BY W. SCOTT DUNBAR,* DAVID M. BOORE, AND WAYNE THATCHER. ABSTRACT. Triangulation surveys carried out in the vicinity of the White Wolf Fault in.
Bulletinofthe SeismologicalSocietyofAmerica,Vol.70, No. 5, pp. 1893-1905,October1980
PRE-, CO-, A N D P O S T S E I S M I C S T R A I N C H A N G E S A S S O C I A T E D W I T H T H E 1952 M L = 7.2 K E R N C O U N T Y , C A L I F O R N I A , E A R T H Q U A K E BY W. SCOTT DUNBAR,* DAVID M. BOORE, AND WAYNE THATCHER ABSTRACT Triangulation surveys carried out in the vicinity of the White Wolf Fault in 1932, 1952, 1953, and 1963 are used to delineate the strain changes preceding, accompanying, and following the 1952 earthquake. The strain rate (engineering shear) during the preseismic interval (1932 to 1952) was 0.36 + 0.10/~strain/yr and was nearly uniform across the 70-km-long triangulation arc, with the plane of maximum left-lateral shear oriented N44 ° __. 7°E, nearly parallel to the White Wolf Fault. The coseismic observations (1952 to 1953), supplemented by leveling data, are matched using a dislocation model with the following characteristics Dip = 6 0 ° S E Strike -- N 5 0 ° E Length = 70 km Left-Lateral Strike-Slip -- 2.4 _ 0.1 meter (m) Reverse Dip-Slip = 1.9 to 0 . 6 m (decreasing to the NE) Seismic moment _-> 0 . 9 x 1027 dyne-cm.
The data also require most of the slip to have occurred below ~5 km (5 to 20 km in our model), on roughly the southwest half of the fault, with the slip occurring at shallow depths to the northeast. The postseismic triangulation data (1953 to 1963) indicate that the average shear strain rate in the 10 yr following the earthquake (0.80 _+ 0.20/Lstrain/yr) was about twice that during the 20 yr preceding it. The postseismic strain changes were concentrated closer to the fault than those determined for the preseismic time interval, and the 1953 to 1963 data are explained well by episodic postseismic slip of about 2 m (leftlateral strike-slip) occurring on the down-dip extension of the coseismic fault plane.
INTRODUCTION T h e K e r n C o u n t y e a r t h q u a k e of July 21, 1952 is one of the most significant e a r t h q u a k e s to occur in the conterminous United States since 1906. Its magnitude (Ms = 7.4 to 7.7, Gutenberg, 1955b; M L ---- 7.2, K a n a m o r i and Jennings, 1978; Bolt, 1978) is larger t h a n any e v e n t since the 1906 San Francisco earthquake. It occurred on the White Wolf Fault, to the n o r t h of the intersection of the Garlock and San Andreas faults (Figure 1). Although the White Wolf Fault was recognized as active, the occurrence of the e a r t h q u a k e came as a surprise and alerted people to the hazard associated with the range front faults in the vicinity of the "Big B e n d " in the San Andreas Fault. T h e hazard was reemphasized by the occurrence of the 1971 San Fernando e a r t h q u a k e ( M L = 6.4). Despite the importance of the e a r t h q u a k e and the availability of the data, surprisingly few geophysical studies have been m a d e of this earthquake. Most of the * Present address: Weidlinger Associates, 3000 Sand Hill Road, Building 4, Suite 245, Menlo Park, California 94025. 1893
1894
w.
SCOTT D U N B A R , D A V I D M. B O O R E , A N D W A Y N E T H A T C H E R
studies appeared in 1955 as Bulletin 171 of the California Division of Mines (now the Division of Mines and Geology). In that volume, Gutenberg (1955a, b) used regional and teleseismic recordings to estimate the origin time, location, and magnitude. He found that P-wave first motions implied faulting on a plane dipping 63 ° in a direction S40°E. This roughly agreed with field and aftershock studies. The triangulation and leveling data were consistent with left-lateral, reverse faulting, but no attempt was made to fit the data to a model of the fault. The distribution of surface wave amplitudes showed an azimuthal variation which Benioff qualitatively explained by the directivity associated with northeasterly propagation of the fault rupture from the epicenter at the southern end of the fault. \ \ \
N \
\
\
\
\ SAN ANDREAS
C~x\4/~.
\#
%;
/
- \
J
J
Fro. 2. Triangulationnet and levelingsurveyroutes along Highways99 and 58. The numberedpoints are the triangulation stations. The point marked FC and the straight line marked N50E, respectively, denote the center and orientation of a 70-kin-longdislocationmodel used to interpret the data. and eEN a r e the tensor shear strains. Given T1 and "/2, estimates of the azimuth of elongation • (clockwise from north, tensile strain being positive) and the total strain ), can be made using
eNE
1
-72
~/ = ['I/12 + -y22] 1/2 .
Estimates of y1 and 72 using both a standard least-squares estimator and one based on the absolute value norm (Claerbout and Muir, 1973) are given in Tables 1 to 3. This latter estimator is stable in the presence of gross errors in the data, and large differences in the values of ~,1 and 72 given by the two estimators may indicate the presence of spurious data.
1896
W. SCOTT D U N B A R , DAVID M. BOORE, AND W A Y N E T H A T C H E R TABLE 1 PRESEISMIC STRAIN ANALYSIS*
Polygon Stations
Least Squares
Distance from Fault (km)
Absolute Value NOITn
Tl
8 8 10 14
15 18
19
2 8 6 5 7 9 11 12 14 15 16 17 16 19 19 22
4 4 7 13 11 11 12 13 13 16 18 15 22 22 22 20
5 7 8 12 10 10 14 17 17 18 t 17 18t 19 20 21 t 21
-1.4 7.0 7.8 10.4 10.9 11.5 13.4 15.9 17.4 20.5 20.8 21.3 22.4 24.0 25.0 25.2
15± -1± 11± 9± 6± 6± 7± 8± 2±_ -1 ± 6± -29 ± 1± 13± -2± 8±
y2
1 5 4 2 5 6 7 3 4 10 8 26 3 1 3 5
0± -2___ -1± 18± 4± 1± 3± 6± 7± -14 ± -5± -18 ± 3± -11± -4± -4±
1 3 4 8 5 8 6 3 2 10 7 10 5 1 3 6
Tl
y2
15 1 10 12 4 12 9 5 5 -1 1 3 5 12 -5 10
0 2 -7 28 6 4 -2 6 4 -6 -3 -18 8 -9 0 0
* All strain estimates and standard errors are rounded to the nearest whole number. T h e r e is no s t a n d a r d error estimate for the absolute value norm. t N o t plotted in Figure 3. TABLE 2 COSEISMIC STRAIN ANALYSIS* Polygon Stations
Least Squares
Distance from Fault (kin) Y1
2
3 3
8 8 10 14
15 18
19 21
1 3 2 4 1 1 4 3 4 8 3 6 5 7 9 11 12 14 15 16 17 16 19 19 22 20 21
2 2 4 3 4 4 7 4 7 4 6 7 13 11 11 12 13 13 16 18 15 22 22 22 20 23 20
3 4 5 1 3 5 6* 8 8 7 8 8 12 10 10 14 17 17 18 t 17 18 19 20 21 t 21 25t 25
-2.7 -2.2 -1.4 -1.5 2.3 3.1 4.4 6.1 6.2 7.0 7.0 7.8 10.4 10.9 11.5 13.4 15.9 17.4 20.5 20.8 21.3 22.4 24.0 25.0 25.2 29.2 29.3
31_ 1 9± 5 49_ 6 23± 7 -50_17 154 ± 76 120 ± 30 41_ 1 41±12 56± 1 22± 3 0± 6 -29± 1 -34± 8 -44± 5 -39_ 5 -51± 2 -53± 2 5±10 7± 5 32± 6 -27_ 2 -7± 6 -2± 9 -9± 4 -5± 1 -3± 6
Absolute Value Norm y~
1± I 17±12 83±18 1__.13 -41± 3 - 8 0 ± 54 -38___ 19 -50± 2 -9±13 16± 1 6± 4 0± 6 7± 3 -7± 8 -5± 6 6± 4 1± 2 -1± 1 11± 9 10± 4 15± 2 -12 ± 4 5± 6 -5± 9 -2± 5 -4± 1 -5± 3
y~
y2
31 16 42 31 -67 56 102 40 44 58 23 -8 -28 -36 -41 -32 -52 -54 17 5 40 -24 -12 7 -9 -6 4
1 9 87 1 -37 -7 22 -47 3 16 12 -5 11 -5 -12 7 1 1 24 3 15 -7 13 -16 -2 -4 -10
* All strain estimates and standard errors are rounded to the nearest whole number. T h e r e is no standard error estimate for the absolute value norm. t N o t plotted in Figure 3.
PRE-, CO-, AND POSTSEISMIC STRAIN CHANGES
1897
T h e v a l u e s ~,1 a n d 72 w e r e a r b i t r a r i l y a s s i g n e d t o t h e c e n t e r o f t h e a p p r o p r i a t e quadrilateral. The data were then plotted as a function of perpendicular distance of t h e c e n t e r o f t h e q u a d r i l a t e r a l f r o m t h e f a u l t . { T h i s p l o t t i n g is f o r c o n v e n i e n c e o n l y and implies no assumption of two-dimensionality in the faulting, the interpretation being based on three-dimensional models.) Plotted error bars are one standard deviation values obtained in each case from a least-squares fit of the angle change data to a uniform strain field. Thus, the error bars represent both measurement errors and any actual departures from the assumed spatial uniformity of the strain f i e l d . T h e r e s u l t s a r e s h o w n i n F i g u r e 3. N o t e t h e d i s t i n c t i v e s h a p e a n d a m p l i t u d e TABLE 3 POSTSEISMIC S T R A I N ANALYSIS* Polygon Stations
Least Squares
Distance from Fault (km) Tl
2
3 3
8 8 10 14
15 18
19 21
1 3 2 4 1 1 4 3 4 8 3 6 5 7 9 11 12 14 15 16 17 16 19 19 22 20 21
2 2 4 3 4 4 7 4 7 4 6 7 13 11 11 12 13 13 16 18 15 22 22 22 20 23 20
3 4 5 1 3t 5~ 6 8~ 8 7 8 8 12 10 10 14 17 17 18 17 18 19 20 21~ 21 25t 25
-2.7 -2.2 -1.4 -1.5 2.3 3.1 4.4 6.1 6.2 7.0 7.0 7.8 10.4 10.9 11.5 13.4 15.9 17.4 20.5 20.8 21.3 22.4 24.0 25.0 25.2 29.2 29.3
4+ 4 -5_ 3 7+ 1 2 +_ 3 -26+_ 96 123 + 219 4 0 ± 27 12_ 4 17 ± 4 23± 4 -1 ± 2 11 + 1 5± 1 5± 4 13 ± 2 21_ 4 6_ 4 -3 ± 3 9 +_ 4 6± 4 -20 _ 4 4± 3 10 ± 4 -6 ± 1 0_ 4 10_ 2 4 __ 7
Absolute Value Norm y=
1_ 5 25_ 8 -5_ 1 5_ 6 -8_ 15 - 9 2 _ 155 -28_ 17 -10_ 6 -3 ± 5 2± 3~ 0+ 3 10 ± 1 -17 ± 1 2+ 5 3± 3 -2 ± 3 6± 4 7± 2 6± 4 5± 3 3± 1 2± 5 -6 ± 4 -3 _ 1 5 +_ 4 3_ 2 7 __ 4
yl
T3
0 -10 7 1 71 406 35 14 18 29 -1 11 5 6 12 26 7 -1 15 9 -25 4 13 -5 -7 9 -5
4 31 -4 4 -30 -304 -34 -18 -4 3 5 12 -16 4 4 -4 10 4 11 2 3 1 -11 -4 7 4 12
* All strain estimates and standard errors are rounded to the nearest whole number. There is no standard error estimate for the absolute value norm. t Not plotted in Figure 3.
of the coseismic data as compared with that of the intervals before and after the main shock. Also note that the average engineering shear strain rate for the p o s t s e i s m i c p e r i o d (0.80 ± 0.2 # s t r a i n / y r ) is a b o u t t w i c e t h a t f o r t h e p r e s e i s m i c i n t e r v a l (0.35 ± 0.1 # s t r a i n / y r ) . T h e p r e s e i s m i c r a t e i s c o m p a r a b l e t o r a t e o f s t r a i n accumulation along various parts of the San Andreas fault system (Thatcher, 1975a, b, 1979; P r e s c o t t et al., 1979). Leveling lines along State Highways 99 and 58 have been surveyed a number of t i m e s . F i g u r e 4 s h o w s t h e d a t a f o r t i m e p e r i o d 1926 t o 1952 ( p o s t - e a r t h q u a k e ) , assuming a fixed point at Bakersfield (data have been taken from a contour map in
1898
w . SCOTT DUNBAR, DAVID M. BOORE, AND WAYNE THATCHER
W h i t t e n , 1955). M o r e d e t a i l e d c o s e i s m i c m o d e l i n g using a m o r e e x t e n s i v e s e t of l e v e l i n g data h a s b e e n r e c e n t l y carried o u t b y S t e i n et al. (1981), a n d their r e s u l t s are c o n s i s t e n t w i t h t h e m o d e l i n g carried o u t in t h i s paper. T h a t is, t h e 1952 c o s e i s m i c
200
CO 1952-1955
PRE
1952-1952
150
71
POST •
75.
)'l
7" I
6 5C
I00
50--
1955-1965
-4
-2
25
2"~ -2
!I
I
oi
z_
:L
\
z -507
%
::k
%
50--
lOG
50
, ~.
7. z
Y2
Yz
-4
5(
i
ol
~
I '
H
-25 t
- 5,
0I
i
' I0
'
2'0
'
-50
-25
- I0(
- 50
I
50
I IO DISTANCE
I
] 20
I
I
I
I I
50
-5
0
I
t I0
I
I 20
I 50
, km
FIG. 3. Pre-, co-, and postseismic strain estimates for individual polygons of the triangulation net shown in Figure 2 (see Tables 1 to 3). The strains are plotted versus the perpendicular distance of the center of the polygon from the fault model shown in Figure 2. The bars denote the standard deviation of each estimate. Ordinate units are ~strain; units of #strain/yr are also shown for pre- and postseismic
intervals.
slip d e c r e a s e s in m a g n i t u d e and o c c u r s at s u c c e s s i v e l y s h a l l o w e r d e p t h s t o w a r d t h e n o r t h e a s t along t h e W h i t e W o l f Fault. Preliminary interpretation. T h e s e r i e s o f t h e o r e t i c a l c u r v e s in Figure 5 are useful
PRE-~ CO-~ AND POSTSEISMIC STRAIN CHANGES
1899
for a preliminary interpretation. These curves are derived from formulas given in Mansinha and Smylie (1971). S h o w n are ~'1 and ),2 as a function of distance along a line perpendicular to the mid-point of a 70-km fault dipping 60 ° in the direction S40°E. The fault orientation and length were taken from studies of Gutenberg NWY 58 Ld
-o.4 7
/ +
2~0 K M HWY 99
-0.8
LOCATION OF FAULT T R S C E
-0,4
o
+
8
5~~) KM +
+
+
H-
0.4 ÷
÷
0.B FAULT
MODEL
tabulated Fk,rn-r at the 5 per cent level. Details of this method may be found in Searle (1971). Lawson and Hanson (1974) describe algorithms for solving the least-squares problem with equality constraints. The following hypotheses were tested 1. S S 1 =
zero strike-slip in segment 1
0;
2. D S 3 = D S 4 ;
equal dip-slip in segments 3 and 4
3. S S ~ = S S 4 ;
equal strike-slip in segments 3 and 4. TABLE
4
K E R N COUNTY HYPOTHESES* Hypothesis
SSC
SSE
SS1 = 0
1007
954
( k = 1) DS3 = DS4
1162
954
957
954
F
(SSC - SSE)/k = SSE/(m - r)
Fk.m r.o.o5
Reset
5.8
3.9
22.9
(F1,105,0.ol = 6.9) 3.9
Marginal Reject
3.9
Accept
(k = 1) SS3 = SS4 (k
=
0.33
1)
* m - r = 113 - 8 = 105. All s u m s o f s q u a r e s a r e d i m e n s i o n l e s s .
if the model matrix A is arranged such that the slip estimates in the vector x are in the following form x t =
[SS1, DS1, SS2, DS2 .... SS4, DS4],
then hypothesis I is tested by making B a I × 8 matrix with the (1, 1) element equal to 1 and c = 0. The second hypothesis is tested by making B a 1 × 8 matrix with the (1, 6) element equal to 1 and the (1, 8) element equal to -1. The vector c is again equal to zero. The equality constraints for the third hypothesis are constructed in a similar fashion. The results of the tests are shown in Table 4. Hypothesis 1 was found to be marginally acceptable; i.e., if a 1 per cent significance level was chosen, it would be acceptable. Hypothesis 2 was found unacceptable, while the third hypothesis was accepted. REFERENCES Ben-Menahem,
(1978). S o u r c e m e c h a n i s m
Interiors 1 7 , 1 6 3 - 1 8 1 .
o f t h e 1906 S a n F r a n c i s c o e a r t h q u a k e , Phys. Earth Planet.
PRE-, CO-, AND POSTSEISMIC STRAIN CHANGES
1905
Bolt, B. A. {1978). The local magnitude ML of the Kern County earthquake of July 21, 1952, Bull. Seism. Soc. Am. 68, 513-515. Claerbout, J. F. and F. Muir (1973). Robust modeling with erratic data, Geophysics 38, 826-844. Dunbar, W. S. (1977). The determination of fault models from geodetic data, Ph.D. Thesis, Stanford University, Stanford, California, 201-213. Frank, F. C. {1966). Deduction of earth strains from survey data, Bull. Seism. Soc. Am. 56, 35-42. Gutenberg, B. (1955a). The first motion in longitudinal and transverse waves of the main shock and the direction of slip. Bull. 171, Calif. Div. Mines and Geol., 165-170. Gutenberg, B. (1955b). Magnitude determination for larger Kern County shocks, 1952; effects of station azimuth and calculation methods, Bull. 171, Calif. Diw Mines and Geol., 171-175. Hanks, T. C., W. Thatcher, and J. A. Hileman {1975). Seismic moments of the larger earthquakes of the southern California region, Bull. Geol. Soc. Am. 86, 1131-1139. Kanamori, H. and P. C. Jennings, (1978). Determination of local magnitude, ML, from strong-motion accelerograms, Bull. Seism. Soc. Am. 68, 471-485. Lawson, C. L. and R. J. Hanson (1974). Solving Least Squares Problems, Prentice-Hall, Inc., New Jersey, 134-143. Mansinha, L. and D. E. Smylie (1971). The displacement fields of inclined faults, Bull. Seism. Soc. Am. 61, 1433-1440. Prescott, W. H., J. C. Savage, and W. T. Kinoshita (1979). Strain accumulation rates in the western United States between 1970 and 1978, J. Geophys. Res. 84, 5423-5436. Richter, C. F. (1955). Foreshocks and aftershocks, Bull. 171, Calif. Div. Mines and Geol., 177-197. Searle, S. R. {1971). Linear Models, John Wiley and Sons, Inc, New York, 110-113. Stein, R. S., W. Thatcher, and R. O. Castle (1981). Late Quaternary and modern deformation along the fault-bounded northwest margin of the southern California uplift. J. Geophys. Res. 86, (in press). Thatcher, W. (1975a). Strain accumulation and release mechanism of the 1906 San Francisco earthquake, J. Geophys. Res. 80, 4862-4872. Thatcher, W. (1975b). Strain accumulation on the northern San Andreas fault zone since 1906, J. Geophys. Res. 80, 4873-4880. Thatcher, W. (1979). Horizontal crustal deformation from historic geodetic measurements in southern California, J. Geophys. Res. 84, 2351-2370. Thatcher, W. and T. C. Hanks (1973). Source parameters of southern California earthquakes, J. Geophys. Res. 78, 8547-8576. Whitten, C. A. (1955). Measurements of earth movements in California, Bull. 171, Calif. Div. Mines and Geol., 75-80. DEPARTMENT OF GEOPHYSICS STANFORD UNIVERSITY STANFORD,CALIFORNIA94305 (W.S.D., D.M.B.) Manuscript received March 13, 1980
U.S. GEOLOGICALSURVEY 345 MIDDLEFIELD ROAD MENLO PARK, CALIFORNIA94025 (D.M.B., W.T.)
