The goal of this project remains to be the achievement of a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effect of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate/viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformations. In the present period, special focus is placed on the 3-D effect of irregular fault locked patches on the ground measured deformation fields. Specifically, use is made of a newly developed 3-D boundary element program to analyze the fault slip and vertical ground motion in the Parkfield area on the San Andreas

Li, Victor C.

English

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STRAIN ACCUMULATION AND SURFACE DEFORMATION ALONG
THE SAN ANDREAS, CALIFORNIA
Semi-annual Technical Report
Period: Jan 1, 1989- June 30, 1989
Grant No. NAG 5-740 '_
Grant Recipient: Massachusetts Institute of Technology
Principal Investigator: Professor Victor C. Li
NASA Technical Officer: Dr. Herbert Frey
Government Gran:, Officer: Genevieve.E. Wiseman
Effective Date of Grant: March 1, 1986
Effective Expiration Date: March 31,1990
Submitted Date: Oct l, 1989
Sponsored by the
Crustal Dynamics Program
National Aeronautics and Space Administration
Disclaimer: The views and conclusions contained in this document are those of the
author and should not be interpreted as necessarily representing the official policies,
either expressed or implied, of the United States Government.
(NA!"A-C_-IU589J) STRAIN ACCd_ULATIqN A_.&
SIJ_["ACr.. DffFCR_ATInN ALONG THE oAN A;-JDc_E A:_,
CAL[F-rSKNI_ Semiannual ]'ethnical R,,,port, I
Jan. - 30 Jun. l_B9 (_fT) !3 r" CSCL Od'S
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https://ntrs.nasa.gov/search.jsp?R=19900004578 2020-03-19T23:35:27+00:00Z
Victor C. Li (P.I.)
1-229, Department of Civil Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
(617) 253-7142
INTRODUCTION
This is a semi-annual technical report of the project entitled "Strain Accumulation and
Surface Deformation Along the San Andreas, California" supported by NASA Crustal
Dynamics Program, for the period Jan 1, 1989 - June 30, 1989, based on funding from the
Grant No. NAG 5-740 awarded to MIT.
The goal of this project remains to be the achievement of a better understanding of the
regional and local deformation and crustal straining processes in western North America,
particularly the effect of the San Andreas and nearby faults on the spatial and temporal
crustal deformation behavior. Construction of theoretical models based on the mechanics
of coupled elastic plate/viscoelastic foundation and large-scale crack mechanics provide a
rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts
in forecasting the stability of plate boundary deformations.
In the present period, special focus is placed on the three dimensional effect of
irregular fault locked patches on the ground measured deformation fields. Specifically, we
make use of a newly developed three dimensional boundary element program to analyze the
fault slip and vertical ground motion in the Parkfield area on the San Andreas.
SUMMARY OF PROJECT ACHIEVEMENTS TODATE
Major achievements for the duration of the project are summarized below:
1. Developed and completed a model of coupling between the elastic lithosphere and
viscoelastic asthenosphere which incorporate the sub-mantle steady state motion as a
long term driving force, and the transient loading and reloading of the plate boundary
in earthquake cycles. This model suggests significant non-linearity in the stress-
accumulation process over an earthquake cycle at a plate boundary.
3. Developed and completed the modeling of crustal deformation (referred to as the Li-Rice
model hereon) which varies with time and space at a strike-slip plate boundary
embedded in the plate structure described in (1) above.
. From (1) and (2), and whole cycle San Andreas composite geodetic data, the surface
elastic plate thickness is constrained to 20-30 kin, and the viscoelastic relaxation time
is constrained to 10-16 yr.
. The predicted surface velocity profiles are in good agreement with geodetic
measurements at several locations along the San Andreas where such data is
available. Locations studied include Point Reyes area and the Palmdale area.
Predicted surface velocity profile at Palmdale area agree with the recently obtained
field data. Note that model prediction is made independently of the geodetic field data
indicated.
. Development of a model similar to the Li-Rice model for complex plate boundaries,
including plate boun.daries exhibiting surface fault creep, and plate boundaries "with
sub-parallel faults. Application of this model to the Parkfield area in Central
California and to the Coachella-Valley area in Southern California is performed. The
predicted surface velocity for the Coachella-Valley area can be fitted to recent VLBI
and ground based geodetic data.
. Comparison of the single line dislocation model of Savage and Burford with the Li-Rice
model reveals that the locked depth and deep aseismic slip rate are significantly
overestimated for the single line dislocation model using geodetic data as constraining
information. Further, over the span of an earthquake cycle, the single line dislocation
model is shown to predict a shallower locked depth and a larger deep slip rate for a
velocity prof'tle associated with a time earlier in an earthquake cycle in comparison to
that associated with a time later in an earthquake cycle. This is physically implausible.
The suggestion from this analysis is that while the Savage/Burford single line-
dislocation model is simple to use and understand, it also imposes severe limitation in
direct physical interpretation of fault locked depth and deep aseismic slip rate, as well
as other tectonic implications.
Since the last technical report, our work has focused on the study of three
dimensional effect of locked patches on the ground deformation field based on a three-
dimensional boundary element program developed recently by our research group. The
study is made in connection with the Parkfield region on the San Andreas.
4INVESTIGATIONON FAULT SLIPAND GROUNDDEFORMATION
ON THE SANANDREASNEARPARKFIELD
Thefault sectionof theSanAndreasnearParkfieldhasbeenthefocusof extensive
research.This extensiveresearchis mainlydueto therelativelyshortrecurrenceinterval
and repeatablecharacterof moderateearthquakesoccurring near Parkfield, and the
plausiblerelationshipbetweenaParkfieldearthquakeandamajorrupture. Accordingto
Baken and McEvilly (1979, 1984), at least five earthquakesof similar magnitude
(M=5.5-6)andepicenterhaveoccurredat21+8year intervals(1881, 1901,1922,1934,
1966). Recentworks by Rice and others, however, have raised doubts about the
regularity issue,and the influence of viscoelastic wave transfer from large nearby
ruptures.
The use of mechanical models to study fault regions usually involve the
determinationof elasticfields dueto slip distributionsoverapredeterminedfault surface
andcaneitherbekinematicor non-kinematicin nature."Kinematicmodelsusesurfac_
deformationsnear_e fault traceasa direct constraintto obtain the slip distributions,
irrespectiveof theensuingstressdistributionon thefault surface.Non-kinematicmodels
use frictional boundary conditions on the fault surface in order to obtain the slip
distributions.
Severalnon-kinematicmodelsof thefault regionnearParkfieldareavailable.Quasi
3-D non-kinematicmodelsbasedon theline-springprocedurewereproposedby Li and
Fares (1986) and by Tse et al (1985). However, the line spring technique is not
considered accurate enough when suddenchange in geometry occurs, or when
determiningtheelasticfields at locationsthataretoocloseto thefault. A detailed3-D
non-kinematicforecastmodelof theParkfieldregionhasbeendevelopedby Stuartet al
(1985). Their model usedslip patchesin a halfspacewith a free surfaceand a slip-
weakeningfrictional boundarycondition. Oneof theshortcomingsof this modelis that
theelastichalfspacemodelcannotaccountfor timedependentviscoelasticeffectsarising
from thepresenceof theasthenosphere.Theassumptionof afully relaxedasthenosphere
(resulting in the lithosphere as a free riding plate) also cannot be conclusively
demonstrated,especially in view of the relatively short recurrencetime of Parfield
earthquakes.Nevertheless,aplatemodelis in generalmoreappropriatethanahalfspace
modelbecausetherecurrencetimeinterval of Parkfieldearthquakesof 21yearsis longer
thanthe 10-16yearsestimatedcharacteristicrelaxationtimeof theasthenosphere(Li and
Rice,1987).
5Thenon-kinematic3-Dmodelof thefault regionnearParkfieldis shownin Figure
1. Themodelassumeslippageto occuroverasurfacelying in a plateandwith simple
frictional boundaryconditionsspecifyingthatall slippingregionshavethesameconstant
level of frictional resistance.Such a frictional boundary condition requires the
determination of which region of the fault is slipping and which is locked. The
determinationof thegeometryof theslippingregionof thefault requiresextensivestudies
andhasnotbeenperformed.Thegeometryof theslippingregionin thefault regionnear
Parkfieldhasbeendeterminedby referringto previouskinematicstudiesby Harris and
Segall(1987),whereasthelengthof theslipping(or "creeping")zonenorthof Parkfield
hasbeendeterminedfrom surfacedeformationdataalong thecentralsectionof theSan
Andreasfault (Figure2a,b). In determiningthe geometryof theslippingregionof the
fault,, the thicknessof the plate "H" is taken to be 20-22km., which implies that the
length of the slipping zoneis around8H (i.e. 160-180km.). Finally, the geometry
detailsat theendx = 8.75H of theslippingfault region is assumedto havea negligible
effecton thefault regionnearParkfield,andhencehavebeenassumedto bethesimplest
possible(asshownin Figure2a).
FINDINGS
Thevariation of the surface slip along the fault is shown in Figure 3a. The surface
distribution is very similar to the thickness averaged slip of a mode II plane stress crack
whose length is around 8.3 H, except along the interval from 0<x/H<l.75. Along the
0.2<x/H<l.6, the surface slip consists of a relatively constant surface slip level whose
magnitude can approximately be obtained from an antiplane analysis of a doubly cracked
plate (e.g. Tse et al, 1985) with a far-field stress of 1.5 to 2 times the actual far-field
stress. Rather narrow transition intervals at each end (0<x/H<0.2 and 1.6<x/H<l.75)
are observed (Figure 3b). The variation of the lower surface slip is shown in Figure 3c.
Note that the lower surface slip distribution does not contain a region for which an
antiplane analysis could adequately model the slip variation.
The stress intensity factor (SIF) values in mode III along the upper edge
(z/H=0.05, 0<x/H<l.75) shown in Figure 4a and along the lower edge (z/H=0.5,
1.25<x/H<l.75) shown in Figure 4b are consistent with the observed slip distributions
along the upper and lower surfaces. The SIF values also show especially high values
near the edge of the semi-locked and through thickness slipping region of the fault (i.e. at
x/H = 1.75). Finally the mode II stress intensity factors along the edge between the
semi-locked and through thickness slipping region of the fault (i.e. x/H = 1.75,
0.05<z/H<0.5) shows (Figure 5) a normalized KII level of around 4.6 which for a
nominal crack length of 8.3H implies a far field stress level amplification of around 1.3.
6The computed surface uplift values near the fault trace at yffrI=0.01 and -
0.5<x/H<2.25 are shown in Figure 6. Note that surfaceuplift values can only be
obtainedusing a 3-D model sinceuplift occursdue to pinching effectsintroducedby
gradientsof slippagealongthefault. Themaximumchangein uplift acrossthefault trace
is at mostaround10%thechangein surfaceslip valuesacrossthesamelocationson the
fault trace. As expected,thesurfaceuplift is highestat thelocationwherethegradientsin
surfaceslippageis highestandreducesto alow levelalongtheintervalwheresurfaceslip
is relatively flat. Finally thesurfaceuplift in the interval -0.5<rdH<l.0 is observedto
increasein thenegative"x" directionwith a smallhumpat x/H --0.0.This observation
couldbeexplainedby therelative increasein gradientsof slippagethatoccurswhenthe
semi-lockedsurfaceof the fault is lockedat its upperedgeat x/H = 0.0 (andhencethe
hump)andthenlockedat its loweredgeat x/H =-1.25(andhencethegradualincreaseof
surfaceuplift in thenegative"x" directionwhich isexpectedto decreaseagainafterx/H =
-1.25is reached).
The abovedescribedfault model for the Parkfield region is a preliminary one
requiringfurtherextensiveparametricsr,_diesbeforecomparisonswith geodeticsurface
deformationdatacanbeperformed. "
REFERENCES
BakunW.H. and McEvilly T.V., EarthquakenearParkfieldCalifornia: Comapringthe
1934and 1966sequences,Bull. Seism.Soc.Am., 70, 671-689,1979.
Bakun W.H. and McEvilly T.V., Recurrence models and Parkfield, California
Earthquakes, J. Geophys. Res., 89, 3051-3058, 1984.
Harris, R.A. and Segall P. 1987, Detection of a locked zone at depth on the Parkfield,
California, Segment of the San Andreas Fault, J. Geophys. Res., 92, 7945-7962.
Li V.C. and Fares, N., Rupture Processes in the Presence of creep zones, in Earthquake
Source Mechanics, ed. S. Das, J. Boatwrigth and C.H. Scholz, Maurice Ewing, V. 6,
71-80, 1986.
Li, V.C. and Rice, J.R., Crustal deformation in great California earthquake cycles, 92,
Bll, 11533-11551, 1987.
Stuart, W. D., Archuletta R.J. and Lindh A.G., Forecast model for moderate
earthquakes near Parkfield, California, J. Geophys. Res., 90, 592-604.
Tse S.T., Dmowska,R. and Rice, J.R., Stressingof locked patchesalong a creeping
fault, Bull. Seism.Soc.Amer., 75,709-736,1985.
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Strain accumulation and surface deformation along the San Andreas, California

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