an
elastic model will have a negative MRI. In the case of the
TUBI postseismic data, jrVEjis the mean of the absolute
values of the displacements (67.5 mm) because the displace-
Table 1
Detailed Parameters of the Earthquakes Taken into Account in the Viscoelastic Block Models
Length of
Rupture (km) M0(N·m) Mw
Average
Slip (m)
Recurrence
Interval (yr) References
1 January 1 B.C.E.
(south)
67 3:16 ×1019 7.0 1.0437 2050 *
1 January 1 B.C.E.
(north)
102 3:16 ×1019 7.0 0.6910 2050 *
1 January 121 48 1:26 ×1020 7.4 5.8822 2050 Ambraseys and Jackson (2000) and Ambraseys (2002)
1 September 1065 36 1:59 ×1019 6.8 0.9652 1000 Ambraseys and Jackson (2000) and Ambraseys (2002)
1 June 1296 46 3:16 ×1019 7.0 1.5354 1000 Ambraseys and Jackson (2000) and Ambraseys (2002)
15 March 1419 49 6:31 ×1019 7.2 2.8636 1000 Ambraseys and Jackson (2000) and Ambraseys (2002)
10 September 1509 95 6:31 ×1019 7.2 1.4772 600 Ambraseys and Jackson (2000) and Ambraseys (2002)
10 May 1556 52 6:31 ×1019 7.2 2.7174 600 Ambraseys and Jackson (2000) and Ambraseys (2002)
6 March 1737 37 3:16 ×1019 7.0 1.8893 500 Ambraseys and Jackson (2000) and Ambraseys (2002)
22 May 1766 40 4:47 ×1019 7.1 2.4295 500 Ambraseys and Jackson (2000) and Ambraseys (2002)
5 August 1766 54 1:26 ×1020 7.4 5.1916 500 Ambraseys and Jackson (2000) and Ambraseys (2002)
28 February 1855 55 4:47 ×1019 7.1 1.8175 500 Ambraseys and Jackson (2000) and Ambraseys (2002)
10 July 1894 99 8:91 ×1019 7.3 2.8259 100 Barka (1999)
9 August 1912 70 8:91 ×1019 7.3 2.8471 400 Ambraseys and Jackson (2000) and Ambraseys (2002)
26 December 1939 263 4:11 ×1020 7.7 3.4679 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
20 December 1942 44 1:74 ×1019 6.8 0.8776 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
26 November 1943 270 2:51 ×1020 7.6 2.0665 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
1 February 1944 101 1:48 ×1020 7.4 3.2406 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
13 August 1951 38 2:12 ×1019 6.9 1.2237 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
8 March 1953 47 4:47 ×1019 7.1 2.1193 400 Ambraseys and Jackson (2000) and Ambraseys (2002)
26 May 1957 31 1:35 ×1019 6.7 0.9781 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
22 July 1967 61 2:82 ×1019 7.0 1.0186 400 Barka (1992,1996) and Lorenzo-Martín et al. (2006)
*Hypothetical ancient earthquakes that are not in the historic record.
Figure 5. Map of the locations and sizes of the historic earthquakes included in the viscoelastic block models. For the purposes of this
article, we have included the effects of only the historical earthquakes that likely occurred along the strands included in the block model
geometry (Barka, 1992,1996;Ambraseys and Jackson, 2000;Ambraseys, 2002). The detailed model parameters of these earthquakes are
listed in detail in Table 1.
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 7
BSSA Early Edition

ments due to the postseismic perturbation only for an elastic
model are 0.
The model with the best-fit viscosity structure
(ηM1018:6Pa·s and ηK1018:0Pa·s) explains the post-
seismic time series with a mean residual displacement of
3.27 mm, which corresponds to an MRI of 95.16% (Figs. 4a
and 6a). Holding the best-fit Kelvin viscosity constant, an in-
crease in Maxwell viscosity to ηM1019:0Pa·s decreases the
MRI to 79.71% (mean residual displacement of 13.96 mm),
whereas a decrease in Maxwell viscosity to ηM1018:0Pa·
s decreases the MRI to 37.25% (mean residual displacement of
42.36 mm) (Fig. 6a). Overall, mean residual displacements are
less sensitive to changes in Kelvin viscosity; holding the best-
fit Maxwell viscosity constant, an increase in Kelvin viscosity
to ηK1019:0Pa·s corresponds to an MRI of 80.27% (mean
residual displacement of 13.31 mm), and a decrease to ηK
1017:0Pa·s corresponds to an MRI of 90.92% (mean residual
displacement of 4.00 mm) (Fig. 6a).
Modeling the Pre-İzmit Earthquake Interseismic
Velocity Field
We consider 3D block models (Fig. 1) taking into
account the viscoelastic effects of historical earthquakes
for Maxwell and Kelvin viscosities ranging from 1017:0to
1023:0Pa·s. These block models also incorporate homog-
enous internal block strain (e.g., Meade and Loveless, 2009),
and we enforce three tensile slip-rate constraints on the cen-
tral and southern strands of the NAF in the Sea of Marmara to
damp fault normal motion. We summarize the viscoelastic
block model results (Figs. 7–10) in six major points.
1. In the models considered here, fault-slip-deficit rate es-
timates and block model residual velocities are most
sensitive to variations in Maxwell viscosity (Fig. 9). Slip-
deficit rate estimates along the central and eastern NAF
may vary by as much as ∼23% (4–5mm=yr), depending
on the assumed Maxwell viscosity (Fig. 9), whereas var-
iations in Kelvin viscosity in the 1017:0to 1023:0Pa·s
range lead to changes of less than 3%–4% (<∼1mm=yr)
in estimated slip-deficit rates along the central NAF. The
relative insensitivity of these results to Kelvin viscosity is
likely due to the timing of the historic earthquakes; the
most recent earthquake included in the block models
occurred in 1967, and the effects of the transient Kelvin
viscosity have largely abated after 30 yrs. Because of the
difference in sensitivity, we present estimated fault-slip-
deficit rates as functions of Maxwell viscosity, at a fixed
ηKof 1019:0Pa·s (Fig. 9).
2. Slip-deficit rate estimates do not vary monotonically
with increases or decreases in assumed Maxwell viscosity
(Fig. 9). Assuming a Maxwell viscosity ηM1020 Pa·s
and a Kelvin viscosity ηK1019 Pa·s, slip-deficit rate es-
timates along the central NAF are ∼22 mm=yr. A decrease
in assumed Maxwell viscosity to ηM1019 Pa·s lowers
slip-deficit rate estimates to ∼21 mm=yr, and a further de-
crease in assumed Maxwell viscosity to ηM1017 Pa·s
raises the estimated slip-deficit rate to 24 mm=yr (Fig. 9).
The reasons why slip-deficit rate estimates are nonmono-
tonic functions of Maxwell viscosity can be seen from
equation (4). The viscoelastic correction added to the
GPS velocity field for a single set of periodic earthquakes
is −vVEηM;ηK;t−teq 
vVEηM;ηK;TThe earth-
17 19 21 23
17
19
21
23
0.5
0.5
0.5
0.5
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
2.0
2.0
2.0
2.0
2.5
17 19 21 23
17
19
21
23
20
20
20
20
20
20
20
20
20
40
40
40
40
40
40
40
40
40
60
60
60
60
60
60
60
60
60
60
80
80
80
80
(a) (b)
Figure 6. (a) Contour plot of mean residual improvement (MRI; equation 11) as a function of assumed viscosity structure for the post-
seismic GPS data from TUBI. The viscosity structure that allows the model to fit the data best, a Maxwell viscosity ηM1018:6Pa·s and a
Kelvin viscosity ηK1018:0Pa·s, is highlighted by a red circle. This model fits the time series with a mean residual displacement of
3.27 mm, which corresponds to an MRI of 95.16%. (b) Contour plot of MRI (equation 11) as a function of assumed viscosity structure
for the interseismic GPS data from 1988 to 1999 (Reilinger et al., 2006), before the İzmit earthquake. The viscoelastic block models best
explain the GPS velocity field with a Maxwell viscosity ηM1019:0Pa·s and a Kelvin viscosity ηK1019:0Pa·s. This best-fit model is
indicated by a red circle and explains the corrected interseismic velocity field vηM;ηK(equation 8) with a mean residual velocity of
3:14 mm=yr, which corresponds to an MRI of 2.73%.
8P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

quakes we take into account in these models (Fig. 5;
Table 1) took place between 1 B.C.E. and 1967, and there-
fore 30 <t−teq <1997 yrs. For low viscosities
(ηM<1019 Pa·s; ηK<1019 Pa·s), after ∼100 yrs, the
first term −vVEηM;ηK;t−teq ≈0because all stresses
are rapidly relaxed, and the mean velocity term

vVEηM;ηK;Tdominates the viscoelastic correction. As
a result, the viscoelastic correction added to the GPS veloc-
ity field is in the same direction as the near-fault velocities,
increasing their magnitudes and leading to slip-deficit rate
estimates that are generally faster than elastic block model
estimates (Fig. 9).
For high viscosities (ηM>1020 Pa·s; ηK>1020 Pa·s),
the magnitudes of the viscoelastic corrections are small
compared tothe magnitude ofthe observed GPS velocities.
The mean magnitude of the viscoelastic corrections across
all stations for viscosity structures with ηM>1020 Pa·s
and ηK>1020 Pa·s is less than 0:4mm=yr (<3% of the
mean magnitude GPS station velocity). As a result, the
estimated slip-deficit rates approach elastic block model
slip-deficit rates for these high viscosities (Fig. 9).
The slip-deficit rate estimates assuming midrange viscos-
ities (1018 Pa·s <ηM<1020 Pa·s, 1018 Pa·s <ηK<
1020 Pa·s) are perhaps the most interesting (Fig. 9). These
slip-deficit rate estimates depend on the relative magni-
tudes of the two terms in the viscoelastic corrections for
each earthquake. For earthquakes that occurred more than
a few centuries ago, −vVEηM;ηK;t −teq≈0and

vVEηM;ηK;Tare the larger magnitude terms. In this
case, for the same reason as low-viscosity cases, the slip-
Figure 7. (a) Observed (blue) and modeled (red) interseismic GPS velocity fields for the best-fit viscosity structure highlighted in Fig-
ure 6b (Maxwell viscosity ηM1019:0Pa·s and a Kelvin viscosity ηK1019:0Pa·s). The observed velocity field shown here is the cor-
rected interseismic velocity field vηM;ηK(equation 8). (b) Residual velocities for the case shown in (a). Note the different scale from (a).
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 9
BSSA Early Edition

Figure 8. The components of the modeled interseismic velocity field (equation 2) for the best-fit viscoelastic block model (Maxwell
viscosity ηM1019:0Pa·s and a Kelvin viscosity ηK1019:0Pa·s), with velocity magnitude and direction shown with white arrows and the
logarithm of velocity magnitude shown in color to emphasize subtle spatial variations. (a) Velocities due to long-term block motion, (b) the
viscoelastic effects of the most recent earthquake along the fault segment, (c) the velocities due to the accumulated slip deficit, (d) the mean
velocity throughout the earthquake cycle, and (e) the velocities due to the homogenous intrablock strain. Interseismic velocities (f) are
modeled as the sum of the velocity components in (a), (b), (c), and (e) with the mean velocity throughout the earthquake cycle velocity
(d) subtracted to ensure that over many earthquake cycles, the displacements everywhere are equal to the long-term block displacements.
Figure 9. Sensitivity of viscoelastic block model slip-deficit rate estimates to variations in assumed Maxwell viscosity at a fixed Kelvin
viscosity of ηK1019 Pa·s for selected fault segments. Dotted gray lines indicate slip-deficit rate estimates from an elastic model with
internal strain. In each panel, elastic slip-deficit rates do not coincide exactly with slip-deficit rates at high Maxwell viscosities because
the Kelvin viscosity ηKis fixed at 1019 Pa·s.
10 P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

deficit rate estimates would likely be faster than elastic
block model estimates. However, the viscoelastic correc-
tions for the more recent 1939–1967 earthquakes are
dominated by −vVE ηM;ηK;t−teq , and therefore the
viscoelastic corrections added to the GPS velocity field for
these earthquakes are in the opposite direction as the near-
fault velocities, decreasing their magnitudes and leading to
slip-deficit rate estimates that are slower than elastic block
model results (Fig. 9).
3. The incorporation of homogeneous internal block strain
has a substantial effect on slip-deficit rate estimates along
the entire fault system. Along the central NAF, slip-deficit
rate estimates from an elastic block model with no inter-
nal strain are ∼27–28 mm=yr, and after incorporating in-
ternal strain, these estimates decrease by ∼20% to
21–22 mm=yr (Fig. 10). Slip-deficit rate variations due to
viscoelastic effects assuming the best-fit viscosity struc-
tures (Fig. 6) are comparatively small (<1–2mm=yr;
Fig. 10) along the central and eastern NAF. In contrast,
the addition of internal block strain leads to an
∼0:5–2:5mm=yr increase in slip-deficit rate estimates
relative to an elastic block model along the northern
strand of the NAF in the Sea of Marmara (Fig. 10).
Variations in slip-deficit rate due to viscoelastic effects
across the best-fit models along this northern strand are
of comparable magnitudes (Fig. 10).
4. In the Sea of Marmara region, the variations in estimated
slip-deficit rates are complex functions of viscosity struc-
ture (Figs. 9and 10). After incorporating the effects of
previous earthquakes with the best-fit viscoelastic struc-
tures (Fig. 6b), slip-deficit rate estimates decrease by
1–2mm=yr along the central NAF, but increase on the
northern strand of the western NAF by a more substantial
∼2–3mm=yr (Fig. 9). The slip-deficit rate differential
between the northern Sea of Marmara strand and the cen-
tral NAF is the largest after taking into account both inter-
nal block strain and viscoelastic effects; slip-deficit rate
estimates on the northern strand, less than 50 km from
Istanbul, are ∼20% faster than slip-deficit rate estimates
along the central NAF for viscoelastic block models with
the best-fit viscosity structures (Fig. 6b) but only ∼15%
faster for an elastic model with internal strain (Fig. 10).
In addition, the senses of slip on the two southern Sea of
Marmara strands reverse depending on assumed viscosity
structure. In the elastic limit, the middle strand of the NAF
that runs along the southern coast of the Sea of Marmarais
right lateral with a slip-deficit rate of ∼5mm=yr and the
southernmost strand of the NAF is left lateral with a
slip-deficit rate of <1mm=yr. For Maxwell viscosities
ηM<1020:0Pa·s, the sense of slip on the southernmost
strand becomes left lateral, and for Maxwell viscosities
ηM<1018:7Pa·s, the sense of slip on the middle strand
Figure 10. Viscoelastic block model slip-deficit rate estimates along strike assuming the best-fit viscosity structures (Fig. 6):
ηM1019:0Pa·s, ηK1019:0Pa·s (blue), and ηM1018:6Pa·s, ηK1018:0Pa·s (red). For comparison, slip-deficit rates from an elastic
block model incorporating internal strain are plotted in gray, and those for an elastic block model with no internal strain are in green. For
simplicity, only the slip-deficit rate estimates on the northernmost segments of the fault in the Sea of Marmara region are shown. White circles
labeled (a) indicate Meghraoui et al. (2012), (b) Dolan et al. (2009) and Uçarkuş(unpublished thesis, 2010; see Data and Resources),
(c) Pucci et al. (2008), (d) Kozacıet al. (2007), (e) Hubert-Ferrari et al. (2002), (f) Kozacıet al. (2009), and (g) Kondo et al. (2004),
and corresponding error bars represent geologic slip-rate estimates and reported uncertainties.
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 11
BSSA Early Edition

becomes right lateral. The trade-off in slip sense between
the two southern strands is largely due to the complicated
fault geometry in this region and sparse geodetic obser-
vations due to the location of the Sea of Marmara (Fig. 1).
The most distinct gradient in GPS velocities occurs across
the northern strand of the NAF (Fig. 1); farther south, the
velocity gradient is less distinct, allowing a trade-off in
slip sense between the two southern NAF strands.
5. Overall, the viscosity structure that best explains the inter-
seismic GPS data from 1988 to 1999 (Reilinger et al.,
2006), before the İzmit earthquake, is a Maxwell viscosity
ηM1019:0Pa· s and a Kelvin viscosity ηK1019:0Pa·s
(Figs. 6b,7,and8). This model fits the corrected interseis-
mic velocity field vηM;ηK(equation 9) with a mean
residual velocity of 3:14 mm=yr, which corresponds to
an MRI (equation 10) of 2.73% (Figs. 6b and 7).
6. Slip-deficit rate estimates and changes in block model re-
siduals are most sensitive to the earthquakes that occurred
since 1500 C.E. Removing the effects of the pre-1500 C.E.
earthquakes does not change the major conclusions of this
article. Estimated slip-deficit rates change by less than
∼2mm=yr (ⒺFig. S1, available in the electronic supple-
ment to this article) and the best-fit viscosity structure
for the interseismic GPS data changes slightly from ηM
1019:0Pa·s and ηK1019:0Pa·s to ηM1018:8Pa·s
and ηK1019:0Pa·s (ⒺFig. S2).
Discussion
We have systematically modeled both pre- and post-
İzmit observations with two-layer Burgers viscoelastic
models with Maxwell and Kelvin viscosities ranging from
1017:0to 1023:0Pa·s. The viscosity structure that best ex-
plains the TUBI postseismic data is a Maxwell viscosity
ηM1018:6Pa·s and a Kelvin viscosity ηK1018:0Pa·s
(Fig. 6a), and the viscosity structure that best explains the
interseismic data is a Maxwell viscosity ηM1019:0Pa·s
and a Kelvin viscosity ηK1019:0Pa·s (Fig. 6b).
AcomparisonoftheMRI values for the pre- and post-
earthquake data as a function of viscosity structure (Fig. 6)
reveals that the two best-fit models are remarkably similar, and
both sets of data may be explained with a single geodetically
constrained Burgers rheology of ηM1018:6–1019:0Pa·s
and ηK1018:0–1019:0Pa·s. The variation in slip-deficit rate
estimates along the central NAF for viscosities within this best-
fit range is <1mm=yr (Fig. 10). An elastic block model that
incorporates homogenous internal block strain, but does not
incorporate viscoelasticity, yields slip-deficit rate estimates
that are 1:0–1:5mm=yr faster than the best-fit viscoelastic
models along the central NAF (Fig. 9). For comparison, an
elastic block model that does not incorporate both homog-
enous strain and viscoelasticity leads to slip-deficit rate esti-
mates that are 5mm=yr faster along the central NAF than an
elastic model incorporating internal strain (Fig. 9).
The viscoelastic block model results (Figs. 9and 10)sug-
gest that slip-deficit rate estimates along the central NAF
(31° E–38° E; Fig. 1) with a geodetically constrained rheology
of ηM1018:6–1019:0Pa·s and ηK1018:0–1019:0Pa·s are
only 1–2mm=yr (5%–10%) slower than those of an analo-
gous elastic block model that incorporates internal block strain
(Fig. 10). Conversely, on the northern strand of the NAF in
the Sea of Marmara, slip-deficit rate estimates with the
geodetically constrained rheology are significantly faster
(2–3mm=yr or 10%–15%) than slip-deficit rates from an
elastic model that incorporates internal strain. Slip-deficit rate
estimates along the northern strand of the NAF, after account-
ing for viscoelastic effects with the geodetically constrained
rheology, are the fastest in the entire fault system
(27–28 mm=yr; Fig. 10). In other words, the viscoelastic
effects of historical earthquakes, when not accounted for, may
partially mask very fast (∼27–28 mm=yr) slip-deficit rates
along the northern strand of the NAF. The slip-deficit rate es-
timates along the northern strand of the NAF are especially
significant, because it runs less than 50 km from Istanbul,
acitywithmorethan14millionpeople.
The geodetically constrained rheology can explain both
the pre-İzmit nominally interseismic (late in the earthquake
cycle) GPS velocities and the postseismic (early in the earth-
quake cycle) displacements from GPS station TUBI (Fig. 6).
The goal of explaining geodetic observations from across the
earthquake cycle is to develop unified earthquake cycle mod-
els that can simultaneously provide a physical explanation
for both rapid postseismic deformation and more slowly
varying, nominally interseismic, deformation (Hetland,
2006;Meade et al., 2013). Previous viscosity structures
estimated based on both pre- and postearthquake geodetic
observations along the NAF (transient relaxation timescale
τKηK=μKof 2–5 yrs, corresponding to a Kelvin viscosity
ηKof ∼0:8×1018 to ∼1:9×1018 Pa·s for the shear modulus
used here, and a steady timescale of τMηM=μMof more
than 400 yrs, corresponding to a Maxwell viscosity ηMof
∼1:5×1020 Pa·s; Hetland, 2006) may be slightly higher
than the best-fit viscosities found here (Fig. 6) but are not
directly analogous to the present study, because they are
based on 2D modeling without a block model framework or
internal block strain. To explain both the postseismic defor-
mation and the pre-earthquake velocity gradient across the
NAF observed before 1999, a subsequent study suggested
that a combination of afterslip and a Burgers rheology with
two viscosities (2–5×1019 Pa·s and at least 2×1020 Pa·s)
might be necessary (Hearn et al., 2009).
Geodetic observations across strike-slip faults from both
early and late in the earthquake cycle now exist at several
locations worldwide. In Tibet, Interferometric Synthetic
Aperture Radar (InSAR) and GPS measurements across the
Kunlun fault in Tibet reveal localized velocity profiles with
differential velocities of ∼3and ∼12 mm=yr across the faults
prior to the 1997 Mw7.6 Manyi (Bell et al., 2011) and 2001
Mw7.8 Kokoxili (Zhang et al., 2004) earthquakes, respec-
tively. After these Tibet earthquakes, GPS and InSAR data
recorded postseismic motions up to 10 times larger in mag-
nitude than pre-earthquake velocities (Ryder et al., 2007,
12 P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

2011;Zhang et al., 2009). In 2D, geodetic data from both
early and late in the earthquake cycle in Tibet have been
modeled with layered Maxwell models (DeVries and Meade,
2013), and more globally, geodetic data from across 15
strike-slip faults worldwide are consistent with a 2D, two-
layer Burgers model (Meade et al., 2013). More recently,
localized shear zones have been used to explain representa-
tive velocity profiles before and after large strike-slip earth-
quakes (Hearn and Thatcher, 2015) as well as data from
before and after the İzmit earthquake (Yamasaki et al., 2014).
Along the central and eastern NAF, previous geodetic
slip-deficit rate estimates (e.g., Reilinger et al., 1997,2006;
McClusky et al., 2000) were ∼1–10 mm=yr faster than geo-
logic slip-rate estimates (Fig. 10; e.g., Hubert-Ferrari et al.,
2002;Okumura et al., 2003;Kondo et al., 2004;Kozacıet al.,
2007,2009). This discrepancy may be partially explained if
the geologic slip-rate estimates are considered to be mini-
mum bounds (Kozacıet al., 2007;Dolan, 2009). However,
here, after taking into account internal block strain and the
viscoelastic effects of historic earthquakes along the NAF, the
discrepancy between geodetic slip-deficit rate and geologic
slip-rate estimates decreases along the central NAF; indeed,
the geodetic slip-deficit rate is, within error, the same as the
fastest geological slip rate of 21:55:5mm=yr (Kozacı
et al., 2007) along the central NAF (Fig. 10), suggesting that
there may be no discrepancy between the different rates
along this part of the system.
Finally, the NAF is often considered to be a seismically
active analog of the SAF system in California; the fault sys-
tems are of similar size and both delineate major transform
plate boundaries. Recent viscoelastic block modeling studies
focused on California have suggested that faults that are late
in the earthquake cycle may have higher slip rates than pre-
viously estimated in classic block models (Johnson et al.,
2007;Chuang and Johnson, 2011;Hearn et al., 2013;Tong
et al., 2014). These results are perhaps analogous to the results
of the present study along the western NAF, where slip-rate
estimates from a viscoelastic block model are 2–5mm=yr
higher than those from an elastic model (Fig. 10).
Conclusions
GPS data from both before and after the 1999 İzmit earth-
quake may be simultaneously explained with a two-layer
Burgers rheology incorporated into 3D block models with
ηM1018:6–1019:0Pa·s and ηK1018:0–1019:0Pa·s in the
lower layer. Viscoelastic block models of the interseismic
velocity field observed prior to the 1999 earthquake fit the
GPS data best with a viscosity structure of ηM1019:0Pa·s
and ηK1019:0Pa·s, and the TUBI postseismic data are
best explained by a two-layer viscoelastic model with ηM
1018:6Pa·s and ηK1018:0Pa·s. In addition to a unified de-
scription of surface deformation prior to and after a large
strike-slip earthquake, these viscoelastic block model results
suggest that: (1) the fastest slip-deficit rate estimates along
the entire fault system (∼27–28 mm=yr) occur along the
northern strand of the NAF in the Sea of Marmara, less than
50 km from Istanbul; (2) slip-deficit rate estimates do not
vary monotonically with Maxwell viscosity along the central
and eastern NAF; (3) the senses of slip on the two NAF
strands in the southern Sea of Marmara region reverse de-
pending on assumed Maxwell viscosity; (4) slip-deficit rate
estimates from viscoelastic block models with a geodetically
constrained rheology along the central and eastern NAF are
1–2mm=yr slower than equivalent elastic models; and
(5) after taking into account internal block strain and the vis-
coelastic effects of historic earthquakes with the best-fit vis-
cosities estimated here, the discrepancy between the geodetic
slip-deficit rate estimates and geologic slip-rate estimates de-
creases along the central NAF.
Data and Resources
All data used in this article came from published sources
listed in the references. The computations in this article were
run on the Odyssey cluster supported by the Faculty of Arts
and Sciences (FAS) Division of Science Research Computing
Group at Harvard University. This study used the following
numerical inverse Laplace transform written by K. J. Hollen-
beck in 1998, INVLAP.M: A MATLAB function for numeri-
cal inversion of Laplace transforms by the de Hoog algorithm
(https://www.mathworks.com/matlabcentral/answers/uploaded_
files/1034/invlap.m;, last accessed November 2016). Finally,
the detailed citation for the reference Uçarkuş(unpublished
thesis, 2010) in the main text is G. Uçarkuş(2010), Active
faulting and earthquake scarps along the North Anatolian
fault in the Sea of Marmara, unpubl. Ph.D. Thesis, Istanbul
Technical University, Istanbul, Turkey.
Acknowledgments
We thank Jeff Freymueller, an anonymous reviewer, and Associate
Editor William Hammond for thoughtful reviews that led to substantial im-
provements. This work was supported by Harvard University and the De-
partment of Energy Computational Science Graduate Fellowship Program of
the Office of Science and National Nuclear Security Administration in the
Department of Energy under Contract DE-FG02-97ER25308.
References
Ambraseys, N. (2001). The earthquake of 10 July 1894 in the Gulf of İzmit
(Turkey) and its relation to the earthquake of 17 August 1999, J. Seis-
mol. 5, 117–128.
Ambraseys, N. (2002). The seismic activity of the Marmara Sea region over
the last 2000 years, Bull. Seismol. Soc. Am. 92, no. 1, 1–18.
Ambraseys, N. N., and J. A. Jackson (2000). Seismicity of the Sea of
Marmara (Turkey) since 1500, Geophys. J. Int. 141, F1–F6.
Bakun, W.H., and A. G. Lindh (1985). The Parkfield, California, earthquake
prediction experiment, Science 229, no. 4714, 619–624.
Barka, A. (1992). The North Anatolian fault zone, special issue, Ann. Tect.
IV (Suppl.), 164–195.
Barka, A. (1996). Slip distribution along the North Anatolian fault
associated with the large earthquakes of the period 1939 to 1967, Bull.
Seismol. Soc. Am. 86, no. 5, 1238–1254.
Barka, A. (1999). The 17 August 1999 İzmit earthquake, Science 285,
no. 5435, 1858–1859.
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 13
BSSA Early Edition

Bell, M. A., J. R. Elliott, and B. E. Parsons (2011). Interseismic strain
accumulation across the Manyi (Tibet) prior to the 1997 Mw7.6 earth-
quake, Geophys. Res. Lett. 38, L24302, doi: 10.1029/2011GL049762.
Bürgmann, R., S. Ergintav, P. Segall, E. Hearn, S. McClusky, R. E. Reilinger,
H. Woith, and J. Zchau (2002). Time-dependent distributed afterslip on
and deep below the İzmit earthquake rupture, Bull. Seismol. Soc. Am. 92,
no. 1, 126–137.
Chopra, P. N. (1997). High-temperature transient creep in olivine rocks,
Tectonophysics 279, 93–111.
Chuang, R. Y., and K. M. Johnson (2011). Reconciling geologic and
geodetic model fault slip-rate discrepancies in southern California:
Consideration of nonsteady mantle flow and lower crustal fault creep,
Geology 37, no. 7, 627–630.
de Hoog, F. R., J. H. Knight, and A. N. Stokes (1982). An improvedmethod
for numerical inversion of Laplace transforms, SIAM J. Sci. Stat.
Comput. 3, 357–366.
DeVries, P. M. R., and B. J. Meade (2013). Earthquake cycle deformation in
the Tibetan plateau with a weak mid-crustal layer, J. Geophys. Res.
118, 3101–3111.
Dolan, J. F. (2009). Accelerated strain accumulation along the western North
Anatolian fault: A possible precursory signal to an impending earth-
quake, American Geophysical Union Fall Meeting Abstract T13D-
1920, San Francisco, California, 14–18 December.
Dolan, J., Ö. Kozacı, and R. Hartleb (2009). Paleoseismology of the North
Anatolian fault: Implications for earthquake occurrence and seismic
hazard assessment, Proc. of the International Symposium on Historical
Earthquakes and Conservation of Monuments and Sites in the Eastern
Mediterranean Region, 500th Anniversary Year of the 1509 September
10 Marmara Earthquake,10–12 September 2009, Istanbul Technical
University Press, Istanbul, Turkey, 30–33.
Drab, L., A. Hubert-Ferrari, S. Schmidt, P. Martinez, J. Carlut, and M. El
Ouahabi (2015). Submarine earthquake history of the Çınarcıkseg-
ment of the North Anatolian Fault in the Marmara Sea, Turkey, Bull.
Seismol. Soc. Am. 105, no. 2A, 622–645.
Ergintav, S., R. Bürgmann, S. McClusky, C. Çakmak, R. E. Reilinger, O.
Lenk, A. Barka, and H. Özener (2002). Postseismic deformation near
the İzmit earthquake (17 August 1999, M 7:5) rupture zone, Bull.
Seismol. Soc. Am. 92, no. 1, 194–207.
Ergintav, S.,S. McClusky, E. Hearn, R. Reilinger, C. Cakmak, T. Herring, H.
Ozener, O. Lenk, and E. Tari (2009). Seven years of postseismic
deformation following the 1999, M 7:4and M 7:2,İzmit -Duzce,
Turkey earthquake sequence, J. Geophys. Res. 114, no. B07403, doi:
10.1029/2008JB006021.
Fukahata, Y., and M. Matsu’ura (2005). General expressions for internal
deformation fields due to a dislocation source in a multilayered elastic
half-space, Geophys. J. Int. 161, 507–521.
Fukahata, Y., and M. Matsu’ura (2006). Quasi-static internal deformation
due to a dislocation source in a multilayered elastic/viscoelastic
half-space and an equivalent theorem, Geophys. J. Int. 166, 418–432.
Hashima, A., M. Fukahata, C. Hashimoto, and M. Matsu’ura (2014). Quasi-
static strain and stress fields due to a moment tensor in elastic-
viscoelastic layered half-space, Pure Appl. Geophys. 171, 1669–1693.
Hearn, E. H., and W. R. Thatcher (2015). Reconciling viscoelastic models of
postseismic and interseismic deformation: Effects of viscous shear zones
and finite-length ruptures, J. Geophys. Res. 120, no. 4, 2794–2819.
Hearn, E. H., R. Bürgmann, and R. E. Reilinger (2002). Dynamics of İzmit
earthquake postseismic deformation and loading of the Düzce earth-
quake hypocenter, Bull. Seismol. Soc. Am. 92, 172–193.
Hearn, E. H., S. McClusky, S. Ergintav, and R. E. Reilinger (2009). İzmit earth-
quake postseismic deformation and dynamics of the North Anatolian fault
zone, J. Geophys. Res. 114, no. B08405, doi: 10.1029/2008JB006026.
Hearn, E. H., C. T. Onishi, F. F. Pollitz, and W. R. Thatcher (2013). How do
“ghost transients”from past earthquakes affect GPS slip rate estimates
on southern California faults?, Geochem. Geophys. Geosyst. 14, no. 4,
828–838.
Hetland, E. A. (2006). Models of interseismic deformation with an analytic
framework for the inclusion of general linear viscoelastic rheologies,
Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge,
Massachusetts.
Hetland, E. A., and B. H. Hager (2005). Postseismic and interseismic dis-
placements near a strike-slip fault: A two-dimensional theory for gen-
eral linear viscoelastic rheologies, J. Geophys. Res. 110, no. B10401,
doi: 10.1029/2005JB003689.
Hetland, E. A., and B. H. Hager (2006). The effects of rheological layering
on post-seismic deformation, Geophys. J. Int. 166, 277–292.
Hildebrand, F. B. (1987). Introduction to Numerical Analysis, Second Ed.,
Dover Publications, Mineola, New York, 704 pp.
Hilley, G. E., K. M. Johnson, M. Wang, Z.-K. Shen, and R. Bürgmann
(2009). Earthquake-cycle deformation and fault slip rates in northern
Tibet, Geology 37, no. 1, 31–34.
Hubert-Ferrari, A., R. Armijo, G. King, B. Meyer, and A. Barka (2002).
Morphology, displacement, and slip rates along the North Anatolian
fault, Turkey, J. Geophys. Res. 107, no. B10, 2235.
Johnson, K. M, G. E. Hilley, and R. Bürgmann (2007). Influence of lithosphere
viscosity structure on estimates of fault slip rate in the Mojave region of
the San Andreas fault system, J. Geophys. Res. 112, no. B07408
Klöckner, A., A. Barnett, L. Greengard, and M. O’Neil (2013). Quadrature
by expansion: A new method for the evaluation of layer potentials,
J. Comput. Phys. 252, 332–349.
Kondo, H., V. Özaksoy, C. Yildirim, Y. Awata, Ö. Emre, and K. Okumura
(2004). 3D trenching survey at Demir Tepe site on the 1944 Bolu-
Gerede earthquake ruptures, North Anatolian fault system, Turkey,
Seismol. Res. Lett. 75, no. 2, 292.
Kozacı, Ö., J. Dolan, and R. Finkel (2009). A late Holocene slip rate for the
central North Anatolian fault, at Tahtaköprü Turkey, from cosmogenic
10Be geochronology: Implications for fault loading and strain release
rates, J. Geophys. Res. 14, no. B01405, doi: 10.1029/2008JB005760.
Kozacı, Ö., J. Dolan, R. Finkel, and R. Hartleb (2007). Late Holocene slip
rate for the North Anatolian fault, Turkey, from cosmogenic 36Cl geo-
chronology: Implications for the constancy of fault loading and strain
release rates, Geology 35, no. 10, 867–870.
Lorenzo-Martín, F., F. Roth, and R. Wang (2006). Elastic and inelastic trig-
gering of earthquakes in the North Anatolian fault zone, Tectonophy-
sics 424, 271–289.
Matsu’ura, M., and R. Sato (1975). Static deformation due to the fault
spreading over several layers in a multi-layered medium, part II: Strain
and tilt, J. Phys. Earth 23, 1–29.
Matsu’ura, M., and T. Sato (1989). A dislocation model for the earthquake
cycle at convergent plate boundaries, Geophys. J. Int. 96, 23–32.
Matsu’ura, M., D. D. Jackson, and A. Cheng (1986). Dislocation model for
aseismic crustal deformation at Hollister, California, J. Geophys. Res.
91, no. B12, 12,661–12,674.
McCaffrey, R. (2002). Crustal block rotations and plate coupling, in Plate Boun-
dary Zones, S. Stein and J. T. Freymueller (Editors), in Geodyn. Ser.,
Vol. 30, AGU, Washington, D.C., 101–122, doi: 10.1029/GD030p0101.
McClusky, S. C., S. C. Bjornstad, B. H. Hager, R. W. King, B. J. Meade, M.
M. Miller, F. C. Monastero, and B. J. Souter (2000). Global Position-
ing System constraints on plate kinematics and dynamics in the eastern
Mediterranean and Caucasus, J. Geophys. Res. 105, 5695–5719.
Meade, B. J., and B. H. Hager (2005). Block models of crustal motion in
southern California constrained by GPS measurements, J. Geophys.
Res. 110, no. B03403, doi: 10.1029/2004JB003209.
Meade, B. J., and J. P. Loveless (2009). Block modeling with connectedfault-
network geometries and a linear elastic coupling estimator in spherical
coordinates, Bull. Seismol. Soc. Am. 99, no. 6, 3124–3139.
Meade, B. J., B. H. Hager, S. C. McClusky, R. E. Reilinger, S. Ergintav, O.
Lenk, A. Barka, and H. Özener (2002). Estimates of seismic potential
in the Marmara Sea region from block models of secular deformation
constrained by Global Positioning System measurements, Bull. Seis-
mol. Soc. Am. 92, no. 1, 208–215.
Meade, B. J., Y. Klinger, and E. A. Hetland (2013). Inference of multiple
earthquake-cycle relaxation timescales from irregular geodetic sam-
pling of interseismic deformation, Bull. Seismol. Soc. Am. 103, no. 5,
2824–2835.
14 P. M. R. DeVries, P. G. Krastev, J. F. Dolan, and B. J. Meade
BSSA Early Edition

Meghraoui, M., M. E. Aksoy, H. S. Akyüz, M. Ferry, A. Dikbaş, and E.
Altunel (2012). Paleoseismology of the North Anatolian fault at
Guzelkoy (Ganos segment, Turkey): Size and recurrence time of
earthquake ruptures west of the Sea of Marmara, Geochem. Geophys.
Geosyst. 13, no. 4, 1–26.
Nur, A., and G. Mavko (1974). Postseismic viscoelastic rebound, Science
183, 204–206.
Okada, Y. (1992). Interal deformation due to shear and tensile faults in a
half-space, Bull. Seismol. Soc. Am. 82, no. 2, 1018–1040.
Okumura, K., T. K. Rockwell, T. Duman, F. Tokay, H. Kondo, C. Yoldirim,
and V. Ozaksoy (2003). Refined slip history of the North Anatolian fault
at Gerede on the 1944 rupture, American Geophysical Union Fall Meet-
ing Abstract S12B-0384, San Francisco, California, 8–12 December.
Pollitz, F. F. (1992). Postseismic relaxation theory on a spherical earth, Bull.
Seismol. Soc. Am. 82, no. 1, 422–453.
Pollitz, F. F., P. McCrory, J. Svarc, and J. Murray (2008). Dislocation models
of interseismic deformation in the western United States, J. Geophys.
Res. 113, no. B4, doi: 10.1029/2007JB005174.
Pollitz, F. F., P. McCrory, D. Wilson, J. Svarc, C. Puskas, and R. B. Smith
(2010). Viscoelastic-cycle model of interseismic deformation in the
northwestern United States, Geophys. J. Int. 181, no. 2, 665–696.
Pucci, S., P. M. De Martini, and D. Pantosti (2008). Preliminary slip rate
estimates for the Düzce segment of the North Anatolian fault
zone from offset geomorphic markers, Geomorphology 97, no. 3,
538–554.
Reilinger, R., S. C. McClusky, M. B. Oral, R. W. King, M. N. Toksoz,
A. A. Barka, I. Kinik, O. Lenk, and I. Sanli (1997). Global Position-
ing System measurements of present-day crustal movements in the
Arabia-Africa-Eurasia plate collision zone, J. Geophys. Res. 102,
9983–9999.
Reilinger, R., S. McClusky, P. Vernant, S. Lawrence, S. Ergintav, R. Cakmak,
H. Ozener, F. Kadirov, I. Guiliev, R. Stepanyan, et al. (2006). GPS
constraints on continental deformation in the Africa–Arabia–Eurasia
continental collision zone and implications for the dynamics of plate
interactions, J. Geophys. Res. 111, no. B5, doi: 10.1029/2005JB004051.
Reilinger, R. E., S. Ergintav, R. Bürgmann, S. McClusky, O. Lenk, A. Barka,
O. Gurkan, L. Hearn, K. L. Feigl, R. Cakmak, et al. (2000). Coseismic
and postseismic fault slip for the 17 August, M 7:5,İzmit, Turkey
earthquake, Science 289, no. 5484, 1519–1524.
Ryder, I., R. Bürgmann, and F. Pollitz (2011). Lower crustal relaxation
beneath the Tibetan plateau and Qaidam basin following the 2001
Kokoxili earthquake, Geophys. J. Int. 187, 613–630.
Ryder, I., B. Parson, T. J. Wright, and G. J. Funning (2007). Post-seismic
motion following the 1997 Manyi (Tibet) earthquake: InSAR obser-
vations and modeling, Geophys. J. Int. 169, no. 3, 1009–1027.
Sato, R. (1971). Crustal deformation due to dislocation in a multi-layered
medium, J. Phys. Earth 19, no. 1, 31–46.
Sato, R., and M. Matsu’ura (1973). Static deformation due to the fault
spreading over several layers in a multi-layered medium, part I:
Displacement, J. Phys. Earth 21, 227–249.
Sato, T., and M. Matsu’ura (1988). A kinematic model for deformation of
the lithosphere at subduction zones, J. Geophys. Res. 93, no. B6,
6410–6418.
Savage, J. C., and R. O. Burford (1973). Geodetic determination of relative
plate motion in central California, J. Geophys. Res. 78, no. 5, 832–845.
Savage, J. C., and W. H. Prescott (1978). Asthenosphere readjustment and
the earthquake cycle, J. Geophys. Res. 83, no. B7, 3369–3376.
Smith, B. R., and D. T. Sandwell (2006). A model of the earthquake cycle
along the San Andreas fault system for the past 1000 years, J. Geo-
phys. Res. 111, no. B1, doi: 10.1029/2005JB003703.
Stein, R. S., A. A. Barka, and J. H. Dieterich (1997). Progressive failure on
the North Anatolian fault since 1939 by earthquake stress triggering,
Geophys. J. Int. 128, no. 3, 594–604.
Straub, C., H. Kahle, and C. Schindler (1997). GPS and geologic estimates
of the tectonic activity in the Marmara Sea region, NW Anatolia,
J. Geophys. Res. 102, no. B12, 27,587–27,601.
Toksöz, M. N., A. F. Shakal, and A. J. Michael (1979). Space–time migra-
tion of earthquakes along the North Anatolian fault zone and seismic
gaps, Pure App. Geophys. 117, 1258–1270.
Tong, X., B. R. Smith-Konter, and D. T. Sandwell (2014). Is there are discrep-
ancy between geological and geodetic slip rates along the San Andreas
fault system? J. Geophys. Res. 119, no. B010765.
Wang, L., R. Wang, F. Roth, B. Enescu, S. Hainzl, and S. Ergintav (2008).
Afterslip and viscoelastic relaxation following the 1999 M 7.4 İzmit
earthquake from GPS measurements, Geophys. J. Int. 178, 1220–1237.
Yamasaki, T., T. J. Wright, and G. A. Houseman (2014). Weak ductile shear
zone beneath a major strike-slip fault: Inferences from earthquake
cycle model constrained by geodetic observations of the western North
Anatolian fault zone, J. Geophys. Res. 119, 3678–3699.
Zhang, C., J. Cao, and Y. Shi (2009). Studying the viscosity of lower crust of
Qinghai-Tibet plateau according to post-seismic deformation, Sci.
China Earth Sci. 5, no. 3, 411–419.
Zhang, P.-Z., Z. Shen, M. Wang,W. Gan, R. Bürgmann, P. Molnar, Q. Wang,
Z. Niu, J. Sun, J. Wu, et al. (2004). Continuous deformation of the
Tibetan plateau from global positioning system data, Geology 32,
no. 9, 809–812.
Department of Earth and Planetary Sciences
20 Oxford Street
Cambridge, Massachusetts 02138
phoeberobinson@fas.harvard.edu
meade@fas.harvard.edu
(P.M.R.D., B.J.M.)
Research Computing
Harvard University
38 Oxford Street
Cambridge, Massachusetts 02138
plamenkrastev@fas.harvard.edu
(P.G.K.)
Department of Earth Sciences
Zumberge Hall of Science (ZHS)
University of Southern California
3651 Trousdale Parkway
Los Angeles, California, 90089
dolan@usc.edu
(J.F.D.)
Manuscript received 24 February 2016;
Published Online 29 November 2016
A Unified Earthquake Cycle Representation of Pre- and Postseismic Geodetic Observations 15
BSSA Early Edition