Properties of the seismic nucleation phase

TECTONOPHYSICS ELSEVIER

Tectonophysics 261 (1996) 209-227

Properties of the seismic nucleation phase a*

G r e g o r y C. B e r o z a , , W i l l i a m L. E l l s w o r t h b a Department of Geophysics, Stanford University Stanford, CA 94305-2215, USA b US Geological Survey Menlo Park, CA 94025, USA

Received 25 August 1995; accepted 15 November 1995

Abstract

Near-source observations show that earthquakes begin abruptly at the P-wave arrival, but that this beginning is weak, with a low moment rate relative to the rest of the main shock. We term this initial phase of low moment rate the seismic nucleation phase. We have observed the seismic nucleation phase for a set of 48 earthquakes ranging in magnitude from 1.1-8.1. The size and duration of the seismic nucleation phase scale with the total seismic moment of the earthquake, suggesting that the process responsible for the seismic nucleation phase carries information about the eventual size of the earthquake. The seismic nucleation phase is characteristically followed by quadratic growth in the moment rate, consistent with self-similar rupture at constant stress drop. In this paper we quantify the properties of the seismic nucleation phase and offer several possible explanations for it.

1. Introduction

Theoretical models (e.g., Andrews, 1976; Dieterich, 1979 Dieterich, 1986, 1992; Das and Scholz, 1982) and laboratory experiments (e.g., Dieterich, 1979; Ohnaka et al., 1986) designed to simulate shear failure on a fault indicate that failure will begin with an episode of slow, stable sliding over a limited region of the fault, known as the nucleation zone. Slip within the nucleation zone gradually accelerates until a critical state is attained. This critical state occurs when the stiffness (stress drop per unit fault slip) falls below a critical level (Rice and Gu, 1983). At this time the process can become unstable with rupture propagating away from the nucleation zone at high rupture velocity in an earthquake. * Corresponding author, Fax: +1 415 7257344; e-mail: beroza@ pangea.stanford.edu.

A purely steady acceleration of slip on a fault should result in seismic waves that gradually emerge from the background noise. Direct observation of this sort of a slow nucleation process has been reported in the case of only a few earthquakes (Dziewonski and Gilbert, 1974; Sacks et al., 1978; Jordan, 1991; Ihml6 et al., 1993; Ihml6 and Jordan, 1994) and some of these observations are controversial (Okal and Geller, 1979; Kedar et al., 1994). More typically, the initial P waves from earthquakes appear impulsive rather than emergent, which has been interpreted as evidence that the nucleation zone of earthquakes must be too small to detect seismically (Dieterich, 1986). Recent observations from borehole strainmeters prior to a number of earthquakes place additional constraints on the total amount of slow premonitory slip that could have occurred as part of the nucleation process over longer time scales (Agnew and Wyatt, 1989; Johnston et al., 1990, 1994; Wyatt et al., 1994).

0040-1951/96/$15.00 Copyright© 1996 Elsevier Science B.V. All fights reserved. PH S0040- 1951(96)00067-4

210

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996)209-227

Although the first arriving P waves from earthquakes are impulsive, recent observations have shown that they are weak compared to the waves that follow them (Iio, 1992, 1995). Iio (1995) found that microearthquakes began with a slow initial phase that grew in time as t~ (2 < n < 4). He found that the duration of the slow initial phase was proportional to the size of the earthquake and associated it with the time required for the slip-weakening displacement to occur. For larger earthquakes these relatively weak first arrivals have sometimes been described as a "foreshock" or "preshock" (Spudich and Cranswick, 1984; Anderson et al., 1986; Christensen and Ruff, 1986; Choy and Dewey, 1988; Shimazaki and Somerville, 1988; Bezzeghoud et al., 1989; Frankel and Wennerberg, 1989; Beck and Christensen, 1991; Singh and Mortera, 1991; Wald et al., 1991; Hwang and Kanamori, 1992; Mendoza, 1993; Abercrombie and Moil, 1994; Ruff and Miller, 1994; Velasco et al., 1994; Abercrombie et al., 1995). In this paper we extend our earlier study of the initial P-wave arrivals (Ellsworth and Beroza, 1995) to 48 earthquakes ranging in size from M = 1.1-8.1. The data from 28 of these events were originally reported by Ellsworth and Beroza (1995), who determined their moment-rate functions by deconvolution and used them to quantify the initial growth of these earthquakes. We find a weak initial phase for all events that we studied. Although the properties of the weak initial phase vary for different events, we find strong evidence for systematic scaling. The duration of the seismic nucleation phase, when normalized by the duration of the entire earthquake, is consistent with a log-normal distribution with a mean of 0.16. The average seismic moment of the seismic nucleation phase, however, is less than 1% of the total seismic moment of the earthquake. Thus, the seismic nucleation phase is not properly characterized as the first of a series

of similar subevents comprising an earthquake. Both the size and the duration of the seismic nucleation phase scale with the size of the eventual earthquake, suggesting that the ultimate size of an earthquake is strongly influenced by the nucleation process. 2. Characterization of the seismic nucleation phase by the m o m e n t - r a t e function

Historically, the great majority of near-source data have been recorded on analog seismographs with insufficient dynamic range and bandwidth to capture the initiation process. The initial P waves from earthquakes are usually not strong enough to trigger strong-motion instruments, but are large enough to clip high-gain seismographs, and hence are usually not clearly observed. The ongoing deployment of high dynamic range, digital seismographs has begun to change this picture, and we assemble here data on the initiation of 48 events, Mw = 1.1-8.1 (Table 1) recorded on such instruments. The Northridge earthquake is an example for which multiple on-scale recordings (Fig. 1) of the initiation were obtained in the near-source region (Steidl et al., 1994; Hauksson et al., 1994). We use this earthquake to illustrate how we derive the moment-rate function, and to test some of the assumptions made in this analysis. Fig. la shows magnified low-gain recordings of the Northridge earthquake at 5 different stations. These data demonstrate that the earthquake began with an impulsive P wave arrival; however, the lowgain recordings of the first 2.5 s of the earthquake shown in Fig. lb, indicate that this impulsive beginning is completely dwarfed by what follows. Onehalf second into the event, there is a sharp, linear increase in the ground velocity. The clear change in the slope of the velocity at t = 0.5 s argues for a sudden transition from a low to a high level of dynamic stress release. We define the interval between

Properties of the initial stages of the earthquakes discussed in the text. Moment-rate functions were derived for 28 of the 48 events assuming Vp = 6 km/s, Vp/Vs = 1.73, and/z = 30000 MPa for a surface receiver at radial distance, R, from the hypocenter. Letters following the date identify: Northridge aftershocks (N); Earthquakes near Anza, California (A); earthquakes recorded at the 1-km-deep Varian borehole in Parkfield, California (P); earthquakes in Long Valley Caldera recorded in the Long Canyon borehole (L). The total duration of the earthquake is the duration of the seismic nucleation phase, v, plus the time from breakout to the cessation of rupture, r. Seismic moment release during the seismic nucleation phase, M~o,given as a percentage of the mainshock seismic moment, lifo. Computation of the nucleation radius, ru, is derived by matching the stress drop, Atrb, of the breakout phase as described in the text. We assume a rupture velocityof 80% of Vs in determination of Aab.

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

211

Table 1 Earthquake nucleation parameters No.

Date

Mw

Mo (N m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

19 Sep. 1985 28 Jun. 1992 25 Apr. 1989 18 Oct. 1989 17 Jan. 1994 15 Oct. 1979 9 Jun. 1980 2 4 Oct. 1993 28 Jun. 1992 23 Apr. 1992 31 May. 1990 28 Jun. 1991 2 0 Mar. 1 9 9 4 N 3 Dec. 1988 16 Jan. 1993 14 Nov. 1993 3 Feb. 1 9 9 4 N 18 Feb. 1 9 9 0 A 6 Feb. 1 9 9 4 N 5 Oct. 1 9 8 4 A 2 Feb. 1 9 9 4 N 22 Dec. 1 9 8 9 A 27 Oct. 1 9 9 1 A 6 Feb. 1 9 9 4 N 18 Feb. 1 9 9 4 N 14 May. 1 9 8 5 A 5 Feb. 1 9 9 0 A 9 Jul. 1 9 9 1 A 26 Oct. 1992P 1 Feb. 1 9 9 4 N 2 Jan. 1 9 9 0 A 9 Feb. 1 9 9 4 A 4 Feb. 1994N 8 Mar. 1 9 9 4 N 30 Jan. 1 9 8 8 M 25 Dec. 1 9 9 2 P 26 Oct. 1 9 9 2 P 8 Nov. 1 9 9 2 L 19 Nov. 1 9 8 7 M 20 Nov. 1 9 8 7 M 26 Oct. 1992P 28 Oct. 1992P 28 Oct. 1992P 26 Oct. 1992P 26 Oct. 1992P 26 Oct. 1992P 26 Oct. 1992P 14 Nov. 1 9 9 2 P

8.1 7.3 6.9 6.9 6.7 6.5 6.4 6.4 6.2 6.1 5.9 5.5 5.3 4.9 4.9 4.8 4.2 4.1 4.1 3.9 3.8 3.7 3.7 3.7 3.7 3.6 3.6 3.6 3.6 3.6 3.5 3.5 3.5 3.4 3.3 3.3 3.2 2.6 2.4 2.4 2.1 2.1 1.8 1.7 1.4 1.2 1.2 1.1

1.4 9.0 2.4 2.8 1.0 6.0 4.8 5.8 2.0 1.4 7.5 2.8 8.9 2.4 2.4 2.0 2.0 1.4 1.4 7.1 5.0 3.5 3.5 3.5 3.5 2.5 2.5 2.5 2.5 2.5 1.8 1.8 1.8 1.3 8.1 8.9 6.3 7.9 4.1 4.2 1.4 1.4 5.0 3.5 1.3 6.3 6.3 4.5

× × x × × x x x x x x x x x x x x x x x x x x × × × × × × × × x × × × × × x × x × x x x × x × x

1021 1019 1019 1019 1019 1018 1018 1018 1018 1018 1017 1017 1016 1016 1016 1016 1015 1015 1015 1014 1014 1014 1014 1014 1014 1014 1014 1014 1014 1014 1014 l014 1014 1014 1013 1013 1013 1012 1012 1012 1012 1012 1011 1011 1011 101° 101° 101°

R (km)

v (s)

25 21 27 25 19 19 13 32 26 44 24 23 22 16 29 15 26 14 24 22 17 15 15 23 21 13 15 8 11 11 16 16 16 22 2 10 11 6 1 2 10 10 10 10 10 11 11 5

5.0 2.3 0.53 1.6 0.5 0.59 0.88 0.36 0.46 0.12 0.082 0.34 0.127 0.11 0.17 0.20 0.047 0.018 0.026 0.025 0.039 0.013 0.038 0.030 0.104 0.022 0.021 0.022 0.022 0.013 0.032 0.028 0.008 0.047 0.027 0.02 0.02 0.004 0.0075 0.0078 0.015 0.016 0.014 0.017 0.01 0.012 0.01 0.008

r (s) 50 20 9 6 15. 4 1.7 0.8 0.87 0.8 0.8 0.3 0.26 0.24 0.3 0.14 0.27 0.16 0.10 0.32 0.14 0.17 0.12 0.18 0.05 0.24 0.11 0.19 0.21 0.15 0.17 0.05 0.03 . 0.035 . . . . .

.

. . . . .

M~o (%)

r~, (m)

0.2 0.4 0.02 1.6 0.2 0.6 0.8 0.03 0.16 0.01 0.04 1.6 1.31 1.4 2.2 0.8 0.43 0.13 0.30 0.6 0.25 1.8 0.10 0.6 0.45 0.71 1.0 0.2 . . . . . .

6300 3400 850 2200 600 1000 1400 520 560 150 130 480 230 220 300 410 73 46 66 52 36 28 32 39 35 100 18 11 . . . . . .

A~rb (MPa) 5.0 4.1 3.4 1.9 40 14 6.0 5.5 8.1 17 64 18 42 15 8.8 1.1 9.6 8.0 2.3 6.5 8.3 100 3.4 8.2 8.4 0.4 60 5.4

212

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

(a) High-Gain

34.5* N

,/' 33.5 ° N 119.0" W

-"

,,, 117.5* W

,

/

(b) Low-Gain

34.5° N

i

~'~m,1/," "' 33.5 ° N

s

u~u

vv

117.5" W

Fig. 1. Map view of the Northridge mainshock and aftershocks, shown as filled octagons. Triangles indicate station locations. (a) Vertical component velocity seismograms of the initial P waves of the Northridge earthquake. SMF is a high-gain velocity record that quickly clips. The other traces are magnified and artificially clipped to simulate typical high-gain records and demonstrate that at this scale the onset appears abrupt. The station at PUB is a dilatational strain record, all others are velocity. (b) Low gain recordings of the initial P waves of the Northridge earthquake at the same sites. In each case the arrow indicates the first arriving waves seen in the upper panel. The onset, though abrupt, remains weak until about 0.5 s into the mainshock. the first-arriving P wave and the sudden increase in growth of the velocity seismogram for this earthquake as the seismic nucleation phase, and denote its duration as v. We also define the beginning of the linear increase in ground velocity as the breakaway phase.

We use the point-source moment-rate function to quantify the temporal growth of the earthquake source. We determine the moment-rate function by modeling the P-wave displacement seismograms that are obtained by integration of instrument-corrected broadband velocity or acceleration records. We assume half-space Green's functions (Johnson, 1974) and use fault plane solutions for each earthquake, determined independently from either first-motion data (e.g., Reasenberg and Oppenheimer, 1985) or waveform moment-tensor inversions (e.g., Dziewonski et al., 1981). Deconvolution of the half-space Green's functions from the data yields the moment-rate function, Mo(t). The validity of this procedure and the use of the moment-rate function to characterize the initial growth rate of the earthquake depends on several assumptions. The fundamental assumption is that the extent of the source generating the seismic nucleation phase is small so that the effects of spatial variations in Green's functions and the spatial extent of the source are negligible compared with effects arising from the time dependence of the slip. For most of the events studied, the duration of the nucleation phase is less than 1 s. The distance that rupture is likely to propagate in that time is small compared to the distance between the hypocenter and the recording station (Table 1), which is typically tens of km, so the spatial variability of the Green's function during the seismic nucleation phase is likely to be slight. Another issue is the effect of directivity on our measurements. Directivity becomes a dominant effect when the rupture velocity approaches the propagation velocity of the seismic wave being recorded. This effect should not be too strong because we are analyzing P waves. Although there are instances where seismologists have found evidence for rupture propagation at velocities approaching the P-wave velocity (Archuleta, 1984; Beroza and Spudich, 1988), these examples are for a limited part of the fault and occur after earthquake rupture has propagated tens of km along the fault with large accompanying dynamic stresses. A more reasonable expectation for rupture velocity during the seismic nucleation phase is that it might be as high as the average rupture velocity in earthquakes, "-~80% of the S-wave velocity. In this case directivity will still exert an effect on the shape and amplitude of the moment-rate function. If we assume: a

G.C. Beroza, W.L Ellsworth/Tectonophysics 261 (1996) 209-227

Poisson solid, that the rupture velocity during the seismic nucleation phase is 80% of the shear-wave velocity, and the extreme case for which a station is directly lined up with the rupture direction, then directivity can change the P-wave amplitudes by up to a factor of 1.9. Thus, we should be off by less than a factor of 2 from the true point-source moment-rate amplitude in our estimated moment-rate amplitude from a single station. A similar argument indicates that the apparent duration of the nucleation phase as measured using P waves should be within ± 5 0 % of the true duration. This simple analysis suggests that effects related to spatial finiteness ought to be small for our study, but we can test the validity of our assumptions directly using multiple recordings of the Northridge earthquake. The similarity of the recordings of the P waves at different stations (Fig. 1) is consistent with our assumptions; however, we can test this quantitatively by analyzing two stations independently. Fig. 2 shows that both the timing and amplitude of Me(t) obtained at stations SMF and USC are nearly identical (the amplitudes of the velocity seismograms

,t\ [

/"", b

U (ha-S sflpC a(lC ye)rU edS)C,

0.5

.l

"

~

1.0

1.5

2.0

Seconds

Fig. 2. Moment-rate functions determined for the Northridge earthquake for the first 2 s of rupture at stations SMF and USC. USC is at a distance of 32 kin from the mainshock and an azimuth of 132°. SMF is at a distance of 23 kin from the mainshock and an azimuth of 158°. The moment magnitude of the earthquake after 0.5 s is 4.7. In the next 0.5 s, the earthquake grows to moment magnitude 5.7. Like other recent California earthquakes, the Northridge event began slowly and then accelerated suddenly into a large earthquake. The solid and the dotted lines show the moment-ratefunctions determined using the USC seismogramfor a half-spaceand a layered model.

213

differ by a factor of 5), which confirms that the point-source assumption used in the deconvolution is reasonable, at least for the first second of this earthquake. We can also use the Northridge earthquake to test the validity of the half-space Green's functions. Because the dominant heterogeneity in the Earth's crust is vertical, we compare results obtained assuming a vertically layered half space appropriate for the Northridge region using the wavenumber integration technique of Saikia (1994) to calculate Green's functions with results obtained by assuming a homogeneous half-space model. Fig. 2 shows that we obtain similar results for either assumption at station USC. Differences between the two models are less than about 20% at these very short distances. This difference is sufficiently small for the purposes of this study because we are primarily interested in determining v and Mo(t)for the seismic nucleation phase relative to the rest of the earthquake. Momentrate functions for a representative sample of small, moderate, and large earthquakes that we have studied are shown in Fig. 3. When the nucleation phase is short, there are several issues that must be considered. First, there is a lower limit on the duration of the seismic nucleation phase that can be measured with band-limited, discretely sampled data. A seismic nucleation phase that is shorter than the sampling interval will be difficult or impossible to detect. The sampling interval for data used in this study ranges from 20 to 500 samples per second (sps). Propagation effects may also be important when v is small. Propagation effects such as velocity dispersion due to intrinsic attenuation (Gladwin and Stacey, 1974) and forward scattering (Mukerji et al., 1995) can distort the velocity pulse shape. Hence the measurements of v in Table 1 for earthquakes smaller than about magnitude 4.0 may be biased by propagation effects. In this case it is impossible to be certain that events such as event 33 (Fig. 7) have a seismic nucleation phase. Data for the magnitude 2.6 earthquake (event 38 in Table 1) at Long Valley (Fig. 4) was recorded at 500 sps at 2.0 km depth in a borehole located 6 km from the earthquake so that the waves did not propagate through the highly attenuating nearsurface layers. For this event we studied the seismic

214

G.C. Beroza, W.L. Ellsworth / Tectonophysics 261 (1996) 209-227

Large-Magnitude Earthquakes

%)6.9,': gg

M 6.9t (4) I I

M 6.7 ¢~= o =

(5) /

M 6,4

/

. (7)

/.."" I/

~

I

I

,'" :

," M 7.3 (2)| S I,

;'

"','/

M 8.111

I~'

,"

,"

. , /I / " /•.Se" ",..J

'%

/

I

I

I

/

I

,..:.

o

~

~

~

~

Seconds alter Event Initiation

M0derate-Magnitude Earthquakes : : I M4.9: M6.1/ (15~'~J*

M53~

o

7 So/"/ ~15i5 //

(13,/

~0 o

/

o'

M6.2/ (),

-

/ / /

/".///

3. Properties of the seismic nucleation phase

o

o'

o.o

o'.4

0'.2

0'6

o's

1.0

Seconds after Event Initiation

Small-Magnitude Earthquakes o

e,i" M 4.2,; ; ; ' ~ M 4'9

to

~o o

M3.7" (a4)/

E o

/

o"

j 3.~""

o. o.o

nucleation phase using empirical Green's function deconvolution (Frankel et al., 1986) to account for propagation effects. We performed the deconvolution as a least-squares estimation problem in the time domain and enforced positivity and smoothness constraints on the derived source time function. The deconvolution of a co-located magnitude 0.8 aftershock from the magnitude 2.6 "mainshock" results in a bump of 4 ms duration at the beginning of the source time function (Fig. 5). By accounting for propagation effects through such empirical Green's function analysis we should be able to extend greatly the magnitude range over which we can study the seismic nucleation phase. The magnitude 3.6 event in Table 1, which was recorded at a depth of 1.0 km in the Varian Well near Parkfield at 500 sps, was also analyzed using the same empirical Green's function analysis. We were not able to perform this analysis on the other small events in Table 1 because we require a co-located Green's function event of the same mechanism and much smaller magnitude.

o.bs

030

o3s

0.2o

Seconds after Event Initiation

Fig. 3. Moment-rate functions for the initiation of small, medium, and large earthquakes determined by deconvolution. Numbers in parentheses refer to the numbers used in Table 1. Each earthquake begins weakly then abruptly accelerates. Each panel is plotted at a different time scale. The time between initiation (t = 0 on the plot) and the initiation of high moment rate varies systematically with earthquake size.

We can use the duration of the seismic nucleation phase, the characteristics of the moment-rate function, and the seismic moment and duration of the entire earthquake to explore the properties of the seismic nucleation phase for 28 of the 48 earthquakes listed in Table 1. Of particular interest are the scaling properties of the seismic nucleation phase with the overall size of the eventual earthquake. Note that we have included a number of small events in Table 1 for which the Green's function deconvolution analysis, using either an empirical Green's function or a theoretical Green's function, was not performed. These events were not analyzed by Ellsworth and Beroza (1995) and can be identified in Table 1 by the lack of an estimate of the moment of the seismic nucleation phase, M~o. Because the duration of the seismic nucleation phase is so short for these events, there is the possibility that the measurements are biased by propagation effects. Fig. 6 shows our pick of the initial P-wave arrival from the hypocenter. In each case we picked the digital sample where the signal clearly emerges from the noise. If there is a weaker initial arrival that is masked by ambient or instrumental noise, it would

G.C. Beroza, W.L.Ellsworth/Tectonophysics 261 (1996) 209-227

215

o d (D <5

ci

<5

~o

o 6

o i

?

cD

o, 0.0

0.05

0.10

0.15

Seconds

0.0

0.05

0.10

0.15

0.20

0.25

Seconds

Fig. 4. Borehole accelerometerrecord of the magnitude 2.6 event recorded on the Long Canyon borehole at Long Valley at a depth of 2 km is shown at two time scales. The left panel shows that the onset is abrupt and the right panel shows that this abrupt start is very weak compared to the rest of the earthquake. We analyzed this event by deconvolving a magnitude 0.8 aftershock from it and found that the duration of the seismic nucleation phase was 0.004 s. make the true duration of the weak initial phase longer than what we have measured. The moment rate function is integrated over time to measure the moment release during the seismic nucleation phase, M~: Mo,~ =

Mo(t)dt

(1)

The seismic nucleation phase, is typically interrupted by a marked increase in Mo(t) characterized by approximately linear growth in the velocity seismograms (Figs. 1 and 7). We term this interval of linear growth the breakaway phase. Because the Pwave displacement seismogram is proportional to the moment-rate (Aki and Richards, 1980, p. 81), it follows that the P-wave velocity seismogram is proportional to the moment acceleration. Thus, the observed linear increase in the velocity seismograms during the breakaway phase implies that the growth of the moment-rate function is quadratic in time. Quadratic growth of the moment-rate function is predicted by models of self-similar rupture growth at constant stress drop (Kostrov, 1964). Therefore, we can use this observation to estimate the dynamic stress drop, Aab, (Boatwright, 1980) during the breakaway phase using the relation:

Mo(t)

= D(v)AabV3t

2

(2)

Eq. (2) describes the evolution of the moment-rate for a circular shear crack of constant stress drop that

expands at a constant rupture velocity, v. Of course self-similar growth during the breakaway phase must be of limited duration because the finite size of the fault, stress, and/or strength heterogeneities will influence subsequent rupture propagation. Moreover, for near-source observations at a single station, the moment-rate function derived by our deconvolution can only be used to characterize the growth rate of the earthquake when the source is of limited spatial extent. Hence, even if self-similar growth were to continue, its expression in the P-wave velocity seismograms would become more complex than simple linear growth as the earthquake grew larger. It is relatively straightforward to pick the first arrival (Fig. 6). The only appreciable uncertainty is whether or not we have detected the true first arrival. The data has limited dynamic range and if the first arrival is weak, we may be unable to pick it accurately. This is particularly true with the larger events, for which much of the data comes from digital strong motion accelerographs with least significant bit resolution of 1 cm/s 2. The bias in this case would be for the true seismic nucleation phase to be longer than we have measured, that is, it would accentuate the effect we are documenting in this study. It is much more difficult to pick the end of the seismic nucleation phase than it is to pick the first arrival. This is due in part to the great variation in earthquake size, but also is due to the range of

G,C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

216

Empirical Green's Function ,,

:

.

c:5 v

o_ =

/

d \ \

¢5 0.0

0.01

0.02

0.03

/

0.04

0.05

T i m e (s)

Data and Predicted Data

\ ¢a -0.01

0.0

0.01

0.02

0.03

0.04

0.05

T i m e (s)

Moment-Rate Function from Deconvolution

oE c

0.0

0.01

0.02

0.03

0.04

0.05

0.06

T i m e (s)

Fig. 5. Fit to the data for the magnitude 2.6 event shown in Fig. 3 from the time-domaindeconvolution. The apparent source time function has a short initial phase of 4 ms that is difficult to detect in the data before the deconvolution. behavior seen during the seismic nucleation phase for different earthquakes (Fig. 7) and makes it difficult to implement a single objective criterion for picking the duration of the seismic nucleation phase, v. For the smaller events the bandwidth can be inadequate to discriminate between the seismic nucleation phase as an initial weak arrival rather than a short period of slow growth in the velocity seismogram. The band limitations arise both from the band-limitations of the recording system and from the fact that high frequencies are severely attentuated in the near-surface. For this reason we have used

downhole instruments that operate at high sampling rates to study the smaller events. Events marked with a P, L, or M in Table I refer to recordings from downhole instruments in Parkfield, Long Valley, and from two mines in South Africa (McGarr, 1992) respectively. A few of the seismograms used in our analysis were recorded on systems that use a finiteimpulse response (FIR) filter in the digital waveform sampling. FIR filters have the potential to create an acausal arrival if there is significant amplitude near the Nyquist frequency. We corrected for the filter response for data that were recorded on such systems to address this potential problem. To measure v for the smaller events we follow Iio (1995) who used the projection of the maximum slope of the velocity seismogram to predict when the earthquake would have started if the growth rate was constant (as in the self-similar model). The difference between this time and the earlier first arrival time is his definition for the duration of the slow initial phase. We have used this same approach for the smaller events in our study for which the velocity seismogram starts with a low amplitude and gradually increases. For most of these events, the time projected from the maximum slope marks a distinct phase arrival (the breakaway phase) that can be identified without appeal to the acceleration in moment rate described by Iio (1995). For the larger events, however, it is more appropriate to measure v using the moment-rate functions (Fig. 3). Because the duration of the seismic nucleation phase is longer for large events, other effects can become important. For example, the duration of the nucleation phase for the M = 8.1 1985 Michoacan earthquake was determined to be 5.0 s. This weak initial arrival was also noted by Anderson et al. (1986). The duration of the seismic nucleation phase in this case is longer than the S-P time. Thus, it is necessary to measure v using the moment-rate function (Fig. 3), which takes account of the S-wave arrival, rather than the velocity seismogram (Fig. 7), which does not. Moreover, near the larger events near-field contributions to the Green's functions are important, and would lead to deviations from the linear growth in velocity for the far-field term that is predicted by the constant stress drop model. Because the duration of the seismic nucleation phase is longer for the larger events, the observation

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227 1. M8.1, 2 0 K i n

•~o

48

"O6

44

©2

0~}

.10

7. M6.4, 12Krn

I0

45

oo

~36

-02 0 0

-02

00

-1o

02

05

I0

02

-06

~2

O0

-lo

02

4.4

,02

~s

-os

5. M 6.7, 23 Km

.io 4s .0e `0~ `02 oo

oo

.lO

10. M6.1, 4 1 K m

-0, -o~ oo o~

.1~

.06

-02

0O

`0e

~

6. M 6.5, 25 Km

oo oz

1~

11. M5.9, 2 7 K m

02

-10

16. M4.8, 10Km

`08

-0.6

44

-02

-0s

o~ oo o2

12. M5.5, 2 0 K i n

•lo

Q0

17. M4.2, 24Kin

.o6

-02 oo o2

18. M4.1, 11Krn

,p

.o~

~.z

oo

02

-o~

.*o

42 oo o~

.IQ

21. M3.8, 17Kin

20. M3.9, 15Kin

19. M 4.1, 21 Km

-0s

15. M4.9, 3 9 K i n

14. M4.9, 4 K m

it

-08

9. M 6.2, 26 Km

8. M6.4, 3 2 K i n

13. M5.3, 17Km

~0

46

4. M 6.9, 20 Km

3. M 6.9, 25 Km

2. M7.3, 66Krn

217

,0.6

,02 0 0

02

t .10

22. M 3.7, 5 Km

-06

4z

O0 0 2

.IC

23. M3.7, 19Kin

-08

-0£

-0~..32

O0

24. M 3.7, 21 Km

i •,o

.oe

.t.o .o.s

~.2 oo 02

-01

-O2 00 02

.1.o -o.a -oe -o4 -02 oo

-~o .oe .06 -04 -0.2 00

28. M3.6, 12Kin

27. M 3,6, 11 Km

26. M3.6, 13Km

25. M 3.7, 11 Km

,0.~

.~o

29. M3.6, 4 K i n

~

42 o.o o2

30. M 3.6, 10 Km

o

,o

.1.o .o~ -0* -0.4 42

~e -0e `04 42 o.o

.10

,08

`06

44

`02

O0

-10

34. M3.4, 19Km

33. M 3.5, 15 Km

32. M3.5, 17Km

31. M 3.5, 10 Krn

00

,08

-011 -64

`02

oo

.10

35. M3.3, 2 K m

46

42

oo

02

36. M 3.3, 4 Krn

r" o

,o

oe

,0~

`04

.o2

.io 4.e o.e `04 -o2 oo

oo

-10

38. M2.6, 6 K i n

37. M 3.2, 5 Km

-0e

42

oo

o2

.~.o ~s

40. M2.4, 2 K i n

39. M 2.4, 1 Km

46

4.4 -02 oo

.~o 4e

41. M2.1, 4 K i n

as

-04 -02

oo

42. M2.1, 4Krn

o

.lo 43. M1.8, 4 K m

~,s -os -o4 42 44. M1.7, 4 K i n

oo

Z-. .lO

-0e

~e

,04

`02

45. M 1.4, 5 Km

.

.

.

oo

46. M1.2, 3 K m

47. M1.2, 4 K m

O sllcon¢~

9-1o -0s -oe ~4

l

oo

48. M1.1, 3 K i n

-I0 ~

~2

-08

-06

-04

~,2

O0

$ecotlds

Fig. 6. Onset of the first P-wave arrivals for the 48 earthquakes that we studied. Time increases from left to right and is at a different scale for each seismogram. Accelerograms (cm/s 2) are displayed at high gain to show the onset of the first P-wave arrival, which is marked with a vertical dashed line and zero on the time scale. Headings give event number in Table 1, moment magnitude, and epicentral distance.

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

218 1. M8.1, 2 0 K i n

2

o

4

s

-o.s

IO

s

/

.r

.1

I

o

-os

2

O0

~o

~'

.lo

02

2

~

~1 c

.04

20. M3.9, 15Km

19, M 4.1, 21 Km

os

io

-05 o.o 05

-02

5, M 6.7, 23 Km

6. M 6.5. 25 Km

~s

•~ o

10. M 6 . 1 , 41 Kin

to

•O2

15. M4.9, 39Km

14. M4.3, 4 K i n

13. M5.3, 17Kin

-O2

os

o.o

oo

4. M 6.9. 20 Km

9. M 6.2, 2 6 Km

8. M 6.4, 32 Km

7. M6.4, 12Kin

.2

3. M 6.9, 25 Km

2. M 7.3, 66 Km

oo

-OZ

16. M4,8, 1OKra

6

0

"04 -O~

oo

2

o

o.o

Ol

02

.1o

17. M4.2, 2 4 K i n

oE

~io

22. M 3 . 7 , 5 K i n

21. M3.8, 17Km

-O~

oo

o~

oo

o~

io

,s

12. M5.5, 2 0 K i n

11. M 5 . 9 , 2 7 K i n

02

-o~

~s

oo

os

~o

18. M4.1, 11Km

OlO

'-o~o

23. M3.7, 19Km

.oo~

.002

o

24. M 3.7, 21 Km

o~

d

o

~

.O,lO

-005

oo

005

.04

25. M3.7, 11Krn

43

"O2 0~ 00

O~ 02

-oo~

oo

oo~

05

-010

O~

-OlO -oo~

04

-00S

00

00S

-o ~o

-o~

oo

oo~

oo

oos

.OlO .oo5

0~0

28. M 3.6, 12 Km

27, M 3.6, 11 Km

~.1o

.oos

oo

o.os

.OlO

.o ~o

~

.0.o2

oo2

.o~o

oo

005

% lo

oo

oo~

oio

oo5

o~o

~os

oo

oo5

30. M3.6, l O K m

-o 10

35, M 3.3, 2 Kin

~.1o

.o.~

o.e

oos

-0,06

~02

o o2

36, M 3.3, 4 Kin

%olo

41. M 2.1, 4 Km

40. M 2.4, 2 Km

39. M 2,4, 1 Km

38. M 2.6, 6 Kin

-oos

oo

29. M 3.6, 4 Km

34. M3.4, 19Km

33. M3,5, 15Krn

32. M3.5, 17Krn

37. M 3.2, 5 Km

~°

O0

26. M3.6, 13Km

31. M 3.5, 10 Kin

-olo

4.2

.oo5

oo

005

42. M 2.1, 4 Krn

8

-

~.~o 43. M 1.8, 4 Km

.o~

.oo2

002

.01o

~.~o

~.o2

002

-o lo

46. M1.2, 3 K i n

45. M 1.4, 5 Km

44, M 1.7, 4 Km

-006

.ooe

-o.o2

o02

-o ~o

47. M 1.2, 4 Km

-oos

.0.02

0o2

48. M1.1, 3 K i n

o

~ ~.o.~o

-~.~

-o.o2

~O.lO

e.oz

S~onds

-0.06

-0,02 Seco~s

-O.lO

..ooe

-o,o2 SKO~

~-o.~o

-o.o6

-o.o2

.o.1¢

-006

.0.02 Sec~nOs

O02

Fig. 7. The seismic nucleation phase for the 48 earthquakes that we studied shown using velocity seismograms (cm/s). Zero time on the plot and the first dashed line indicates the arrival time of the first seismic wave. The interval between that and the second dashed vertical line spans the duration, v, of the nucleation phase. Self-similar growth of a constant stress drop crack predicts a linear increase in velocity with time, which we typically don't observe until the end of the seismic nucleation phase. We term the linear growth that starts at the end of v the breakaway phase.

219

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996)209-227

o

~ \o.

% c~

,~\°

" . ~' ~.~\o o. z

u~

c o

z "5 _o =

<:5

§ ,5

v 0

• This study o Umeda(1990) v lio (1992)

Magnitude 2

4

6

Z

¢u o.

• m

8

o. 108

I 10~0

1012

10~4

I 1016

, 1018

, 10~0

I 1022

Seismic Moment (N-m)

Fig. 8. The seismic moment, Mo, is plotted versus v on a log-log scale. The straight line has a slope of 1/3 indicating a power law scaling of Mo ~ v3. All events in Table 1 are plotted as solid circles. Also plotted are data from Umeda (1990) and Iio (1992).

of the seismic nucleation phase is not limited by the bandwidth of the signal as it is for smaller events. For these larger events it was usually possible to pick a distinct arrival that marked the onset of the breakaway phase, during which the growth of the moment acceleration is linear with a steep slope that is proportional to the dynamic stress drop listed in Table 1. Fig. 8 shows the duration of the seismic nucleation phase, v, versus the total seismic moment Mo. To our set of 48 events, we have added data on the duration of the initiation process for an additional 21 events studied in a similar way by Umeda (1990) and Iio (1992), which are shown with different symbols. The line with a slope of 1/3 indicates that v scales approximately as the cube root of the total seismic moment. If we associate the duration with a length scale, then this scaling is suggestive of the constant stress drop scaling observed for earthquakes over a very large magnitude range (Kanamori and Anderson, 1975; Abercrombie and Leafy, 1993). In the present case, however, the comparison is between the duration of the seismic nucleation phase alone and the moment of the entire earthquake. This correlation suggests that there is information related to the eventual size of the earthquake in the process that generates the seismic nucleation

o

o. 10

13

10 TM

10 is

10 is

1017

10 t8

1019

1020

1'021 -

Main Shock Moment (N-m)

Fig. 9. The moment of the nucleation phase, M~, versus the moment, Mo, of the entire earthquake is shown. The average ratio of the two quantities is 0.005 indicating that the seismic nucleation phase represents only a small fraction of the eventual seismic moment. Only the events for which we were able to perform a stable deconvolution are shown (Table I).

phase; however, it is not obvious how to interpret the seismic nucleation phase directly in terms of source properties. If it represents slip during the transition from an aseismic nucleation process to dynamic rupture, then the fact that we do not know the rupture velocity prevents us from determining the source dimension. Indeed, models of nucleation predict that rupture will occur in place before propagating away from the nucleation zone (e.g., Dieterich, 1992). It is straightforward, however, to take the ratio of the cumulative seismic moment in the nucleation phase, M S, to the ultimate seismic moment, Mo, in the earthquake. Fig. 9 shows the variation of the two quantities on a logarithmic scale for the events in Table 1. There is considerable scatter, but in all cases, the seismic nucleation phase represents only a small fraction of the total seismic moment - about 0.5% on average. Moreover, there is no systematic variation of the fraction of the moment during the seismic nucleation phase, with the total moment of the earthquake. During nucleation the character of moment release shows considerable variation; however, for most events it is episodic rather than gradual

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

220

as can be seen in the moment-rate functions (Fig. 3) and the velocity seismograms (Figs. 1 and 7). Although we can't directly relate v to Mo using a characteristic dimension, we can gain some insight by examining the distribution of the ratio of v to r, the duration, in seconds, of the earthquake measured from the end of the nucleation phase to the end of the moment-rate function. For large events we use estimates of the moment-rate function derived from other studies; however, moment-rate functions are not available for the smaller events. For these we use the deconvolution results described earlier to determine the duration of the moment-rate function. The distribution of v/r is distinctly long-tailed, and there are a few instances for which v is comparable to r (Table 1). The distribution is approximately log-normal (Fig. 10) with a mean value of 0.16. A 1/t distribution, which describes the temporal decay of aftershock rates (Omori, 1984) and the temporal growth of foreshock rates (Jones and Molnar, 1979) does not fit the observations. The log-normal distribution is interesting because it arises in systems where failure occurs at a threshold and growth toward the threshold is randomly proportional to growth that has already occurred (Kao, 1965). Although the log-normal distribution is longtailed, the mean value of 16% indicates that the

1.00.8-

~

~~

/ ~ .4 0,2 0.0

0.01

0.03

0.10

Normalized Duration of

0.32

1.00

3.16

10,00

Nucleation (v/x)

Fig. 10. The ratio of the duration, v, of the nucleation phase to the duration, r, of the rest of the earthquake is shown as a distribution function. The peak of the distribution is at about 16%, but the distribution is long-tailed (Table 1). The ratio can be fit quite well with a log-normal distribution. Insert shows quantile--quantile plot of a normal distribution versus observed values of log(v/r).

duration of the seismic nucleation phase is a significant fraction of the duration of the entire earthquake. Fig. 9 shows that the seismic moment of the seismic nucleation phase is about 0.5% of the total seismic moment of the earthquake (see also Table 1). Thus, the seismic moment-rate during the seismic nucleation phase is much smaller than the moment-rate during the main part of the earthquake. This is a clear indication that the seismic nucleation phase is not properly described as the first of a series of similar subevents comprising an earthquake.

4. Extent of the nucleation zone from stress-drop matching It is straightforward to determine the moment of the seismic nucleation phase by integrating the moment-rate function; however, we need more information to determine the spatial extent of and slip within the nucleation zone. We could assume a rupture velocity and multiply by the duration of the nucleation phase, v, to estimate the source dimension; however, we judged this approach to be problematic because the seismic nucleation phase may represent the transition to dynamic rupture and in that case using a typical average rupture velocity for an earthquake would be inappropriate. That is, it would only provide an upper bound on the dimension of the nucleation zone. Instead, we chose to equate the dynamic stress drop during the breakaway phase to the static stress drop during the nucleation phase. Assuming our assumption of stress drop matching is correct, this should provide a lower bound on the dimension of the nucleation zone. The stress-drop matching procedure allows us to estimate the extent of and average slip within the nucleation zone. It rests on the assumption that when the earthquake begins, the stress and strength conditions within the nucleation zone are grossly similar to conditions over the rest of the fault. The formula for the static stress drop, Aa~ , within the nucleation zone for a circular crack of constant stress drop is (Keilis-Borok, 1959): A,rv - -

7M~ 16r 3

(3)

Equating Atrv with the dynamic stress drop in the surrounding zone, Atrb, which can be calculated

G.C. Beroza, W.L.Ellsworth/Tectonophysics 261 (1996) 209-227 104

using Eq. (2), and solving for the radius of the nucleation zone, r~, we obtain: r~ =

( 7 M j ) ~/3 16 A~rb

ytS /zrr r~

;1) c

(4)

to

1000

o Z

•

100

1

rr

010

1012

10 TM

1016

1018

Nucleation Seismic Moment (N-m)

104

(5)

The set of 28 earthquakes that we determined the moment-rate functions for were shallow so we assumed that the shear modulus,/z, was 30 000 MPa for all events. The results of the stress drop matching analysis are listed in Table 1 and plotted in 3 panels of Fig. 11. Fig. 1 la shows r~ and M~o for the seismic nucleation phase. The data follow a power law relationship consistent with constant stress drop scaling (M~o ~ ) for the nucleation zone. Fig. l i b compares the radius of the nucleation zone with the total seismic moment, Mo, of the entire earthquake Again, we find a power law relationship, Mo -~ ~. This result could have been anticipated by the result illustrated in 1 la together with the observation that moment during the nucleation phase does not vary with moment of the entire earthquake (Fig. 9). Finally, the average slip within the nucleation zone is shown in Fig. 1 lc. This too follows a power law relationship, Mo ~ Au~3 consistent with constant stress drop. There are two points illustrated in Fig. 11 that are important to our discussion of the process responsible for the seismic nucleation phase. Fig. 1 lb shows that the size of the nucleation zone scales with the size of the eventual mainshock and that the nucleation zone becomes larger than 1 km in diameter for earthquakes Mw > 6.5. Fig. I Ic shows that the average slip during the seismic nucleation phase is substantial. Standard earthquake scaling relationships indicate that slip within the nucleation zone is about 20% of the average slip in earthquakes with

~'"'~I '""~1 ' " ' ' I """"1 J~'""l '"'"1 '~'"~"1 *'"""1 ~/,

a.

This estimate will be relatively insensitive to both the geometry of the nucleation zone, provided the process involves the failure of contiguous areas, and to the estimated quantities, M~o or Aab, since it varies as their cube root. Because the seismic moment is the product of the area of faulting, the average slip, and the shear modulus, we can also solve for the average slip within the nucleation zone, Au~, which is given by Au~, - -

221

"'1 b,,,.m} '"''I '""~ '"'~ "mr'l '"'"ff ,r.]n~ ,,i,,, I ,Hn

b. O

1000 C 0 m Q)

•

egO

"G :7

"6 ._~

lOO

" :"t

1012

1014

l 1016

1018

1020

1022

Main Shock Seismic Moment (N-m)

1

C.

•

01L

•

:

•

a

|

•oo

•

0.01

08 •

Z

•

• Q 0.001

i,,,,,,J ,,,,,~,,,,,,J ......J ......,J ,,,,,,~ .......I ......~ ......,I ,.'~

1012

1014

1016

1018

1020

1022

Main Shock Seismic Moment (N-m)

Fig. 11. We use the seismic momentof the nucleationphase and the stress drop of the breakaway phase to estimate the radius of the nucleationzone, rv, and averageslip, Auv, during the seismic phase of the nucleationprocess. Panel (a) shows r~ versus M~o. Panels (b) and (c) show rv and Au~ versusMo.

G.C. Beroza, W.L. Ellsworth /Tectonophysics 261 (1996) 209-227

222 10

FreeSmtace 1992 Landers Earthquake (M:7 3)

~ ;

,,

~•

, " 3 km/s

FreeSurface Z

0.1

0.01

1978 Izu-Oshima Earthquake (M=7.8) '

•

,~"

FreeSurface 0.001

I 10

........

J 100

........

i 1000

.

.

.

.

.

.

.

.

.

104

1989 Loma Prieta Earthquake (M=6.9)

Nucleation Radius (m)

Fig. 12. Estimates of v and rv are shown for the seismic nucleation phase of each event. Diagonal lines indicate lines of constant apparent rupture velocity-definedas the ratio: r~/v.

I ~ O

the seismic moments plotted on the vertical axis of Fig. 1 lc. We can also use the results from the stress-drop matching to estimate the apparent rupture velocity during nucleation from r J r . From the values in Table 1, the apparent rupture velocity is about 1.5 km/s (mean = 1.6 km/s, median = 1.4 km/s), and it shows no systematic variation as a function of r~ (Fig. 12). The interpretation of this quantity as a rupture velocity, however, is contingent on the symmetric growth of the nucleation zone outward from the initial hypocenter. This need not be the case. If, for instance, the expansion of the rupture during v is unilateral, then the apparent rupture velocity is 2ro/v and our estimates from Table 1 are in reasonable agreement with normal rupture velocities. A specific model satisfying this condition would be self-similar growth of a crack from a fixed point on its edge rather than from the center. Another observation that bears directly on the dimension of the source zone for the seismic nucleation phase is the distance between the earthquake hypocenter, where the seismic nucleation phase begins, and the hypocenter of the breakaway phase. Because of the difficulty of recording the seismic nucleation phase and the breakaway phase on-scale, this distance has been determined for only a few earthquakes. Results for the 1979 Izu-Oshima earthquake (Shimazaki and Somerville, 1988), the 1992

Hypocenter Point of Breakaway

Fig. 13. The location of the hypocenter (i.e., where the first detectable P wave originates) and the location of the source of the breakaway phase are shown, as projected onto the fault plane for 3 earthquakes: The 1978 Izu-Oshimaearthquake (Shimazaki and Somerville, 1988); the 1989 Loma Prieta earthquake (Dietz and Ellsworth, 1996) and the 1992 Landers earthquake (Abercrombie and Mori, 1994). The information radius, which is defined as 80% of the S-wave velocity times v, is also shown. The small separation of the hypocenterand the point of breakawayfor these events suggests that rupture velocityis quite low in the direction of the breakawaypoint.

Landers earthquake (Abercrombie and Mori, 1994), and the 1989 Loma Prieta earthquake (Dietz and Ellsworth, 1996) are shown in Fig. 13. A similar observation has been made for the 1987 Superstition Hills earthquake (Frankel and Wennerberg, 1989). In these cases the distance divided by v is 20-50% of the shear wave velocity. This observation is consistent with the average rupture velocity during the seismic nucleation phase being lower than typical average rupture velocities of 80% of the shear wave velocity.

5. Two models of the seismic nucleation phase The characteristics of the seismic nucleation phase constrain possible models of how earthquakes begin. It is clear from the change in behavior of the moment-rate function during the seismic nu-

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

Preslip Model

223

C~cade M ~ !

Before Shaking Begins

(Slow Slip in Pre-SlipZone)

(No Activity)

(Final Failureof Pre-SlipZone)

(Initial Stagesof Cascade)

Seismic Nucleation Phase

Breakaway Phase

Fig. 14. Cartoon illustrating the two models of the seismic nucleation phase as discussed in the text. In the pre-slip model an episode of slow, aseismic slip precedes dynamic rupture and establishes the dimensions of the nucleation zone. In the cascade model there is no activity before the mainshock begins. The seismic nucleation phase is generated either when slip in the aseismic nucleation zone accelerates to dynamic rupture velocity (preslip model) or when spontaneous failure triggers a series of triggered subevents (cascade model).

cleation phase and the breakaway phase that any model of purely self-similar growth is inconsistent with the data. Ellsworth and Beroza (1995) proposed two possible models to explain the seismic nucleation phase. These models have very different implications for the rupture process and for the predictability of earthquakes. The time evolution of failure in these models is illustrated schematically in Fig. 14. 5.1. The cascade model

One interpretation of our observations, which we call the cascade model, is that the first arriving P

wave marks the very beginning of the failure process. In this model, earthquakes begin abruptly and there is no difference between the beginnings of large and small earthquakes. A large earthquake occurs when a smaller earthquake triggers a cascade of increasingly larger slip events. This sort of model has been proposed before in various forms (Wyss and Brune, 1967; Brune, 1979; Bak and Teng, 1989; Abercrombie and Mori, 1994). In the cascade model, the seismic nucleation phase represents an accumulation of small events that lead from the first event in the cascade to the largest subevent of the earthquake. The breakaway phase would be identified with the first large slip event.

224

G.C. Beroza, W.L. Ellsworth/Tectonophysics 261 (1996) 209-227

In the cascade model the observed scaling between source parameters for the seismic nucleation phase (M~o, r~, Au~) and source parameters for the entire earthquake (r and Mo) could arise if rupture in earthquakes occurs over a hierarchy of subevent sizes (Fukao and Furumoto, 1985; Rice and BenZion, 1995). The observed scaling could arise if the last jump in subevent size determines the size of the earthquake. The cascade of increasingly larger failures leading up to rupture of the first subevent in the largest hierarchical class would be identified as the seismic nucleation phase. The timing of the successive failure in this hierarchy would have to satisfy the observations on the duration of v. A plausible mechanism for this delay is provided by rate and state variable friction laws. Omori's law of aftershock decay can be explained with such a model (Dieterich, 1994). A consequence of this friction law, however, is that it gives rise to stable preslip as part of the failure process. 5.2. The preslip model

Another interpretation of our observations, which we call the preslip model, is that the beginnings of large and small earthquakes differ. In the preslip model failure initiates aseismically, with an episode of slow stable sliding over a limited region of the fault zone (Dieterich, 1986; Okubo, 1989; Dieterich, 1992; Shibazaki and Matsu'ura, 1992; Ohnaka, 1993). This preslip zone gradually expands and the slip within it increases until it reaches a critical size. The process then can become unstable, with rupture propagating away from the preslip zone at high rupture velocity in an earthquake. In this model, the seismic nucleation phase represents the very last stages of failure within the preslip zone and the breakaway phase is generated when rupture breaches the preslip zone and begins to propagate along the fault with large slip and high rupture velocity. In the preslip model the observed scaling between source parameters for the seismic nucleation phase and source parameters of the entire earthquake are controlled by the preslip zone. Since the seismic nucleation phase would represent the last phase of failure of the preslip zone, it is the dimension of this zone that controls the source properties of the seismic nucleation phase. This would not explain the

observed scaling with the overall size and duration of the earthquake unless the size of the earthquake is determined by the slip amplitude when breakaway begins. The slip amplitudes we determined for the seismic nucleation phase (Fig. 9c) are a large fraction of the average mainshock slip. A possible explanation for the observed scaling is that when the slip amplitude within the nucleation zone is large, the resulting dynamic rupture would be difficult to stop-leading to a large earthquake. In effect the earthquake becomes a large event because it gets a large "push" at the beginning - a possibility first suggested by Bodin and Brune (written communication). Iio (1995) studied earthquakes in the magnitude range -0.7 to 2.7. He too found a slow initial phase that scaled with the size of the microearthquake (Fig. 8). The slow initial phase was characterized by a gradual onset before the velocity seismograms grew linearly with time. He attributed the slow initial phase and the scaling he observed to the time required for the slip-weakening displacement to occur. In our study we find a weak initial phase for earthquakes in the magnitude range 1.1 to 8.1. We also find a scaling of the duration of this weak initial phase with the size of the earthquake similar to Iio (1995) (Fig. 8). In contrast to Iio, we often find that the initial phase is episodic, rather than gradual. This is true even for the M 2.6 microearthquake in Long Valley (Figs. 4 and 5) for which we obtained the moment-rate function by empirical Green's function deconvolution. It is interesting to note that the velocity seismogram for this event showed a gradual onset prior to the deconvolution. It is likely that for many of the other smaller events the nature of the initial arrivals is distorted by propagation effects. For the larger events we have studied, the duration of the nucleation phase is far larger than anything that can be attributed to propagation effects. Our interpretations of the seismic nucleation phase also differ from Iio's. The cascade model explains the seismic nucleation as an accumulation of increasingly large subevents; whereas the preslip model explains the duration of the seismic nucleation phase as the time required for the final failure of a preslip zone. Dieterich (1986) found that the size of the nucleation (preslip) zone scaled with the critical displacement and that steady slip within it was many times the slip weakening displacement prior to instability.

G.C. Beroza, W.L. EUsworth/Tectonophysics261 (1996) 209-227 5.3. Implications of the models for earthquake prediction If the cascade model is correct, the outlook for short-term earthquake prediction is rather bleak. In order to predict a large earthquake, one would have to predict the small earthquake that initiates the cascade and one would have to know that the conditions on the fault would cause the small initial event to trigger a cascade of increasingly larger slip events. If, on the other hand, the preslip model is correct, the outlook for earthquake prediction is somewhat more promising because earthquakes would be preceded by an episode of precursory slip. Although a precursory slip episode is predicted by the preslip model, the size of the nucleation zone need not scale with earthquake size and may be undetectably small (Dieterich, 1986); however, our observations, if interpreted in terms of the preslip model, indicate that the size of the nucleation zone scales with the size of the eventual earthquake. For earthquakes Mw _ 6.5, we find the radius of the nucleation zone ranges from 600-6000 m (Table 1). If this zone develops aseismically then short-term earthquake prediction would be possible - at least in theory. The small dimensions of the zone and limited deformation arising from aseismic slip within it may be extremely difficult to detect directly as a strain signal; however, it might be large enough to generate other detectable signals (Fraser-Smith et al., 1993). Foreshocks provide independent evidence of a slow nucleation process that may take hours or longer to occur (Ohnaka, 1993). Dodge et al. (1995) studied the set of nearly 30 foreshocks that occurred in the seven-hour period immediately preceding the 1992 Landers, California earthquake. Using waveform cross-correlation to pick accurate arrival times for both P and S waves and the first-motion focal mechanisms of the foreshocks, Dodge et al. (1995) were able to demonstrate that the foreshock sequence did not lead to the mainshock through a cascade of failures that loaded the eventual mainshock hypocenter. Instead they found that the foreshock sequence drove the fault at the eventual mainshock hypocenter farther from failure. This may indicate that aseismic slip within the nucleation zone, rather than the foreshocks themselves, is what drives the fault at the mainshock hypocenter closer to failure. In this

225

interpretation the foreshocks are simply the seismic signature of a predominantly aseismic nucleation process.

6. Conclusions Our observation of the seismic nucleation phase for all earthquakes we examined as well as other examples in the literature suggest that it is a common, if not universal feature of the earthquake nucleation process. Its properties rule out self-similar models for earthquake nucleation and growth, including not only the idealized circular, constant stress drop shear crack, but any growth process, regular or irregular, that maintains scale independence. We have presented two models capable of explaining the observations; however, these models have very different implications for the physics of the rupture process and for earthquake predictability. The results presented in this paper do not allow us to discriminate definitively between these two models, but future work with better data sets may. By imaging the spatial and temporal evolution of slip during the seismic nucleation phase and by studying the mechanics of foreshock sequences, we hope to increase our understanding of how the seismic nucleation phase is generated and more generally how earthquakes begin.

Acknowledgements We thank B. Cohee, J. Dieterich, A. Gusev, T. Hanks, R. Madariaga, J. Rice, R Segall, R Spudich, W. Thatcher, J. Vidale and M. Zoback for their comments. J. Brune, Y. Iio and B. Shibazaki provided preprints of their work. J. Anderson, R Harben, E. Hauksson, S. Hough, M. Johnston, R Malin, A. McGarr, G. Simila, J. Steidl, E Vernon, Y. Zeng, University of California at Berkeley, California Division of Mines and Geology, Southern California Earthquake Center, and the US Geological Survey provided the data used in this study. Greg Beroza was supported by National Science Foundation grant EAR-9416546.

References Abercrombie,R. and Leafy,P., 1993. Sourceparametersof small earthquakes recorded at 2.5 km depth, Cajon Pass, Southern

226

G.C. Beroza, W.L. Ellsworth / Tectonophysics 261 (1996) 209-227

California; implications for earthquake scaling. Geophys. Res. Lett., 20:1511-1514. Abercrombie, R. and Mori, J., 1994. Local observations of the onset of a large earthquake, 28 June 1992 Landers, California. Bull. Seismol. Soc. Am., 84: 725-734. Abercrombie, R., Main, I., Douglas, A. and Burton, P.W., 1995. The nucleation and rupture process of the 1981 Gulf of Corinth earthquakes from deconvolved broad-band data. Geophys. J. Int., 120: 393-405. Agnew, D.C. and Wyatt, EK., 1989. The 1987 Superstition Hills earthquake sequence strains and tilts at Pinon Flat Observatory. Bull. Seismol. Soc. Am., 79: 480--492. Aki, K. and Richards, P.G., 1980. Quantitative Seismology: Theory and Methods, Freeman, San Francisco. Anderson, J.G., Bodin, P., Brune, J.N., Pince, J., Singh, S.K., Quaas, R. and M. Ohnate, 1986. Strong ground motion from the Michoacan, Mexico, earthquake. Science, 233: 1043-1049. Andrews, D.J., 1976. Rupture velocity of plane strain shear cracks. J. Geophys. Res., 81: 5679-5687. Archuleta, R., 1984. A faulting model for the 1979 Imperial Valley, California earthquake. J. Geophys. Res., 89: 4559--4585. Bak, P. and Teng, C., 1989. Earthquakes as self-organized critical phenomenon. J. Geophys. Res., 94:15 635-15 637. Beck, S.L. and Christensen, D.H., 1991. Rupture process of the February 4, 1965, Rat Islands earthquake. J. Geophys. Res.~ 96: 2205-2221. Beroza, G.C. and Spudich, P., 1988. Linearized inversion for fault rupture behavior; application to the 1984 Morgan Hill, California earthquake. J. Geophys. Res., 93: 6275-6296. Bezzeghoud, M., Deschamps, A. and Madariaga, R., 1989. Broad-band P-wave signals and spectra from digital stations. In: R. Cassinis, G. Nolet and G.E Panza (Editors), Digital Seismology and Fine Modeling of the Lithosphere. Plenum Press, New York, pp. 351-374. Boatwright, J., 1980. A spectral theory for circular seismic sources; simple estimates of source dimension, dynamic stress drop, and radiated seismic energy. Bull. Seismol. Soc. Am., 70: 1-27. Brune, J.N., 1979. Implications of earthquake triggering and rupture propagation for earthquake prediction based on premonitory phenomena. J. Geophys. Res., 84: 2195-2198. Choy, G.L. and Dewey, J.W., 1988. Rupture process of an extended earthquake sequence: teleseismic analysis of the Chilean earthquake of March 3, 1985. J. Geophys. Res., 93: 1103-1118. Christensen, D.H. and Ruff, L.J., 1986. Rupture process of the March 3, 1985 Chilean earthquake. Geophys. Res. Lett., 13: 721-724. Das, S. and Scholz, C.H., 1982. Theory of time-dependent rupture in the Earth. J. Geophys. Res., 86: 6039-6051. Dieterich, J.H., 1979. Modeling of rock friction: 1 Experimental results and constitutive equations. J. Geophys. Res., 84: 21612168. Dieterich, J.H., 1986. A model for the nucleation of earthquake slip. In: S. Das, J. Boatwright and C.H. Scholz (Editors), Earthquake Source Mechanics. Am. Geophys. Union, M. Ewing, Vol. 6, Geophys. Monogr., 37: 37--47.

Dieterich, J,H., 1992. Earthquake nucleation on faults with rateand state-dependent strength. Tectonophysics, 211:115-134. Dieterich, J.H., 1994. A constitutive law for rate of earthquake production and it application to earthquake clustering. J. Geophys. Res., 99: 2601-2618. Dietz, L. and Ellsworth, W.L., 1996. Afterhocks of the 1989 Loma Prieta earthquake and their tectonic implications. In: E Reasenberg (Editor), The Loma Prieta, California, earthquake of October 17, 1989: Earthquake occurrence. U.S. Geol. Surv. Prof. Pap., 1550: 85. Dodge, D.A., Beroza, G.C. and Ellsworth, W.L., 1995. Evolution of the 1992 Landers, California, foreshock sequence and its implications for earthquake nucleation. J. Geophys. Res., 100: 9865-9880. Dziewonski, A.M. and Gilbert, F., 1974. Temporal variation of the seismic moment tensor and evidence of precursive compression for two deep earthquakes. Nature, 247: 185-188. Dziewonski, A.M., Chou, T.A. and Woodhouse, J.H., 1981. Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J. Geophys. Res., 86: 2825-2852. Ellsworth, W.L. and Beroza, G.C., 1995. Seismic evidence for an earthquake nucleation phase. Science, 268: 851-855. Frankel, A. and Wennerberg, L., 1989. Rupture process of the Ms 6.6 Superstition Hills, California earthquake determined from strong-motion recordings; application of tomographic source inversion, Bull. Seismol. Soc. Am., 79: 515-541. Frankel, A., Fletcher, J.B., Vernon, E, Haar, L.C., Berger. J., Hanks, T.C. and Brune, J.N., 1986. Rupture characteristics and tomographic source imaging of ML 3 earthquakes near Anza, Southern California. J. Geophys. Res., 91: 12 633-12 650. Fraser-Smith, A.C., Bernardi, A., Helliwell, R.A., McGill, ER. and Villard, O.G., 1993. Analysis of low frequency electromagnetic field measurements near the epicenter of the Ms 7.1 Loma Prieta, California, earthquake of October 17, 1989. In: M.J.S,. Johnston (Editor), Preseismic Observations. U.S. Geol. Surv, Prof Pap, 1550-C: C17--C25. Fukao, Y. and Furumoto, M., 1985. Hierarchy in earthquake size distribution. Phys. Earth Planet. Inter., 37: 149-168. Gladwin, M.T. and Stacey, ED., 1974. Anelastic degradation of acoustic pulses in rock. Phys. Earth Planet. Inter., 8: 332-336. Hauksson, E., Hutton, K., Kanamori, H., Jones, L. and Mori, J., 1994. The Mw 6.7 Northridge, California earthquake and its aftershocks. 89th Meeting of the Seismological Society of America, Abstract with Programs. Hwang, L.J. and Kanamori, H., 1992. Rupture processes of the 1987-1988 Gulf of Alaska earthquake sequence. J. Geophys. Res., 97:19 881-19 908. Ihml6, EE and Jordan, T.H., 1994. Teleseismic search for slow precursors to large earthquakes. Science, 266:1547-1551. Ihml6, EE, Harabaglia, E and Jordan, T.H., 1993. Teleseismic detection of a slow precursor to the great 1989 Macquarie Ridge earthquake. Science, 2612: 177-183. Iio, Y., 1992. Slow initial phase of the P-wave velocity pulse generated by microearthquakes. Geophys. Res. Lett., 19: 477480. Iio, Y., 1995. Observation of the slow initial phase of mi-

G.C. Beroza, W.L. Ellsworth/Tectonophysics croearthquakes: implications for earthquake nucleation and propagation. J. Geophys. Res., 100:15 333-15 349. Johnson, L.R., 1974. Green's function for Lamb's problem. Geophys. J. R. Astron. Soc., 37: 99-131. Johnston, M.J.S., Linde, A.T. and Gladwin, M.T., 1990. Nearfield high resolution strain measurements prior to the October 18, 1989, Loma Prieta Ms 7.1 earthquake. Geophys. Res. Lett., 17: 1777-1780. Johnston, M.J.S., Linde, A.T. and Agnew, D.C., 1994. Continuous borehole strain in the San Andreas fault zone before, during and after the 28 June 1992, Mw 7.3 Landers, California, earthquake. Bull. Seismol. Soc. Am., 84: 799-805. Jones, L.M. and Molnar, P., 1979. Some characteristics of foreshocks and their relationship to earthquake prediction and premonitory slip on faults. J. Geophys. Res., 84: 3596-3608. Jordan, T.H., 1991. Far-field detection of slow precursors to fast seismic ruptures. Geophys. Res. Lett., 18: 2019-2022. Kanamori, H. and Anderson, D.L., 1975. Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Am., 65: 1073-1095. Kao, J.H.K., 1965. Statistical models in mechanical reliability. Proc. 1 lth National Symp. on Reliability and Control, IEEE, New York, pp. 240-247. Kedar, S., Watada, S. and Tanimoto, T., 1994. The 1989 Macquarie Ridge earthquake: seismic moment estimation from long-period free oscillations. J. Geophys. Res., 99: 1789317 908. Keilis-Borok, V., 1959. On estimation of the displacement in an earthquake source and of source dimensions. Ann. Geofis. (Rome), 12: 205-214. Kostrov, B.V., 1964. Self-similar problems of propagation of shear cracks. J. Appl. Math. Mech., 28: 1077-1087. McGarr, A., 1992. Moment tensors of ten Witwatersrand mine tremors. Pure Appl. Geophys., 139: 781-800. Mendoza. C., 1993. Coseismic slip of two large Mexican earthquakes from teleseismic body waveforms; implications for asperity interaction in the Michoacan plate boundary segment. J. Geophys. Res., 98: 8197-8210. Mukerji, T., Mavko, G., Mujica, D. and Lucet, N., 1995. Scaledependent seismic velocity in heterogeneous media. Geophysics, 60: 1222-1233. Ohnaka, M., 1993. Critical size of the nucleation zone of earthquake rupture inferred from immediate foreshock activity. J. Phys. Earth, 41:45-56. Ohnaka, M., Kuwahara, Y., Yamamoto, K. and Hirasawa, T., 1986. Dynamic breakdown processes and the generating mechanism for high-frequency elastic radiation during stick-slip instabilities. In: S. Das, J. Boatwright and C.H. Scholz (Editors), Earthquake Source Mechanics. Am. Geophys. Union, M. Ewing Vol. 6, Geophys. Monogr., 37: 13-24. Okal. E.A, and Geller, R.J., 1979. On the observability of isotropic seismic sources; the July 31, 1970 Colombian earthquake. Phys. Earth Planet. Inter., 18: 176-196. Okubo, P., 1989. Dynamic rupture modeling with laboratoryderived constitutive relations. J. Geophys. Res., 94: 1232112335. Omori, F., 1984. Investigation of aftershocks. Rep. Earthquake

261 (1996) 209-227

227

Inv. Comm., 2: 103-139. Reasenberg, R and Oppenheimer, D., 1985. FPFIT, FPPLOT, and FPPAGE: Fortran computer programs for calculating and displaying earthquake fault-plane solutions. US Geol. Surv. Open-File Rep., 85-739: 109. Rice, J.R. and Ben-Zion, Y., 1995. Slip complexity in earthquake fault models. Proc. National Academy of Sciences (submitted). Rice, J.R. and Gu, J.-C., 1983. Earthquake after effects and triggered seismic phenomena. Pure Appl. Geophys., 121: 187219. Ruff, L.J. and Miller, A.D., 1994. Rupture process of large earthquakes in northern Mexico subduction zone. PAGEOPH, 142: 101-171. Sacks, I.S., Suyehiro, S., Linde, A.T. and Snoke, J.A., 1978. Slow earthquakes and stress redistribution. Nature, 275: 599602. Saikia, C.K., 1994. Modified frequency-wavenumber algorithm for regional seismograms using Filon's quadrature-modeling of Lg waves in Eastern North America, Geophys. J. Int., 118: 142-158. Shibazaki, B. and Matsu'ura, M., 1992. Spontaneous processes for nucleation, dynamic propagation, and stop of earthquake rupture. Geophys. Res, Lett., 19:1189-1192. Shimazaki, K. and Somerville, P., 1988. Static and dynamic parameters of the Izu-Oshima, Japan earthquake of January 14, 1978. Bull. Seismol. Soc. Am., 69: 1343-1378. Singh, S.K. and Mortera, F., 1991. Source time functions of large Mexican subduction zone earthquakes, morphology of the Benioff zone, age of the plate, and their tectonic implications. J. Geophys. Res., 96:21 487-21 502. Spudich, P. and Cranswick, E., 1984. Direct observation of rupture propagation during the 1979 Imperial Valley earthquake using a short-baseline accelerometer array. Bull. Seismol. Soc. Am., 74:2083-2114. Steidl, J., Martin, A., Tumarkin A., Lindley, G., Nicholson, C., Archuleta, R., Vernon, E, Edelman, A., Tolstoy, M., Jhin, J., Li, Y., Robertson, M., Teng, L., Scott, J., Johnson, D., Magistrale, H. and USGS Staff, Pasadena and Menlo Park, 1994. SCEC portable deployment following the 1994 Northridge earthquake. 89th Meeting of the Seismological Society of America, Abstract with Programs. Umeda, Y., 1990. High-amplitude seismic waves generated from the bright spot of an earthquake. Tectonophysics, 175: 81-92. Velasco, A.A., Ammon, C.J. and Lay, T., 1994. Recent large earthquakes near Cape Mendocino and in the Gorda Plate; broadband source time functions, fault orientations, and rupture complexities. J. Geophys. Res., 99:711-728. Wald, D.J., Helmberger, D.V. and Heaton, T.H., 1991. Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data. Bull. Seismol. Soc. Am., 81: 1540-1572. Wyatt, F.K., Agnew, D.C. and Gladwin, M.T., 1994. Continuous measurements of crustal deformation for the 1992 Landers earthquake sequence. Bull. Seismol. Soc. Am., 84: 768-779. Wyss, M. and Brune, J., 1967. The Alaska earthquake of 28 March 1964---a complex multiple rupture. Bull. Seismol. Soc. Am., 57: 1017-1023.