A slow earthquake in the Santa Maria basin, California
Bulletin ofthe SeismologicalSocietyofAmerica,Vol. 82, No. 5, pp. 2087-2096, October1992
A SLOW EARTHQUAKE IN T H E SANTA MARIA BASIN, CALIFORNIA BY HIROO KANAMORI AND EGILL HAUKSSON ABSTRACT An M L = 3.5 earthquake near Santa Maria, California, was recorded by the Southern California Seismic Network and a TERRAscope station at Santa Barbara (SBC) on 31 January 1991. The waveform of this event is dominated by 2- to 5-sec waves, and is different from that of ordinary events with similar size. Inquiries into operations in several oil fields in the area revealed that hydro-fracturing at a pressure of about 80 bars was being done at a depth of 100 to 300 m in the Orcutt oil field in the Santa Maria basin from about 9 to 11 a.m. on 31 January and the earthquake occurred in the afternoon. Field evidence of 30-cm displacement to a depth of 300 m was reported. The field evidence as well as the first-motion data indicates that the event had a thrust mechanism with the P axis in the N N E - S S W direction, which is in agreement with the regional stress field. From the analysis of the SBC record and the field evidence, we conclude that the source must be shallower than 1 km and the ratio of the radiated energy to the seismic moment is about 6.2 × 10 -7, one to two orders of magnitude smaller than that of ordinary earthquakes. The occurrence of this earthquake demonstrates that release of regional tectonic stress in shallow sediments can yield significant seismic radiation at periods of a few seconds, the period range of engineering importance for large structures, and has important implications for excitation of long-period ground motions from large earthquakes in sedimentary basins.
INTRODUCTION On 31 J a n u a r y 1991, an anomalous e a r t h q u a k e was recorded at seismic stations of the S o u t h e r n California Seismic Network (SCSN). This event was located at 34.8°N and 120.4°W (origin time: 23:28:18 GMT) n e a r Orcutt in the S a n t a Maria basin, California (Fig. la), felt in the S a n t a Maria area, and was given M L = 3.5. The P wave was very emergent, and no S wave could be identified on the short-period SCSN seismograms (Fig. lb). It was also recorded with the th r ee- c om ponent br oadband seismograph of the TERRAscope station at S a n t a B a r b a r a (SBC) at a distance of 70 km (Fig. la). However, the seismogram recorded at SBC was so u n u s u a l t h a t we could not i m m edi at el y identify it as a regional ear t hqua ke ; we accidentally noticed it while we were examining the S-wave coda of a large ( M s = 6.6, depth = 150 kin) intermediate-depth e a r t h q u a k e in t he H i n d u - K u s h region t h a t occurred at about the same time. Figure 2a compares a Wood-Anderson seismogram of this e a r t h q u a k e (simulated from the SBC TERRAscope br oadband record) with the seismogram of an o r d in ar y event with about the same m a g n i t u d e recorded at about the same distance. The anomalous n a t u r e of this event is evident. N e i t h e r P nor S wave is distinct, and the duration, about 2 minutes, is u n u s u a l l y long for an M L = 3.5 event. Kovach (1974) analyzed seismograms of events caused by collapse in the Wilmington oil field n e a r Long Beach, California. The SBC record of the S a n t a 2087
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Maria event is very similar to the records of the Wilmington events and suggests a similar origin for the Santa Maria event. The epicenter is within the Orcutt oil field in the S a n t a Maria basin (see Fig. la). After several inquiries about oil extraction activities in the oil fields in the area, we found t h a t hydro-fracturing at a pressure of about 80 bars was being done at a depth of 100 to 300 m in the Orcutt oil field from about 9 to 11 a.m. on 31 J a n u a r y 1991. While perforation gear was being lowered into one of the wells, the earthquake occurred (Charlie Catherman, personal comm., 1991). The deformation of liners in several wells at similar depths suggests t h a t the Santa Maria event was caused by failure of sediments at shallow depth. Because of its very shallow depth, the earthquake excited large surface waves at periods near the resonance period of the sedimentary layers. WAVEFORM AT SBC
Figure 2b shows the displacement record at SBC. In addition to the s t a n d a r d three-component (Z, N, and E) traces, the radial and transverse components are shown. The first 60 sec shows a coherent dispersive wave train, suggesting a Rayleigh wave on the vertical and radial components and a Love wave on the transverse component. The latter h a l f (60 to 120 sec) of the wave train is dominated by the E-W component. This is probably a Love wave scattered by the structure between the epicenter and SBC. The path from the epicenter to SBC is primarily in the S a n t a Maria basin, but it crosses the S a n t a Ynez mountains near the SBC station. The scattering could be due to the structures near the basin boundaries. We used the unscattered first 60 sec of the Love wave for the analysis. The group velocity of this wavetrain, ranging from 1.5 to 2 k m / s e c for a period of 5 to 8 sec, is in agreement with the group velocity (Fig. 3) computed for the structure shown in the figure. The P velocities for this structure are t a k e n from the southeastern end of a Gabilan Range profile published by Walter and Mooney (1982). The S velocities were first computed from the P velocities with a Poisson's ratio of 0.25, and later were slightly modified to match the observed group velocities. FIELD DATA
The field d a t a provided by C a t h e r m a n (personal comm., 1991) and Shemeta (written comm., 1992) are summarized in Figure 4. The Orcutt oil field where the hydro-fracturing was performed has five wells in a circular area about 360 m in diameter. All the liners in the casings were deformed into S shape with a m a x i m u m offset of approximately 30 cm. The depths to the S-shaped deformations range from 135 to 280 m. C a t h e r m a n estimates the fault dip to be about 40 ° to SSW. Most bedding planes in the area have dips of 10 to 15 °. The direction of the slip on the fault plane could not be determined. SOURCE PARAMETERS
The first motions from this event recorded at SCSN and the Pacific Gas and Electric Company (PG and E) seismic network were very emergent. Out of 41 first-motion data, 34 were reported as "up," with only seven being reported as "down." Three impulsive firstmmotion data were all up. Since the event is very shallow and the velocity in the source region is very low, all the first motions should plot near the center of the focal mechanism diagram. All the first
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Fie. 4. The field d a t a obtained from the Orcutt oil field. The S-shaped curve is a sketch of the deformed casings. The m e c h a n i s m diagram (stereographic projection of the lower focal hemisphere) is constructed from the field data a n d the first-motion data.
motions should be up if the faulting was reverse on a dipping plane, and down if it was a normal faulting. Thus, the overwhelmingly up first motions suggest a t h r u s t faulting, as shown in Figure 4. Here, the rake is assumed to be 90 °. We interpreted the SBC record using the t h r u s t mechanism. Figure 5a shows the spectrum of the observed Love wave (0 to 60 sec on Fig. 2b). Curve a shows the excitation spectrum for a point source placed at a depth of 500 m in the crust shown in Figure 3. It is computed for a pure reverse fault with a dip angle of 40 ° and a strike of 112.5 °, as suggested from the field data and the first-motion data. The method described in Kanamori and Stewart (1976) is used for this computation. If a source depth of 5 km is used, the excitation function peaks at 7 sec with a rapid roll-off above 0.2 Hz. Thus, the observed large amplitude in periods shorter t h a n 5 sec requires a very shallow source. The observed spectrum exhibits a spectral hole at about 0.3 Hz with a rapid roll-off at frequencies higher t h a n 0.5 Hz. Kovach (1974) found a similar behavior for earthquakes in the Wilmington oil field and explained it with a slow rupture propagation model. We could not determine whether the observed spectral hole and the rapid roll-off at high frequencies were due to slow rupture or slow dislocation particle velocity, but an overall source time constant, To, of about 3 sec is required. Since only one record is available, any combination of rupture length and r u p t u r e velocity with a ratio of 3 sec explains the data. Kovach (1974) obtained a very slow rupture velocity, about 0.13 k m / s e c , for the events in the Wilmington oil field. In Figure 5a, we used a combination of a rupture velocity of 0.13 k m / s e c and a r u p t u r e length of 0.4 kin. Although this combination is not unique, the r u p t u r e length of 0.4 km is comparable to the linear dimension of the area where the wells are distributed and is also consistent with the source dimension estimated from the seismic slip and moment, as will be shown later. Multiplying the finiteness spectrum (BenMenachem, 1961), sin(~rf~'o)/~rfir o, computed for this combination by the point source spectrum, we obtained the source spectrum shown by curve b in Figure 5a, which is similar to the observed spectrum. A seismic moment of 6.1 x 1021 dyne-cm is required to explain the observed amplitude. Figure 5b compares the observed Love wave with the synthetic waveform computed for the source model shown in Figure 5b. In this calculation, the Love-wave Q is assumed to be 100. The overall agreement of the waveform is satisfactory. Thus, although we could
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not d e t e r m i n e the r u p t u r e c h a r a c t e r i s t i c s u n i q u e l y , we consider t h e slow rupt u r e model d e s c r i b e d above to be r e a s o n a b l e . T h e c o m p r e s s i o n axis of t h e m e c h a n i s m s h o w n in F i g u r e 4 is in N N E - S S W direction, w h i c h a g r e e s w i t h t h e direction of r e g i o n a l s h o r t e n i n g d e t e r m i n e d from t h e geodetic d a t a (Feigl et al., 1990). T h e t h r u s t m e c h a n i s m s h o w n in F i g u r e 4 places t h e S a n t a B a r b a r a s t a t i o n fairly close to t h e r a d i a t i o n node of Love waves. C o n s i d e r i n g the u n c e r t a i n t i e s in t h e m e c h a n i s m , we t h e n consider a n a l t e r n a t i v e strike-slip m e c h a n i s m , w h i c h p u t s SBC n e a r t h e r a d i a t i o n m a x i m u m . F o r this m e c h a n i s m , we o b t a i n e d a seismic m o m e n t of 1.2 x 1021 dyne-cm, w h i c h can be c o n s i d e r e d a m i n i m u m seismic m o m e n t for this event. SLIP, SEISMIC MOMENT, AND ENERGY In t h e following calculation, we use a seismic m o m e n t 4 × 1021 d y n e - c m as t h e a v e r a g e of t h e two seismic m o m e n t s e s t i m a t e d above. U s i n g p = 1.8 g / c m 3, a n d fi = 1.54 k m / s e c from F i g u r e 3, we o b t a i n / ~ = pfi2 = 4.3 x 10 l° d y n e / c m 2. I f t h e d i s p l a c e m e n t is 30 cm as s u g g e s t e d b y t h e field data, t h e a r e a S is Mo/I~D = 3.1 × 105 m 2, w h i c h gives a r e p r e s e n t a t i v e d i m e n s i o n of t h e source, S 1/2, of 560 m. This v a l u e is c o m p a r a b l e to t h a t i n f e r r e d from t h e s p e c t r a l hole a n d t h e d i m e n s i o n of t h e a r e a w h e r e t h e wells are distributed. T h e t o t a l e n e r g y r a d i a t e d f r o m this e v e n t can be a p p r o x i m a t e l y e s t i m a t e d as follows. Since the s p e c t r u m of t h e t r a n s v e r s e c o m p o n e n t of t h e g r o u n d - m o t i o n velocity at SBC h a s a s h a r p p e a k at 0.35 Hz, as s h o w n in F i g u r e 6, we a s s u m e t h a t t h e m o s t e n e r g y is c o n t a i n e d in t h e f u n d a m e n t a l m o d e Love wave at f = 0.35 Hz. T h e n t h e t o t a l r a d i a t e d e n e r g y is given b y co
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Here, v(t) is the ground-motion velocity at distance A, p is the density at the surface, c is the phase velocity at 0.35 Hz, k is the attenuation constant (i.e., 7rf/Qc), and h is the thickness of the effective wave guide, which is given by co
-h = fo P(z)Y2(z)dz
p(O)y2(O) where y(z) is the Love-wave amplitude as a function of depth at 0.35 HR. Using the normal mode computed for the structure shown in Figure 3, we obtained = 1.2 km. Integrating the velocity trace of the transverse component, we obtain 3c
fo V(t)2dt = 0.68 × 103 cm2/sec. Substituting this and using c = 1.75 k m / s e c , p = 1.8 g / c m 3 in (1), we obtain E = 2.4 × 1015 ergs. The ratio of the energy E to seismic moment is thus
E l M o = 6.2 × 10 -7, which is much smaller t h a n the ratios 5 × 10 5 to 5 × 10 -6 for ordinary earthquakes (Kanamori, 1977; Vassiliou and Kanamori, 1982), reflecting the slow n a t u r e of this earthquake. CONCLUSION
Although we could not uniquely determine the detailed geometry of the source mechanism, the present result demonstrates t h a t release of regional tectonic stress in shallow sediments can yield significant seismic radiation at periods of a few seconds. The dominant period is much longer t h a n t h a t of ordinary earthquakes with a comparable magnitude and is within the period range of engineering importance for large structures. In this regard, the present result has important implications for excitation of long-period ground motions from large earthquakes in sedimentary basins. ACKNOWLEDGMENT We t h a n k Charlie C a t h e r m a n for providing us with the field data from the Orcutt oil field. We also t h a n k J i m Mori for providing us with the recbrd section of the S o u t h e r n California Seismic Network, and William Savage and Marcia McLaren for providing us with the data obtained from the Seismic Network of the Pacific Gas a n d Electric Company. We t h a n k Julie S h e m e t a for information on the well locations in the Orcutt oil field. This research was partially supported by the U.S. Geological Survey G r a n t 14-08-0001-G1774 a n d a g r a n t from the L.K. Whittier Foundation. Contribution No. 5173, Division of Geological and P l a n e t a r y Sciences, California I n s t i t u t e of Technology, Pasadena, California. REFERENCES Ben-Menachem, A. (1961). Radiation of seismic surface waves from finite moving sources, Bull. Seism. Soc. Am. 51, 401-435. Feigl, K. L., R. W. King, a n d T. H. J o r d a n (1990). Geodetic m e a s u r e m e n t of tectonic deformation in the S a n t a M a r i a fold and t h r u s t belt, California, J. Geophys. Res. 95, 2679-2699.
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H. KANAMORI AND E. HAUKSSON
Kanamori, H. (1977). The energy release in great earthquakes, J. Geophys. Res. 82, 2981-2987. Kanamori, H. and G. S. Stewart (1976). Mode of the strain release along the Gibbs fracture zone, mid-Atlantic ridge, Phys. Earth Planet Interiors. 11, 312-332. Kovach, R. L. (1974). Source mechanisms for Wilmington oil field, California, subsidence earthquakes, Bull. Seism. Soc. Am. 64, 699-711. Vassiliou, M. S. and H. Kanamori (1982). The energy release in earthquakes, Bull. Seism. Soc. Am. 72, 371-387. Walter, A. W. and W. D. Mooney (1982). Crustal structure of the Diablo and Gabilan ranges, central California: a reinterpretation of existing data, Bull. Seism. Soc. Am. 72, 1567-1590. SEISMOLOGICALLABORATORY CALIFORNIAINSTITUTEOF TECHNOLOGY PASADENA,CALIFORNIA91125 Manuscript received 18 June 1992
A SLOW EARTHQUAKE IN T H E SANTA MARIA BASIN, CALIFORNIA BY HIROO KANAMORI AND EGILL HAUKSSON ABSTRACT An M L = 3.5 earthquake near Santa Maria, California, was recorded by the Southern California Seismic Network and a TERRAscope station at Santa Barbara (SBC) on 31 January 1991. The waveform of this event is dominated by 2- to 5-sec waves, and is different from that of ordinary events with similar size. Inquiries into operations in several oil fields in the area revealed that hydro-fracturing at a pressure of about 80 bars was being done at a depth of 100 to 300 m in the Orcutt oil field in the Santa Maria basin from about 9 to 11 a.m. on 31 January and the earthquake occurred in the afternoon. Field evidence of 30-cm displacement to a depth of 300 m was reported. The field evidence as well as the first-motion data indicates that the event had a thrust mechanism with the P axis in the N N E - S S W direction, which is in agreement with the regional stress field. From the analysis of the SBC record and the field evidence, we conclude that the source must be shallower than 1 km and the ratio of the radiated energy to the seismic moment is about 6.2 × 10 -7, one to two orders of magnitude smaller than that of ordinary earthquakes. The occurrence of this earthquake demonstrates that release of regional tectonic stress in shallow sediments can yield significant seismic radiation at periods of a few seconds, the period range of engineering importance for large structures, and has important implications for excitation of long-period ground motions from large earthquakes in sedimentary basins.
INTRODUCTION On 31 J a n u a r y 1991, an anomalous e a r t h q u a k e was recorded at seismic stations of the S o u t h e r n California Seismic Network (SCSN). This event was located at 34.8°N and 120.4°W (origin time: 23:28:18 GMT) n e a r Orcutt in the S a n t a Maria basin, California (Fig. la), felt in the S a n t a Maria area, and was given M L = 3.5. The P wave was very emergent, and no S wave could be identified on the short-period SCSN seismograms (Fig. lb). It was also recorded with the th r ee- c om ponent br oadband seismograph of the TERRAscope station at S a n t a B a r b a r a (SBC) at a distance of 70 km (Fig. la). However, the seismogram recorded at SBC was so u n u s u a l t h a t we could not i m m edi at el y identify it as a regional ear t hqua ke ; we accidentally noticed it while we were examining the S-wave coda of a large ( M s = 6.6, depth = 150 kin) intermediate-depth e a r t h q u a k e in t he H i n d u - K u s h region t h a t occurred at about the same time. Figure 2a compares a Wood-Anderson seismogram of this e a r t h q u a k e (simulated from the SBC TERRAscope br oadband record) with the seismogram of an o r d in ar y event with about the same m a g n i t u d e recorded at about the same distance. The anomalous n a t u r e of this event is evident. N e i t h e r P nor S wave is distinct, and the duration, about 2 minutes, is u n u s u a l l y long for an M L = 3.5 event. Kovach (1974) analyzed seismograms of events caused by collapse in the Wilmington oil field n e a r Long Beach, California. The SBC record of the S a n t a 2087
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Maria event is very similar to the records of the Wilmington events and suggests a similar origin for the Santa Maria event. The epicenter is within the Orcutt oil field in the S a n t a Maria basin (see Fig. la). After several inquiries about oil extraction activities in the oil fields in the area, we found t h a t hydro-fracturing at a pressure of about 80 bars was being done at a depth of 100 to 300 m in the Orcutt oil field from about 9 to 11 a.m. on 31 J a n u a r y 1991. While perforation gear was being lowered into one of the wells, the earthquake occurred (Charlie Catherman, personal comm., 1991). The deformation of liners in several wells at similar depths suggests t h a t the Santa Maria event was caused by failure of sediments at shallow depth. Because of its very shallow depth, the earthquake excited large surface waves at periods near the resonance period of the sedimentary layers. WAVEFORM AT SBC
Figure 2b shows the displacement record at SBC. In addition to the s t a n d a r d three-component (Z, N, and E) traces, the radial and transverse components are shown. The first 60 sec shows a coherent dispersive wave train, suggesting a Rayleigh wave on the vertical and radial components and a Love wave on the transverse component. The latter h a l f (60 to 120 sec) of the wave train is dominated by the E-W component. This is probably a Love wave scattered by the structure between the epicenter and SBC. The path from the epicenter to SBC is primarily in the S a n t a Maria basin, but it crosses the S a n t a Ynez mountains near the SBC station. The scattering could be due to the structures near the basin boundaries. We used the unscattered first 60 sec of the Love wave for the analysis. The group velocity of this wavetrain, ranging from 1.5 to 2 k m / s e c for a period of 5 to 8 sec, is in agreement with the group velocity (Fig. 3) computed for the structure shown in the figure. The P velocities for this structure are t a k e n from the southeastern end of a Gabilan Range profile published by Walter and Mooney (1982). The S velocities were first computed from the P velocities with a Poisson's ratio of 0.25, and later were slightly modified to match the observed group velocities. FIELD DATA
The field d a t a provided by C a t h e r m a n (personal comm., 1991) and Shemeta (written comm., 1992) are summarized in Figure 4. The Orcutt oil field where the hydro-fracturing was performed has five wells in a circular area about 360 m in diameter. All the liners in the casings were deformed into S shape with a m a x i m u m offset of approximately 30 cm. The depths to the S-shaped deformations range from 135 to 280 m. C a t h e r m a n estimates the fault dip to be about 40 ° to SSW. Most bedding planes in the area have dips of 10 to 15 °. The direction of the slip on the fault plane could not be determined. SOURCE PARAMETERS
The first motions from this event recorded at SCSN and the Pacific Gas and Electric Company (PG and E) seismic network were very emergent. Out of 41 first-motion data, 34 were reported as "up," with only seven being reported as "down." Three impulsive firstmmotion data were all up. Since the event is very shallow and the velocity in the source region is very low, all the first motions should plot near the center of the focal mechanism diagram. All the first
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H. K A N A M O R I AND E. H A U K S S O N
Field
Dola
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Distribution of Wells Fault Dips
40 ° to SSW
1St Motion
oo
o
o
Casings
o
360m--~
34 "up"
MaximumOffset 30 cm \
7 "down"
at depths ot 135 to 280 m
Fie. 4. The field d a t a obtained from the Orcutt oil field. The S-shaped curve is a sketch of the deformed casings. The m e c h a n i s m diagram (stereographic projection of the lower focal hemisphere) is constructed from the field data a n d the first-motion data.
motions should be up if the faulting was reverse on a dipping plane, and down if it was a normal faulting. Thus, the overwhelmingly up first motions suggest a t h r u s t faulting, as shown in Figure 4. Here, the rake is assumed to be 90 °. We interpreted the SBC record using the t h r u s t mechanism. Figure 5a shows the spectrum of the observed Love wave (0 to 60 sec on Fig. 2b). Curve a shows the excitation spectrum for a point source placed at a depth of 500 m in the crust shown in Figure 3. It is computed for a pure reverse fault with a dip angle of 40 ° and a strike of 112.5 °, as suggested from the field data and the first-motion data. The method described in Kanamori and Stewart (1976) is used for this computation. If a source depth of 5 km is used, the excitation function peaks at 7 sec with a rapid roll-off above 0.2 Hz. Thus, the observed large amplitude in periods shorter t h a n 5 sec requires a very shallow source. The observed spectrum exhibits a spectral hole at about 0.3 Hz with a rapid roll-off at frequencies higher t h a n 0.5 Hz. Kovach (1974) found a similar behavior for earthquakes in the Wilmington oil field and explained it with a slow rupture propagation model. We could not determine whether the observed spectral hole and the rapid roll-off at high frequencies were due to slow rupture or slow dislocation particle velocity, but an overall source time constant, To, of about 3 sec is required. Since only one record is available, any combination of rupture length and r u p t u r e velocity with a ratio of 3 sec explains the data. Kovach (1974) obtained a very slow rupture velocity, about 0.13 k m / s e c , for the events in the Wilmington oil field. In Figure 5a, we used a combination of a rupture velocity of 0.13 k m / s e c and a r u p t u r e length of 0.4 kin. Although this combination is not unique, the r u p t u r e length of 0.4 km is comparable to the linear dimension of the area where the wells are distributed and is also consistent with the source dimension estimated from the seismic slip and moment, as will be shown later. Multiplying the finiteness spectrum (BenMenachem, 1961), sin(~rf~'o)/~rfir o, computed for this combination by the point source spectrum, we obtained the source spectrum shown by curve b in Figure 5a, which is similar to the observed spectrum. A seismic moment of 6.1 x 1021 dyne-cm is required to explain the observed amplitude. Figure 5b compares the observed Love wave with the synthetic waveform computed for the source model shown in Figure 5b. In this calculation, the Love-wave Q is assumed to be 100. The overall agreement of the waveform is satisfactory. Thus, although we could
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H. KANAMORI AND E. HAUKSSON
not d e t e r m i n e the r u p t u r e c h a r a c t e r i s t i c s u n i q u e l y , we consider t h e slow rupt u r e model d e s c r i b e d above to be r e a s o n a b l e . T h e c o m p r e s s i o n axis of t h e m e c h a n i s m s h o w n in F i g u r e 4 is in N N E - S S W direction, w h i c h a g r e e s w i t h t h e direction of r e g i o n a l s h o r t e n i n g d e t e r m i n e d from t h e geodetic d a t a (Feigl et al., 1990). T h e t h r u s t m e c h a n i s m s h o w n in F i g u r e 4 places t h e S a n t a B a r b a r a s t a t i o n fairly close to t h e r a d i a t i o n node of Love waves. C o n s i d e r i n g the u n c e r t a i n t i e s in t h e m e c h a n i s m , we t h e n consider a n a l t e r n a t i v e strike-slip m e c h a n i s m , w h i c h p u t s SBC n e a r t h e r a d i a t i o n m a x i m u m . F o r this m e c h a n i s m , we o b t a i n e d a seismic m o m e n t of 1.2 x 1021 dyne-cm, w h i c h can be c o n s i d e r e d a m i n i m u m seismic m o m e n t for this event. SLIP, SEISMIC MOMENT, AND ENERGY In t h e following calculation, we use a seismic m o m e n t 4 × 1021 d y n e - c m as t h e a v e r a g e of t h e two seismic m o m e n t s e s t i m a t e d above. U s i n g p = 1.8 g / c m 3, a n d fi = 1.54 k m / s e c from F i g u r e 3, we o b t a i n / ~ = pfi2 = 4.3 x 10 l° d y n e / c m 2. I f t h e d i s p l a c e m e n t is 30 cm as s u g g e s t e d b y t h e field data, t h e a r e a S is Mo/I~D = 3.1 × 105 m 2, w h i c h gives a r e p r e s e n t a t i v e d i m e n s i o n of t h e source, S 1/2, of 560 m. This v a l u e is c o m p a r a b l e to t h a t i n f e r r e d from t h e s p e c t r a l hole a n d t h e d i m e n s i o n of t h e a r e a w h e r e t h e wells are distributed. T h e t o t a l e n e r g y r a d i a t e d f r o m this e v e n t can be a p p r o x i m a t e l y e s t i m a t e d as follows. Since the s p e c t r u m of t h e t r a n s v e r s e c o m p o n e n t of t h e g r o u n d - m o t i o n velocity at SBC h a s a s h a r p p e a k at 0.35 Hz, as s h o w n in F i g u r e 6, we a s s u m e t h a t t h e m o s t e n e r g y is c o n t a i n e d in t h e f u n d a m e n t a l m o d e Love wave at f = 0.35 Hz. T h e n t h e t o t a l r a d i a t e d e n e r g y is given b y co
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Here, v(t) is the ground-motion velocity at distance A, p is the density at the surface, c is the phase velocity at 0.35 Hz, k is the attenuation constant (i.e., 7rf/Qc), and h is the thickness of the effective wave guide, which is given by co
-h = fo P(z)Y2(z)dz
p(O)y2(O) where y(z) is the Love-wave amplitude as a function of depth at 0.35 HR. Using the normal mode computed for the structure shown in Figure 3, we obtained = 1.2 km. Integrating the velocity trace of the transverse component, we obtain 3c
fo V(t)2dt = 0.68 × 103 cm2/sec. Substituting this and using c = 1.75 k m / s e c , p = 1.8 g / c m 3 in (1), we obtain E = 2.4 × 1015 ergs. The ratio of the energy E to seismic moment is thus
E l M o = 6.2 × 10 -7, which is much smaller t h a n the ratios 5 × 10 5 to 5 × 10 -6 for ordinary earthquakes (Kanamori, 1977; Vassiliou and Kanamori, 1982), reflecting the slow n a t u r e of this earthquake. CONCLUSION
Although we could not uniquely determine the detailed geometry of the source mechanism, the present result demonstrates t h a t release of regional tectonic stress in shallow sediments can yield significant seismic radiation at periods of a few seconds. The dominant period is much longer t h a n t h a t of ordinary earthquakes with a comparable magnitude and is within the period range of engineering importance for large structures. In this regard, the present result has important implications for excitation of long-period ground motions from large earthquakes in sedimentary basins. ACKNOWLEDGMENT We t h a n k Charlie C a t h e r m a n for providing us with the field data from the Orcutt oil field. We also t h a n k J i m Mori for providing us with the recbrd section of the S o u t h e r n California Seismic Network, and William Savage and Marcia McLaren for providing us with the data obtained from the Seismic Network of the Pacific Gas a n d Electric Company. We t h a n k Julie S h e m e t a for information on the well locations in the Orcutt oil field. This research was partially supported by the U.S. Geological Survey G r a n t 14-08-0001-G1774 a n d a g r a n t from the L.K. Whittier Foundation. Contribution No. 5173, Division of Geological and P l a n e t a r y Sciences, California I n s t i t u t e of Technology, Pasadena, California. REFERENCES Ben-Menachem, A. (1961). Radiation of seismic surface waves from finite moving sources, Bull. Seism. Soc. Am. 51, 401-435. Feigl, K. L., R. W. King, a n d T. H. J o r d a n (1990). Geodetic m e a s u r e m e n t of tectonic deformation in the S a n t a M a r i a fold and t h r u s t belt, California, J. Geophys. Res. 95, 2679-2699.
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H. KANAMORI AND E. HAUKSSON
Kanamori, H. (1977). The energy release in great earthquakes, J. Geophys. Res. 82, 2981-2987. Kanamori, H. and G. S. Stewart (1976). Mode of the strain release along the Gibbs fracture zone, mid-Atlantic ridge, Phys. Earth Planet Interiors. 11, 312-332. Kovach, R. L. (1974). Source mechanisms for Wilmington oil field, California, subsidence earthquakes, Bull. Seism. Soc. Am. 64, 699-711. Vassiliou, M. S. and H. Kanamori (1982). The energy release in earthquakes, Bull. Seism. Soc. Am. 72, 371-387. Walter, A. W. and W. D. Mooney (1982). Crustal structure of the Diablo and Gabilan ranges, central California: a reinterpretation of existing data, Bull. Seism. Soc. Am. 72, 1567-1590. SEISMOLOGICALLABORATORY CALIFORNIAINSTITUTEOF TECHNOLOGY PASADENA,CALIFORNIA91125 Manuscript received 18 June 1992
