3D MODELING OF EARTHQUAKE CYCLES OF THE
XIANSHUIHE FAULT, SOUTHWESTERN CHINA
Li Xiaofan
MEE09177

Supervisor: Bunichiro Shibazaki ABSTRACT
We perform 3D modeling of earthquake generation of the Xianshuihe fault, southwestern China,
which is a highly active strike-slip fault with a length of about 350 km, in order to understandearthquake cycles and segmentations for a long-term forecasting and earthquake nucleation process fora short-term forecasting. Historical earthquake data over the last 300 years indicates repeated periodsof seismic activity, and migration of large earthquake along the fault during active seismic periods. To
develop the 3-D model of earthquake cycles along the Xianshuihe fault, we use a rate- andstate-dependent friction law. After analyzing the result, we find that the earthquakes occur in thereoccurrence intervals of 400-500 years. The earthquake firstly occurs in the middle part of the fault inthe year of 372. Then the second earthquake in the year of 858 occurs only along the main part of thefault but not the 0-100km part. After two earthquake cycles, the fault has been divided into 3 segments,
which means since the third earthquake cycle, earthquake ruptures only occur in some parts of the fault,
but not the whole fault line. This may be caused by the shape of the fault which has some bendingparts. After comparison of the slip velocity at different depths, we find that the largest slip velocity
occurs at the depth of 10km which is the exact depth of the seismic zone where fast rupture occurs.
Keywords: the Xianshuihe Fault, Earthquake Cycle，Rate- and State-dependent Friction Law, 3DModeling.

1. INTRODUCTION
The Xianshuihe fault is located along the eastern margin area of the Tibetan plateau, southwestern
China (Kato et al. 2007). There is a larger-scale fault system which is combined by the Ganzi-Yushu
fault, the Xianshuihe fault, the Anninghe fault, the Zemuhe fault and the Xiaojiang fault from
northwest to southeast and the slip motion releases strain that is related to collision of the Indian andEurasian plates. As a part of this fault system, the Xianshuihe fault is a highly active strike-slip fault
with the length of about 350 km.
The data that can be used to study earthquake recurrence are quite limited because
recurrence times are generally large – a hundred years or more. As to Xianshuihe fault, we have very
accurate earthquake catalogue since 1700. Historical earthquake data over the last 300 years indicates
repeated periods of seismic activity, and migration of large earthquake along the fault during active
seismic periods. 8 earthquakes of Ms ≥ 7 and 22 earthquakes of Ms ≥ 6 had occurred along the fault
since 1700，among which Kangding Ms=7.8 Earthquake was the biggest one. During recent 50 years(1923-1973), 3 earthquakes of Ms ≥ 7.3 had occurred along the Xianshuihe fault.
Figure 1 indicates the space-time distribution of Ms ≥6.8 earthquakes along the 4 main
segments of the Xianshuihe fault.

Assistant researcher, China Earthquake Network Center, Beijing, China.
Researcher, International Institute of Seismology and Earthquake Engineering, Tsukuba, Japan.

1According to this figure, we findthat most of the earthquake
ruptures only occurred along one
segment or within one segment,
while there were some large
earthquakes ruptured across twosegments of the fault. Therefore,
these segments are somehow
independent to each other and also
have relations among them.
We need to understandearthquake
cyclesandsegmentations for a long-term
forecasting,andearthquake
nucleation process for a short-term
forecasting. Purpose of this study
is to develop a 3-D model and thenwe can investigate the nucleationand earthquake cycles along theXianshuihefault.
Modeldeveloped by Kato et al. (2007) isa 2-D model and they do notconsider the fault slip variation
with depth. However, the fault
zone consists of the unstable anddeeper stable zone. Therefore it isnecessary to develop a 3-D model.

Figure 1. Space-time distribution of Ms ≥ 6.8 earthquakes
along the 4 segments of the Xianshuihe fault. The black fault
line is digitized from Kato et. al. (2007) and the colored one isdetermined by geological survey by Deng et al. (1976). The
blue roman numbers indicate the year in which earthquakes
occurred, the earthquake magnitude (Ms) and the numbers inparenthesis mean the length of rupture zones. Red and solidlines show certain and possible rupture zones, respectively. In
the case of the dotted lines, we know time, magnitude and thefault zone in which the earthquake occurred. The lengths are
determined by the scaling law by Fujii and Matsu’ura (2000).

2. MODELING PROCEDURES
To develop a model of earthquake generation processes, firstly, we need to build a 3D mesh which
represents the fault surface. And then, we have to consider a fault constitutive law which represents aphysical property of the fault zone. Next it is necessary to consider a tectonic loading process in whichstress is accumulated by the delay of the fault slip from the average slip rate of the fault zone. After
that, we use the Runge-Kutta method with an adaptive step size control to gain the output of slip
velocity and stress. Compared with observation, it is necessary to change some parameters to approach
the observed historical data.
2.1 Basic equations
2.1.1 Rate-and state-dependent friction

Since earthquakes can be regarded as a fault slip on the fault zone, a frictional constitutive law isimportant for understanding of earthquake generation processes. One representative friction law israte- and state- dependent friction law, introduced by Dieterich (1981) and Ruina (1983).
The Dieterich/Ruina friction law with cut-off velocities proposed by Okubo (1989) is used
to represent the frictional behavior that exhibits velocity weakening at low slip velocity and velocity
strengthening at high slip velocity. Frictional resistance depends on both slip velocity rate and state:(1)   neff   ( n  Pf )

v
v



 v2 

 Dc   *  a ln  1  1  b ln 2 1
(2)

d
v
 1
dt
Dc

(3)

where
is the coefficient of friction; , a and b are experimentally determined constants;
isthe effective normal stress;is the lithostatic pressure;is the pore pressure;is the instantaneous
sliding velocity,is the cut-off velocity to a direct effect,
is a state variable that characterizes theevolving state of the sliding surfaces both the slip- and normal stress- history; andis the cut-off
velocity to an evolution effect. Further,is a critical displacement scaling for the evolution of thestate variable. The state variable
has the dimensions of time and interpreted to be a measure of theage of the population load-supporting contacts, which evolve with contact time, slip and the changesof normal stress (Dieterich, 2009).
From the equation, we can notice that steady state friction decreases with increasing slip
velocity when a-b<0 and increases with increasing slip velocity when a-b>0. If a-b<0, this case iscalled velocity weakening, and it corresponds to the seismogenic zone, where stick and slip occur. On
the other hand, if a-b>0, the slip is stable, which is called velocity strengthening.
2.1.2 Loading processes
The shear stresson the ij-cell on the fault is accumulated by the delay of the fault slip
long-term fault slip, so that

 i , j   ki i , j  j Vpl t  ui , j  sss

is jssG dui , j2 dtfrom(4)where,andare the shear stress, the left-lateral slip at the ij-cell and the long-term
tectonic slip rate at the ij-cell, respectively; G is the shear modulus andis shear wave velocity;is the elastostatic kernel that is the stress at the center of the ij-cell caused by uniform slip
over the-cell. The first term in the equation represents the tectonics loading due to relative platemotion. Since
does not include dynamic stress changes, the second term is necessary torepresent the dumping factor for energy radiation through seismic waves introduced by Rice (1993).
By solving the coupled constitutive equations (1)-(3) and the equation of tectonics loading(4) using the Runge-Kutta method (Press et. al., 1992), the slip velocity and shear stress histories canbe obtained.
2.2 Model Geometry and Discretization
The Xianshuihe fault is simply modeledby a curved fault surface in a three
dimensional
homogeneous
isotropic
elastic half space. The fault line is takenfrom Kato et. al., (2007). We build amodel of earthquakes generation cycles
on a curved surface of 347km×24km,
which represents the Xianshuihe fault
surface. In this model, depth variation in
frictional properties is included. To
represent the slip velocity distribution on
the fault surface, it is discretized intosubfaults, each of which is 0.8 km by 0.8
km in the x and the y directions as shownin Figure 2. The slip velocity and the statevariable are uniform on each subfault.

Figure 2. Meshes for 3-D model of the Xianshuihe Fault
Surface3

2.3 Distribution of frictional properties
Frictional properties control whether stick-slips
or stable slidings occur on the fault. Frictional
properties change with temperature based onlaboratory experiments. Since temperature
distribution on the plate boundary has not been
known yet, we simply assumed that frictionalparameters basically depend on depth (Hori,2006). The depth distribution of the frictionalparameters a, b andis shown in Figure 3. In
horizontal direction there are no variations infriction parameters. The region where a−b isnegative corresponds to the seismogenic zone,
where stick and slip occur.

Figure 3. (a) The depth dependence of a, b anda-b. (b) The depth dependence of the criticaldisplacement.

3. SIMULATION RESULTS

We simulate several earthquake cycles until around 2700 years. Identical earthquake occurs
repeatedly with almost constant recurrence interval (400-500 years).

Figure 4. (a) Slip velocity distribution along the Xianshuihe fault at depth of 10km. Blue and redcolored areas show the low and high velocity areas. The red line on the right is the fault line according
to the distance along the fault. (b) Slip velocity distribution along the Xianshuihe fault at depth of
10km from the year of 1600 to 2300.

4Figure 4a shows calculated slip velocity distribution along the fault at the depth of 10km
during 2694 years along the Xianshuihe fault. Low and high velocity areas (blue and red colored
areas in Figure 4) can be regarded as stick and seismic slip areas, respectively. In the interseismicperiod, most of the seismogenic zone is stick and stress is accumulated. After comparison of the slip
velocity at different depths, we find that the largest slip velocity occurs at the depth of 10km. This
depth is the exact depth of the seismic zone where fast rupture occurs.
According to this slip velocity distribution, we can find the fault line has been divided into
3 segments, which means since the third earthquake cycle, earthquake ruptures only occur in someparts of the fault, but not the whole fault line. That may be caused by the shape of the fault which hassome bending parts, and somehow it is similar to the reality that the Xianshuihe fault is divided
mainly into 4 segments.

Figure 5. Slip velocity along the fault at
different depths from shallow to deep.

Figure 6. Slip velocity > 0.01m/s
distributions along the fault.

Figure 5 shows the slip velocity of 3 cells at different depths from shallow to deep, 2km,10km and 22km, respectively. It is easy to see that larger slip velocity occur at the depth of 10km, andthe slip velocity becomes smaller while the depth increases and decreases. From Figure 6, we canknow where ruptures occur and how ruptures migrate. In this study, the largest velocity is 0.55m/s,
which is close to the coseismic slip velocity 1m/s. We check the cells of which slip velocity is larger
than 0.01m/sec and we can find that the earthquakes occur in the year of 372, 858, 1273, 1764, 2239
and 2684. The occurrence time is 400-500 years which is larger than the value of historical earthquake
catalogue. The reason of this difference may be caused by the friction parameters that we used in thisstudy.

4. DISCUSSION AND CONCLUSIONS
We need to understand earthquake cycles and segmentation for a long-term forecasting and earthquake
nucleation process for a short-forecasting. In the study herein, we perform a numerical simulation ofseismic activity along the Xianshuihe fault, assuming that the long-term slip rates are consistent withgeologically- and geodetically-derived values, and the friction on the fault obeys a rate- andstate-dependent friction law. We investigate the nucleation and cycles of earthquakes along theXianshuihe fault by a 3-D model. A large number of simulations have been run, and best result hasbeen chosen to report.
According to Figure 6 showing the location of the slip velocity greater than 0.01m/s, wecan find that the earthquakes occur in the year of 372, 858, 1273, 1764, 2239 and 2684; the occurrence
interval is 400-500 years. The earthquake firstly occurs in the middle part of the fault in year of 372,
and then some obvious changes of the slip velocity can be found on the edges of both sides of the fault.
In the year of 858, the second earthquake occurs along the mainly part of the fault except the 0-100km
part of the fault. After two earthquake cycles, we find that the fault has been divided into 3 parts.

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The recurrence interval of each earthquake depends both on a-b and Dc. So we shouldchoose appropriate values of them to get close to the historical earthquake catalogue. If a large Dcvalue is chosen, slip instability becomes weak and no large seismic slip can occur. Whether a rupture
stops or not also depends on the distribution of a-b and Dc values. Their spatial pattern and the valuesof a-b are determined based on other observational or experimental information. Additional
examination is necessary to check if the Dc value used here is reasonable or not.
As we explained above, the fault line used for building the fault mesh is digitized fromKato et al., (2007). For simplicity, they combined the Xianshuihe fault into one main fault with two
small ones. For this study, we just take the main fault into consideration. Actually, the Xianshuihefault is divided into 4 main segments and 2 sub-segments, and the relation between them iscomplicated. It’s better for us to develop a model with several segments to simulate.
The observed coseismic slip velocity is around 1m/s, and in our study, the largest slip
velocity is 0.55m/s which is close to the coseismic slip velocity. The occurrence interval ofearthquakes in this study is 400-500 years and the occurrence interval of the historical earthquakes isless than 200 years. Although we have already changed the parameters of 7 cases, we can not get theideal results. Therefore, we may have to continue making some changes to the values of the frictionallaw parameters or changes to the mesh of fault to get better results.
AKNOWLEDGEMENT
We used the computer systems at the Earthquake Information Center of the Earthquake ResearchInstitute, University of Tokyo, Tokyo, Japan.

REFERENCES
Deng Q. D., Zhang Y. M., Huan W. L. et. al., 1976, Chinese active faults and earthquake epicenter
distribution map (1:3000000), China Earthquake Administration.
Dieterich, J. H., 1981, Constitutive properties of rock with simulated gouge, in mechanical behaviorof crustal rocks, Geophys. Monogr. Ser, vol. 24, edited by N. L. Carter et al., pp. 108-120, AGU,Washington, D. C.
Dieterich, J. H., 2009, Applications of rate- and state- dependent friction to models of fault slip andearthquake occurrence, Earthquake Seismology, 4, 107-129, Elsevier B.V., Netherlands.
Fujii, Y., and Matsu’ura, M., 2000, Regional difference in scaling laws for large earthquakes and its
tectonic implication, Pure Appl. Geophys., 157, 2283-2302.
Hori, T., 2006, Mechanisms of separation of rupture area and variation in time interval and size ofgreat earthquakes along the Nankai Trough, southwest Japan, Journal of the Earth Simulator, 5,8-19.
Kato, N., Lei, X. L., and Wen, X.Z., 2007, A synthetic seismicity model for the Xianshuihe fault,
southwestern China: simulation using a rate- and state-dependent friction law, Geophys. J. Int.
169, 286–300, doi:10.1111/j.1365-246X.2006.03313.x.
Okubo, P.G., 1989, Dynamic rupture modeling with laboratory-derived constitutive relations, J.
Geophys. Res., 94(B9), 12,321-12,335, doi:10.1029/JB094iB09p12321.
Press, W. H., Teukolsky, S. A., Vetterling, W.T., and Flannery, B.P., 1992, Numerical recipes in
Fortran77, 707-752, Cambridge Univ. Press, New York.
Rice, J. R., 1993, Spatio-temporal complexity of slip on a fault, J. Geophys. Res., 98(B6),9885-9907, doi:10.1029/93JB00191.
Ruina, A., 1983, Slip instability and state variable friction laws, J. Geophys. Res., 88(B12),
10,359-10,370, doi:10.1029/JB088iB12p10359.

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