bulletin of the seismological society of america, vol. 81...

Bulletin of the Seismological Society of America, Vol. 81, No. 5, pp. 1622-1646, October 1991

A BROADBAND SEISMOLOGICAL INVESTIGATION OF THE 1989 LOMA PRIETA, CALIFORNIA, EARTHQUAKE:

EVIDENCE FOR DEEP SLOW SLIP?

BY TERRY C. WALLACE, AARON VELASCO, JIAJUN ZHANG, AND THORNE LAY

ABSTRACT

Analysis of regional and teleseismic broadband body waves and long-period surface waves from the 1989 Loma Prieta earthquake demonstrates that a fairly simple average fault model explains most characteristics of seismic wave radiation over a broad period range (1 to 300 sec), but there are some systematic period-dependent characteristics that are not yet understood. Determinations of the preferred point source focal mechanism are consistent for different seismic waves, as long as optimal source-time functions and depths are chosen for each wavetype. The major double couple orientation compatible with the entire period range has a strike = 128 +_ 3 °, dip = 67 _+ 5 ° , and rake = 133 _+ 8% While this source mechanism consistency is encouraging and indicates that the average source process is quite simple, there are some systematic discrepancies in the source parameter estimates from different period waves. The source duration estimated from the principal body-wave ground motions is 8 + 2 sec, compatible with the duration of near-field strong-motion vibrations, but the surface waves indicate total durations of 18 to 30 sec, depending on the earth model selected for computing propagation corrections. The model dependence of the surface-wave results suggests that it may be possible to reconcile the duration estimates with improved earth models, but the discrepancy is quite large. There is some complexity in the source-time function, comprised of three subevents at different depths, but this complexity is only manifested in short-period signals and does not explain the duration discrepancy. Changes of fault geometry or slip direction during rupture, as suggested by recent finite-fault inversions, are unlikely to cause a bias in source duration estimates. The centroid depth determined from our body-wave analysis is 10 to 12 km, consistent with the finite-fault models, which indicate rupture extending from 5 to 18 km. Surface-wave centroid depth estimates (15 to 30 km) vary substantially for different choices of global Q model and lithospheric structure in the source region, but they do tend to be deeper than the body-wave results. It is again not clear whether this depth discrepancy is due to the source process or inadequate earth models. The body-wave and surface-wave seismic moment estimates are also not fully consistent; the moment from our body-wave inversions is 2.4 _+ 0.3 x 1019 N-m, while our surface-wave analysis gives 3.2 _+ 0.5 x 1019 N-m. It is not known whether reasonable changes of the earth models can bring the moment estimates into full agreement. The systematic discrepancies in source duration, centroid depth, and seismic moment, despite the consistency in source orientation, raise the possibility of a deep, relatively slow co-seismic slip component, but trade-offs with modeling assumptions preclude us from confirming this hypothesis at present.

INTRODUCTION

The 18 October 1989 Loma Prieta ear thquake ( M s = 7.1) is one of the best instrumental ly recorded ear thquakes in history. Ground-motion data exist over a very broad frequency band, from 10-Hz vibrations (strong ground motion) to

1622

BROADBAND INVESTIGATION OF D E E P SLOW SLIP 1623

static offsets. Many investigators have modeled specific data sets, such as teleseismic body waves or geodetic observations, developing source models for the earthquake that are appropriate for the corresponding limited frequency band. Ideally, all independently derived source models should be compatible; the slip distribution required to produce the strong-motion records should also account for the geodetic estimate of co-seismic slip. Unfortunately, experience with other large earthquakes has shown that this is not often the case. For example, source parameters such as seismic moment and centroid depth derived by long-period surface-wave analysis are often different from those determined by short-period body-wave modeling. These inconsistencies can result from intrinsic limitations on the bandwidth of the data, which prevent a full source characterization using any one wave type, but they may also reflect incompatible modeling assumptions. The excellent seismic data available for the Loma Prieta earthquake, combined with unprecedented constraints on the faulting process provided by local seismic and geodetic observations, provide an opportu- nity to explore the compatibility and resolution of inversions of various seismic waves. In this article, we investigate the compatibility of source models for the Loma Prieta event derived from broadband body waves (1 to 20 sec) with those derived from Rayleigh and Love waves (150 to 300 sec) in an effort to detect any unusual source complexity and to provide a benchmark for the performance of the separate inversions. This is a necessary step in working toward unified source models that explain all seismic observations.

There is considerable debate as to the significance of the Loma Prieta earthquake and its implications for seismic hazard assessment in northern California; however, from the seismic source modeling perspective, the Loma Prieta event was overall a relatively simple rupture. The hypocenter was located southwest of the San Andreas fault trace in the Santa Cruz Mountains, with rupture initiating at a depth of 18 km (USGS Staff, 1990). The aftershocks in the first few hours following the mainshock outline a fault area roughly 40 km in length, indicating a bilateral, up-dip rupture (USGS Staff, 1990). Focal mechanisms determined from regional network P-wave first motions, teleseismic body wave and surface wave inversions, and geodetic modeling are all consistent with oblique thrust motion on a steeply dipping fault (Plafker and Galloway, 1989; Barker and Salzburg, 1990; Choy and Boatwright, 1990; Kanamori and Satake, 1990; Langston et al., 1990; Lisowski et al., 1990; Romanowicz and Lyon-Caen, 1990; Ruff and Tichelaar, 1990; Zhang and Lay, 1990; USGS Staff, 1990). There apparently was no significant tectonic surface rupture. Modeling of the geodetic data by Lisowski et al. (1990) indicates that the primary slip occurred between the hypocentral depth and 5 km depth, which is consistent with the centroid depths of 10 to 15 km determined from body-wave modeling. The source time function was relatively simple, and, although "subevents" of irregularities in the rupture expansion can be inferred, the total duration of high frequency radiation during the event is probably less than 15 sec. There was no compelling evidence in the initial teleseismic body-wave studies for source complexity such as a change of slip direction during rupture; however, recent finite-source inversions of both teleseismic and strong-motion data indicate that the southeastern segment of the fault had predominantly strike-slip motion, while the northwestern segment had predominantly dip-slip motion (Ammon, 1991; Beroza, 1991; Harzell et al., 1991; Mendez et al., 1990; Steidl and Archuleta, 1991; Wald et al. 1991).

1624 T .C . WALLACE E T A L .

Although most seismological investigations of the Loma Prieta ear thquake have yielded similar average source models, there are differences in detail. The most pronounced of these differences appear to be period dependent. In particular, modeling of long-period surface waves result in est imates of a longer source process time, deeper centroid depth, and larger moment than models determined from the teleseismic body waves. Zhang and Lay (1990) determined a source process t ime of 22 _+ 7 sec, a centroid depth of 19 km, and a moment of 3.4 + 0.5 × 1019 N-m from Rayleigh waves with periods of 150 to 300 sec. Romanowicz and Lyon-Caen (1990) obtained similar results (40 +_ 4 sec, 20 km and 3.3 + 0.5 × 1019 N-m, respectively). There is some spread in body-wave results, but the average source process t ime is about 8 to 10 sec, the centroid depth is 14 _+ 4 km, and the moment is 2.4 + 0.6 × 1019 N-m, (Barker and Salzburg, 1990; Choy and Boatwright, 1990; Kanamori and Satake, 1990; Romanowicz and Lyon-Caen, 1990; Langston et al., 1990; Ruff and Tichelaar, 1990). What is responsible for these discrepancies between t he body and surface wave results? There are two basic possibilities: (1) The inherent limitations of long-period surface-wave analysis for shallow moderate-size events make the resolution of the source parameters unstable, so these discrepancies are not significant; or (2) the long-period surface waves are sensitive to a slower and deeper slip process not resolved by body-wave radiation. This question is of fundamental importance, because such discrepancies are common for large ear thquakes and may shed light on the transit ion from brit t le failure to ductile creep at depth. Many seismological analyses use ad hoc procedures to combine body- and surface-wave results together, such as averaging the source parameters or adding a very long-period (slow rupture) component to the source process time, but this presumes the discrepancies are significant.

In this article, we compare average body- and surface-wave source models for the Loma Prieta earthquake. We do not perform finite-fault inversions for the body waves, preferring to simply characterize the overall source radiation at short periods with simple multiple point source models to abet comparison with the surface-wave results. We investigate model assumptions for the surface-wave analysis including propagation model, source velocity structure, and attenuation model to test the resolution and uniqueness of the source duration, depth, and moment determinations. We also test the possible effects of various "slow slip" models on the body waves. Our final source model for the Loma Prieta ear thquake at tempts to address the uncertainties introduced by using band- limited data.

BODY-WAVE ANALYSIS

The Loma Prieta ear thquake produced numerous seismic recordings at regional and teleseismic distances. Many of the signals were recorded on modern digital seismic systems that provide broadband data for detailed analysis of the seismic rupture process. A few of these stations, affiliated with either the Incorporated Research Insti tutions for Seismology (IRIS) or project GEOSCOPE of the Inst i tute de Physique du Globe de Paris, France, have dial-up access, which allowed near real-time analysis of the source mechanism and seismic moment. At least five different research groups obtained a mechanism and moment within 24 hours of the event (see McNally et al., 1989). These preliminary determinations were data-limited, but they did demonstrate that the ear thquake involved northwest-trending oblique-slip motion, rather than the


pure right lateral strike-slip offset expected for the San Andreas fault. These initial studies used only a few body waves and several long-period surface waves and had a significant scatter in seismic moments, largely at tr ibutable to the instabili ty of moment tensor inversions using fundamental mode surface waves for shallow sources.

Studies utilizing more complete body wave data set were available within a few days after the event. Figure 1 shows the Global Seismic Network (GSN) teleseismic and regional P waves, which were available within 1 week. The complications in the regional waveforms are primarily caused by propagation effects. The simplicity of the overall energy release at the source is indicated by the simple teleseismic P-wave ground motions. Analysis of this restricted data set gives a source model that is nearly identical to that determined with a large data set available 6 months after the ear thquake (Wallace and Lay, 1990). We perform some additional analysis of the extended data set here to confirm the average source properties for the body-wave period range.

We inverted regional distance Pnl waves and teleseismic broadband ground displacement P and SH waves for the stations listed in Table 1 using the joint point source inversion method of Holt and Wallace (1987). The procedure is an iterative, least-squares inversion of time-windowed data. The inversion is repeated over a suite of trial source depths, and the rms errors are used to infer the best centroid depth. The inversion initially assumes a simple trapezoidal time function. Once a good source orientation is determined, a detailed time function is obtained by deconvolution of the instrument, source, and propagation effects from the teleseismic P waves. The deconvolved pulses are averaged and then fit with a series of l-sec duration boxcars of varying height. The entire

LON I I' // ~J

/ TeleseismJc and Regional ANM/~/~A/~--~/~ f v ~ , q Distance P Waves

llI~v VSO ~ ' " Loma Prieta (I0/18/09)

FIG. 1. The teleseismic and regional distance P waves for the Loma Prieta earthquake that were available within I week after the event. The traces shown are broadband ground displacements. Note the difference in time scale for the three regional waveforms.

1626 T. C. WALLACE E T A L .

TABLE 1

STATIONS USED IN BODY-WAVE ANALYSIS

Station Distance (°) Azimuth (°} Phases Used

AFI 69.2 233 P, SH ANMO 12.7 95 Pnl ARU 86.9 0 P, SH COL 31.9 339 P HON 35.0 254 P, SH HRV 38.6 66 P, SH LON 9.7 0 Pnl OBN 85.4 12 P, SH PAS 4.2 132 Pnl RPN 64.9 167 P, SH TOL 84.5 43 P

inversion procedure (for source and depth) is repeated with the detailed time function. Figure 2 shows broadband P and S H waveforms fits for the final step; the source orientation is given by a strike of 128 o + 3 °, dip of 66 + 4 °, and rake of 132 +_ 7 °. The seismic moment is 2.4 +_ 0.3 x 1019 N-m ( M W = 6.9) and the centroid depth is 10 to 12 km. This mechanism is in excellent agreement with the first-motion solution (USGS Staff, 1990), our surface-wave studies, and the many other source studies for which focal mechanisms are summarized in Table 2.

The procedure we used for determining the details of the source-time function requires that there be very little azimuthal variation in the pulse duration. For the Loma Prieta event, the t ime function duration varies by less than 6 per cent as a function of azimuth. Figure 3 shows an expanded version of the final boxcar parameterized time function. The total duration is 8 sec, in agreement with the duration of pr imary moment release in other body-wave studies (Choy and Boatwright, 1990; Langston et al . , 1990; N~b~lek, 1990). Some body-wave studies have indicated later rupture, with minor energy release from 10 to 20 sec after initiation (e.g., Choy and Boatwright, 1990; Kanamori and Satake, 1990; N~b~lek, 1990), but there is no agreement as to the mechanism or moment of this radiation. Our stacked source functions do not indicate significant coherent radiation with the average focal mechanism, but our processing may have suppressed radiation from a very different fault orientation. Our stacked moment rate function is dominated by a "subevent" in the last 5 sec of the pulse, which comprises 78% of the moment. Figure 3 also shows the broadband velocity and displacement records at OBN, along with a synthetic seismogram. The velocity pulse clearly shows the three subevents with increas- ing moment release, as has been noted by others (Choy and Boatwright, 1990; N~b~lek, 1990). These subevents are apparent in the source function.

The relative t iming of the pulses from the velocity records was examined to investigate the effects of possible source directivity. Figure 4 shows the azimuthal variat ion of broadband ground velocity of P waves. Inversion of the relative t iming of the pulses for horizontally distributed subevents indicates tha t the main centroids of the subevents did not extend beyond _+ 10 km along strike from the hypocenter (the limit of resolution using the broadband P waves). This is in agreement with finite slip models obtained from strong ground motion data by Beroza (1991) and Wald et al. (1991). Larger data sets of

B R O A D B A N D I N V E S T I G A T I O N OF D E E P S L O W S L I P 1627

AFI ( , 2.5

Regional a z = 2 3 ~ ~ S waves

PAS 2 2

az=0 2.3 ARU ,,~ V 2.4

OBN ~ / 2.4 . . _ ANM az--12~/~ az=95 2.2

0 50 HRV

az=168 2.1

0 5 I I Time (sec) 0 15

FIG. 2. Ground d i sp lacement waveform compar isons for observed (top traces) and point source syn the t ic (lower traces) regional and te lese ismic P and S H waves from the Loma Pr ie t a ear thquake. Note the difference in t ime scale for t he t h ree regional waveforms. The t ime funct ion is shown at the lower r ight . The focal m e c h a n i s m is t~ = 128 _+ 3 °, 5 = 66 _+ 4 °, X = 132 _+ 7 °, and the seismic m o m e n t is 2.4 × 10 TM N-m.

teleseismic waveforms have also bee used to derive finite source models, although the results are more variable (Ammon, 1991; Hartzell et al., 1991; Wald et al., 1991), and appear to be at the limit of resolution for the teleseismic data. These finite-source studies indicate tha t slip was concentrated in two patches with centroids at 5 to 6 km along strike on either side of the epicenter.

We found tha t we could stably invert for the depths of subevents 2 and 3 using the constraint tha t subevent 1 occurred at the hypocentral depth. The inversion we used is an iterative least-squares fit of the P waveforms and is parameterized in terms of t iming and waveform shape. Figure 5 shows the rms error of the waveforms as a function of subevent depth. Subevent 2 has a depth of 16 to 18 km, which is very similar to the hypocentral depth, whereas the third subevent is significantly shallower at 10 to 12 km. This is not surprising, considering tha t the third subevent dominates the moment release and there- fore should correspond to the centroid depth. The finite-source models indicate that simultaneous radiation of separate patches of predominantly strike-slip and predominantly dip-slip motion may contribute to these subevents, but comparable source depths are obtained in those models.


TABLE 2

SOURCE PARAMETERS FOR LOMA PRIETA EARTHQUAKE

Strike (°) Dip (°) Rake (°) Depth (km) M o (1019Nm) Duration (sec) Reference Data Type

Local / Regional / Teleseismic Body Waves

128 +_ 3 66 _+ 4 132 _+ 7 18, 17, 11" 2.4 ___ 0.3 8.0 + 2.0 This P, SH study

128 70 138 15 3.0 _+ 0.5 7.5-20.0 KS P, SH 125 75 130 15 2.9 KS Pnl

130 _+ 5 65 + 5 140 _+ 5 18, 16, 12 2.0-2.2 7.5-15.0 CB P, SH 138 _+ 6 76 ± 5 120 _+ 10 10-12 2.0 _+ 0.5 9.0 RT P, SH

126 66 138 10 1.7 9.0 RL-C P, SH 130 ± 5 56 +_ 5 158 + 5 18-10 2.3 Letal Psearch

122 58 144 8 2.26 Letal P, SH 130 73 146 18, 14 2.8 8.0-9.0 BS P, SH 128 66 ' 132 18, 16, 12 2.3 7.5 WL P, SH

128 ± 2 63 _+ 2 129 +_ 2 7-12 3.0-3.1 8.0-15.0 N P, SH 130 + 8 70 +_ 10 130 +_ 15 PG PlstMo.

130 + 10 70 + 15 140 + 15 0 PlstMo. 130 ~ 70 ~ Varies 3-18 2.0-12.9 10.0-12.0 A P, SH 128 ~ 70 ~ Varies, 13, 11 2.8 Wetal P, SH

142avg.

Surface Waves

128 +_ 2 69 +_ 3 134 _+ 4 15-23 3.3 _+ 0.5 18 _+ 5 This R,G Study

123 71 128 19 ~ 2.7 40.0 Detal CMT 128 70 137 15 2.5 KS CMT 129 70 ~ 144 15 2.8 KS R, G

127 +_ 5 66 +_ 5 132 +_ 5 20 _+ 5 3.3 _+ 0.5 36.0-44.0 RL-C R 130 +_ 5 70 _+ 5 135 ± 5 19 _+ 3 3.4 ± 0.5 20.0-22.0 ZL R

Geodetic / Near-Field Strong Motions

132 70 136 70 130 t 70 ~

126 ~ 67 ~

130~ 70 ~

126 t 70 t

128 t 70 t

128 ¢ 70 t

146 144

Varies

Varies

Varies

Varies

Varies, 144avg. Varies, 145avg.

6-18 3.2 ~ PG Geodetic 5-17.5 3.0 * Lietal Geodetic 12, 14 1.3-2.5 10.0-12.0 B Strong

Motion 18-2 2.06-3.0 7.5-13.0 Hetal Strong

Motion 3.0 7.0-12.0 Metal Strong

Motion 9-18 3.0 +_ 0.5 < 10.0 SA Strong

Motion 12, 15 3.1 < 10.0 Wetal Strong

Motion 11, 16 3.0 < 10.0 Wetal Strong

Motion/ P, SH

*Subevent centroid depths. tConstrained in inversion. SAssumes rigidity = 3.0"1011 dyne/cm 2. A: Ammon, 1991; BS: Barker and Salzberg, 1990; B: Beroza, 1991; CB: Choy and Boatwright,

1990; Detal: Dziewonski et al., 1990; Hetal: Hartzell et al., 1991; KS: Kanamori and Satake, 1990; Letal: Langston et al., 1990; Lietal: Lisowski et al., 1990; Metal: Mendez et al., 1990; N: N~b~lek, 1990; O: Oppenheimer, 1990; PG: Plafker and Galloway, 1989; RL-C: Romanowicz and Lyon-Caen, 1990; RT: Ruff and Tichelaar, 1990; SA: Steidl and Archuleta, 1991; Wetal: Wald et al., 1991; WL: Wallace and Lay, 1990; ZL: Zhang and Lay, 1990.

BROADBAND INVESTIGATION OF DEEP SLOW SLIP

Inversion Source Time Function

1629

i_ I 0 5

Time (sec)

O4

- 5 ;

101 X

O:

-10

0

Event 2 Event 1 Event 3 Station TOL

. . . . I I ' J ~A ~ + ' ' ' ' J ' '

observed ~ r ~ / i . . . . Displacemen t

10 20 30 40 50

FIG. 3. (Top) Source-time function derived by deconvolution of the Loma Prieta P waves; each boxcar is 1 sec in length. (Bottom) Observed ground velocity and displacement pulses for station OBN. The dashed line is a synthetic computed using the time function shown at the top. The resolution of subevents is clearer in the velocity traces.

While we do not feel tha t we have the resolution to perform a finite-source inversion, the source-time function determined from the broadband P waves can be interpreted in terms of a bilateral, up-dip rupture. The total lateral extent of the rupture is constrained to be on the order of + 20 km along strike from the hypocenter, assuming a rupture velocity of 2.7 km/sec. A total rupture length of 35 to 40 km is consistent with the distribution of aftershocks that immediately followed the event. The USGS Staff (1990) reported an aftershock zone surrounding an elliptical region 40 km long centered above the hypocenter. In addition, dislocation models determined from geodetic displacements (Lisowski et al., 1990) have a fault plane extending 37 km along strike. Subevent 1 had only 5% of the total seismic moment and corresponded to the initiation of rupture at depth. Subevent 2, which initiated 1 sec after the rupture began, was at slightly shallower depth. Subevent 3, the primary moment release episode, represents upward and bilaterally extending rupture.

The part i t ioning of the source-time function into three subevents indicates source complexity. This complexity could simply be due to a temporal burst of moment release along a planar fault caused by variation in slip function, or it could represent moment release on geometrically complex faults. The moment

1630 T.C. WALLACE E T A L .

O

>

t -

O

HIA az=323

Subevent 1

I I

20 30

Time (sec)

ARU az=0

OBN az=12

TOL az=43

HRV az=65

RPN az=168

I I

0 10 40 50

FIG. 4. Teleseismic P-wave ground velocity waveforms ordered as a function of azimuth from the source. Not that over nearly 180 ° azimuthal variation there is little discernable variation in pulse width or relative timing of the subevents.

tensors derived from inversion of our source parameters indicate a nearly pure double couple. The body waves have a CLVD of less than 2% for the final model. Fur thermore , the preferred surface-wave models discussed in the next section have a CLVD as low as 3%. This suggests tha t the overall complexity in the t ime function is not due to a sequential change in fault geometry or slip direction during rupture , a l though simultaneous radiat ion of different slip components cannot be ruled out. The recent finite-source models suggest variable slip directions on a common fault plane, which is somewhat implausible. It seems more likely to use tha t any var ia t ion in slip direction will involve ei ther a contortion of the fault plane or multiple fault surfaces. The aftershock distribution along the southeastern segment of the rupture zone appears to be somewhat more vertical (Dietz and Ellsworth, 1990), indicating t h a t the inferred predominant strike-slip motion in this region may actually be on a steeper dipping plane.

We performed another body-wave inversion to explore the hypothesis tha t the rupture may have some geometric complexity. We inverted seven teleseismic P waves using a t ime dependent moment tensor (TDMT) algori thm (Kim and Wallace, 1988). The five moment tensor elements are allowed to be independent, and the resul t ing inversion is l inear to the frequency domain. If a broad range of frequencies is available, a complete mapping of the rupture history can be recovered. The five moment tensor elements have different t ime histories, which can be interpreted in isolated t ime windows as fault ing episodes. Figure 6 shows the results of the TDMT inversion. The M=y te rm is insignificant, but the other terms all show similar t ime histories. For the initial 8-sec window, the mechanism is near ly identical to the complete body-wave solution and is thus


0.6

0.5 i _

I I I

= E n- 0 . 4 -

0.3 0

Event 2

i I i I ~ I

10 20 30

Depth

i I

4O

Event 3 0.7

0.6

LU 0.5

¢o

0.4 ¸

0.3 = I 0 40

i I i I [ I

10 20 30

Depth

FIG. 5. The rms error for the teleseismic waveform fit for subevents 2 and 3, assuming a depth of 18 km for the very small subevent 1.

consistent with a double couple. It is possible tha t there is a gradual change in mechanism from a steeply dipping oblique fault to a shallower dipping thrust during the 8-sec window, but the change is not resolvable. There is no coherent double couple radiation in the interval from 8 to 20 sec, and we feel tha t the late complexity is likely to be due to inadequate Green's functions. Ruff and Tichelaar (1990) used a similar procedure, but with time domain deconvolution, and also concluded tha t the primary radiation was consistent with a double couple.

SURFACE-WAVE ANALYSIS

Source parameters derived from analysis of long-period surface waves fre- quently differ from models determined from body waves. In particular, seismic moments determined by surface waves are in some cases a factor of 2 or more larger than moments determined from body waves, and source duration and centroid depths are typically longer and deeper, respectively. There are two general explanations for these inconsistencies: (1) The body-wave bandwidth is too limited to resolve the long-period spectral levels of the source, or (2) models used to correct for surface wave propagation (and to a lesser extent, the body waves) are inadequate. The first explanation is associated with

1632 T . C . WALLACE E T A L .

1

E .b, Z 1

0

1

Mx x

__ Myy

. . . . . . . . . . . . . . . . . . . Mxy

o 1

1

,

0 5 10 15 20

Time (sec)

Mxz

Myz

FIG. 6. The time-dependent moment rate functions determined from the teleseismic body waves. Each moment tensor component is allowed to have its own time history.

"frequency-dependent" source models, in which a "low-frequency" component of the source does not excite body waves within the bandwidth of the recording seismometers. This slow slip would increase the overall seismic moment and source duration for long-period waves and may give a deeper centroid depth, if the slow slip is located below the centroid of body wave radiation. The second explanation arises because the earth model near the source is usually poorly known and influences the surface-wave excitation, while the global earth model used to correct the observed surface waves for propagation effects is also subject to errors.

A comparison of Loma Prieta source models derived from body-wave analyses with those determined from long-period surface waves shows that the typical discrepancies exist (Table 2). The Loma Prieta earthquake is an excellent event to test the explanations for the inconsistencies. There is a high-quality broadband digital data set to analyze, and there has been much recent progress in development of aspherical models of ear th structure tha t enable high-resolution source inversions of long-period signals. Also, the event was small enough tha t it should not have saturated the body waves within the recording band unless a very slow slip component took place. Finally, new techniques have been developed which test the compatibility of surface-wave spectral moment tensor inversions and body-wave results (Zhang and Lay, 1989).

For our surface-wave inversion analysis, we used the long-period Rayleigh waves (R 1 and R2) and Love waves (G 1 and G2) recorded on three seismic networks (GSN, IDA, and GEOSCOPE). In order to test the model dependence of our inversions, we consider several propagation, global Q, and source velocity models to determine an ensemble of source models. The surface waves were analyzed with a moment tensor inversion approach developed by Kanamori and Given (1981), modified to a two-step process tha t isolates source finiteness effects from the determination of the centroid depth and moment tensor

B R O A D B A N D I N V E S T I G A T I O N O F D E E P S L O W S L I P 1 6 3 3

(Romanowicz and Guillemant, 1984). Zhang and Lay (1990) reported on prelimL nary analysis of the Rayleigh waves using methodologies identical to those used here for Rayleigh and Love waves, so we will not discuss the details of the inversion technique further.

Earth models for seismic velocity are only relatively well known at long periods (> 150 sec), and, since the Loma Prieta earthquake had a short duration (< 10 sec), we were able to assume a simple source representation. Neither the body*wave nor surface-wave analyses showed significant evidence of directivity, so we used a point source with a finite duration. The first step in the inversion is to determine the total source duration. Figure 7 shows the normalized error, a, which is a measure of variance reduction for boxcar time functions with a range of durations form 0 to 60 sec. The estimates are obtained for a range of periods form 150 to 300 sec. The duration estimates depend on the adequacy of the average phase velocity at each period and, for the aspherical models, on the average phase velocity along each propagation path. The two earth models used for the surface wave propagation corrections are PREM, a spherically symmetric model (Dziewonski and Anderson, 1981), and M84C, an aspherical model (Woodhouse and Dziewonski, 1984).

2; IL l .(; r r

13..

Rayleigh Waves Love Waves Rayleigh and Love Waves f i , i , , i T I , , i i [ ,

No. Per iod(s) I b - - / l / 1 -- 150 4 -- 225 J ~L " ~ J ~12" .., J 2 -- 175 5 - -250 / % ~ - - - - ~ ~ / " / -- , , -} 3 - - 2 0 0 6 - - 2 7 5 | | ' ' . . I ~ - " ~ ~ ~" | ,, 7 - - 3 0 0 / t t ' " ' " ' ' ' ' t [ " " - - - ~]

, " , " - - k ~ ~ - ; , ..." . . . . . . . . . . . . i:.- / t " " ' - - , - , - - " : . : ' - , ' - , 2 - " , - ' " . . . " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' - ~ ..........

~ .,1 .4

20 40 I , I , ~0 "~'0 20 40 ':'l I , I ' 60"% . . . . 20 40 °` 6'0

0 .6

CO

i , i i

No. Period (s) 1 -- 150

.8 2 -- 175 3 -- 200 4 -- 225 5 -- 250 /' 6 -- 275 /,f. 7 -- 300 / / . ' "

", //./5 ./..... / / , '

,,. i X . " / . 4~<. " - ~ 1 ,-,..- / / - . .

• 1 ~ , ~ 2 . . " . - .J:/p<.- '"

"20 20 40 f

i i 1 r 1 l i

.8 / t .8 - / /

/ / | / / / / , / / /

.6 / / , , , . . .6 / / , , , . ", / ,,:..'" ,. / , , ( . ' "

",, / / / , . ; . ' . , ' \ / / ...y.;'" . . . , , , .. , . . . ~ ,

. 4 - " , " : .4

20 40 60.2 ' 2'o' 4'o . . . . . 2E0 ' 4'0 ' 60

A p p a r e n t Duration (s) FIG. 7. The normalized error for the first step inversion of the surface waves as a function of

assumed trapezoid source duration, Seven different periods are shown. The two earth models used for computing propagation corrections were PREM (Dziewonski and Anderson, 1981) and M 8 4 C (Woodhouse and Dziewonski, 1984). The minimum of each curve is the duration estimate for that period• Results are shown for separate and combined analysis of the Rayleigh and Love Waves.

1634 T. C. W A L L A C E E T A L .

Three data sets were analyzed in the determination of source duration: Rayleigh waves, Love waves, and a combination of both. In each case, better overall variance reduction was achieved using M84C for propagation corrections, part icularly for Love waves. The estimate of duration obtained for the different data sets and periods range from 11 to 30 sec. Note that the Rayleigh waves show considerable scatter in the est imate of duration, while the Love waves have a more consistent minimum. This is somewhat surprising given the large scatter in Love wave phase measurements that is typically observed. The simultaneous inversion for both Rayleigh and Love waves gives a best estimate of the source duration of 18 sec, where higher weight is given to the spectra with lower residual misfit. This duration, corresponding to a boxcar source-time function with uniform moment release, is considerably longer than the time function derived from the body-wave analysis. It is important to assess the robustness of this result. Comparison of the PREM and M84C estimates (30 versus 18 sec) indicates tha t ear th model effects can certainly be as large as the 8 to 10 sec discrepancy between short-period and long-period results. While M84C is probably a much bet ter ear th model than PREM for this application, the duration might be reduced even more given a more detailed aspherical mode. This issue is currently being explored using higher resolution models (Velasco et al., manuscript in preparation).

Although the long wavelenghts of the surface-wave data and the limitations of the existing ear th models preclude resolving details of the source-time function, the inversion for source mechanism is not critically dependent on the precise duration estimate. Errors in the earth model that project onto the duration estimate, which correspond to uniform phase shifts, are effectively removed from the spectra. If we arbi trari ly reduce the estimate of the source duration from 18 to 9 sec, the moment tensor obtained in the second step inversion only changes slightly; the moment is reduced by 8% with a significant change in fault plane orientation.

In the second step of the inversion, we determine the seismic moment tensor and the centroid depth. The input "data" for this inversion are the output spectra from the first inversion for a final choice of source duration (18 sec) appropriate for the part icular earth model (M84C) used in calculating the propagation corrections. In addition, we must also assume a near-source elastic structure (seismic velocity, density, shear modulus, and attenuation) and a global a t tenuat ion model. The source crustal structure affects the excitation functions, but the lithosphere structure is even more important for long periods. We use four different models to explore the stabili ty of the depth determination: (1) average and (2) young ocean models of Regan and Anderson (1984) (RA and RAyo respectively), (3) PREM, and (4) a Loma Prieta model (LP) constructed from upper mantle P-wave and SH-wave velocity models for the western United States (Walck, 1985; Grand and Helmberger, 1985), with a crustal model from Walter and Mooney (1982). The variat ion of P velocity, S velocity, and density with depth for each of these models is shown in Figure 8. There are substantial differences between the models in the velocity structure in the upper 300 km, thus comparison of the results for such different models can shed some light on the sensitivity to uncertain lithospheric structure. Our preferred results are for the LP model, but the details of the upper mantle structure are not known for this source region.

We also used three different global Q models for Rayleigh waves in the

B R O A D B A N D I N V E S T I G A T I O N OF D E E P SLOW SLIP 1635

1[ , Velocity., and, Density, Models, 1

Regan and Anderson, young ocean (RA-yo) i Regan and Anderson, average ocean (RA)

1 0 PREM Loma Prieta (LP)

~ 7 E ._,g ~ 6 0

" ~ W a l c k , 1985]

Vs

LP ['FNA from Grand and ~ - Helmberger, 1 9 8 ~

7 / - p

100 200 300 400 500 600 700 Depth (km)

FIG. 8. Source region velocity s t ructures used in the computation of excitation functions for the surface-wave analysis. Model LP has a P velocity s t ructure in the crust t aken from Wal ter and Mooney (1982), with mant le velocity s t ructures t aken from Walck (1985) and Grand and Helm- berger (1984). There is significant uncer ta in ty in the correct s t ructure to use for depths of 100 to 200 km, and this suite of models spans the plausible range of upper mante l models.

surface-wave analysis, MG from Masters and Gilbert (1980), DS from Dziewon- ski and Steim (1982), and PREM from Dziewonski and Anderson (1981). The Love-wave Q model is PREM in every case. The at tenuat ion models most directly affect the variation of the amplitude spectra with period. Figure 9 shows the different Rayleigh wave at tenuat ion models as a function of period. The smooth variations in Q with period can trade-off with corresponding variation of excitation functions with depth and period for different earth models. Our preferred results are given for the model DS, however there is substantial uncertainty in reference Q model, and it is clear that aspherical Q models that are currently under development should improve such inversions.

Figure 10 shows the normalized error in the second step inversion, p, versus source depth for the different source velocity structures for two global Q models. The inversions for centroid depth involve only Rayleigh waves, because the Love waves excitation functions vary only slightly with depth. For a given Q model, the range in source velocity structures results in about an 8-km variation in source centroid depth. Using the MG Q model in combination with the LP model gives a centroid depth of 15 km, in reasonable agreement with the body-wave results (see Table 2); however, there is clearly much uncertainty in this estimate, and most model combinations result in greater centroid depths, even allowing for the water layer in the oceanic models (3 to 5 km of the indicated depths).

1636 T .C . WALLACE E T AL.

Rayieigh Wave Q Models 250 - - i i

Masters and Giiber[ (MG) I 225 Dziewonski and Steirn (DS) ..

PREM / ~ t 2001 MG . -

© 175 ' " ~ ' ~

150 ; ~

125 ~

I I 10~5 ~ 200 250 ~00

Period (seconds)

FIG. 9. Rayleigh-wave global Q models from Masters and Gilbert (1983) (MG), Dziewonski and Anderson (1981) (PREM), and Dziewonski and Steim (1982) (DS). The frequency-dependent variations trade-off with the excitation functions for a given source velocity model, resulting in uncertainty in the source depth.

Rayleigh Wave Depth Resolution for Excitation Models

O.

.11 . . . . . . . . . I . . . . . . ~-'~q . . . . . . ~ ,11 Q Model ol Dziewonski and Steim /

/ /

/ /

I / . / / ,"

~',,, ~ / \'",, / / / ,,'

\',, ~ I / /

\ ,/.."

~'. . , / / / . q . / / . /

P _ ~ REM

LP

, , , J , l ~ l l i l l l L L i i I I I , I , l l l J l

20 30 40 Depth (km)

.10

.09

.08

10

O...

.10

.09

.08

Q Model of Masters and Gilbert ~ / i f /

/ / ,,"

! ] /

t / ;" i ] ,"

/ / / / / /

/ / ,"

t / / / / ."

/ RA/ / / / / /" / '

RA-yo / / /

LP PREM

I ~ l l l L I J I l l l l l L I L I I L ~ L ~ - - 0 20 3O 4O

Depth (kin)

FIG. 10. Depth estimation for various global attenuation models and velocity structures. The source velocity models are shown in Figure 8. For a given Q model, the uncertainty in source velocity structure results in 5 to 6 km uncertainty in depth, the LP model and RA-yo, both of which have more pronounced low-velocity zones than the other models, given the shallowest depths when the Masters and Gilbert (1983) Q model is used.

T h e cho ice of a t t e n u a t i o n m o d e l h a s a s i g n i f i c a n t e f fec t on t h e c e n t r o i d d e p t h , c o m p a r a b l e to t h a t a r i s i n g f r o m u n c e r t a i n t y in l i t h o s p h e r i c s t r u c t u r e . T h e d e p t h v a r i e s f r o m 15 to 28 k m for t h e L P s t r u c t u r e m o d e l i n c o m b i n a t i o n w i t h d i f f e r e n t Q m o d e l s (F ig . 11). W h i l e w e p r e f e r t h e L P m o d e l b e c a u s e i t h a s t h e s a m e c r u s t a l s t r u c t u r e u s e d i n o u r b o d y - w a v e m o d e l i n g , t h e b e s t cho ice for t h e


Q structure is not clear. It is possible to perturb the global Q model in combination with the elastic parameters in the velocity structure to exactly match the body-wave centroid depth, however there is not an objective basis for doing so. Rather, it is apparent that we cannot place great confidence in the 5 to 10-km discrepancy between the centroid depths est imated from body waves (periods 1 to 10 sec) and long-period surface waves (150 to 300 sec). Given the very long-period waves being used, it is remarkable that the agreement is as good as it is. As new aspherical models for shorter-period surface waves are developed, the long-period analysis should improve in resolution by incorpora- tion of shorter wavelength signals• This will help to overcome the trade-offs between excitation function variations with depth and global Q models.

For the determination of the long-period moment tensor, a second-step simultaneous inversion of Rayleigh and Love waves was performed. The joint inversion uses the full period range of the observations and the different wavetypes, which have variable noise characteristics. We thus employ a weighting scheme based on the variance of the source duration inversions. At each frequency, the minimum variance in the first-step inversion for each wavetype is used as a weighting factor for that frequency and ~wavetype in the second-step inversion. Also, since the Loma Prieta ear thquake is shallow, Love waves tend to be particularly unstable for determining the My z and Mxz terms of the moment tensor. We found that the Love waves gave such unstable estimates for Myz that we only used Rayleigh-wave information to invert for that component. Overall, however, we were satisfied with the stability of the Love-wave spectra, contrary to our previous experience. The stable behavior of the Rayleigh-wave and Love-wave spectra at two of the seven periods used in the inversion is

R a y l e i g h W a v e Dep th R e s o l u t i o n for Q m o d e l s

Q.

.11 ' ' ~ - - ~ - ' - ' I . . . . . . . ~-r-I . . . . . . . . Masters and Gilbert (MG)

Dziewonski and Steim (DS)

.10

.09

.08

PREM

\

\

x •

\ ,

MG DS PREM

, , , , , , , , , I , , , , , , , , , I , , , , , , , ,

0 20 30

Depth (kin) 40

FIG. 11. Depth es t imat ion for the LP model in combination with three different global Q models. The choice of global Q model has a major effect on the source depth due to the trade-off between the smooth frequency dependent Q models (Fig. 9), and the smooth changes in excitation functions with depth and frequency.


indicated by Figure 12, which shows the results for the LP source model with the DS Q model. The oblique character of the mechanisms is well constrained by the Rayleigh wave spectra.

Figure 13 shows the moment tensor results for several combinations of Q models and source velocity structures. M~, M ~ , and M~y are well resolved and do not depend strongly on the choice of Q and source models. The inclusion of Love waves in the inversion slightly stabilizes the moment tensor inversions, in particular for M~. The large error bars on the M~ and M~z terms indicate that these are the least constrained elements, which is typical for source inversions using only fundamental mode surface waves. Despite this instabil- ity, the results are very consistent with the solutions obtained by body-wave inversions (see comparisons in Table 2). Figure 14 compares the moment tensor and associated major double couple focal sphere projections for the body-wave

R a y l e i g h W a v e s 1 .... ,

T = 200

.~. ~ . . ,~,

120 240 360

1 - .~ ~ "

120 240 360 1( ....

T = 250

~ _ s , ~

- C_z i - , ~

120 240 360

' , " 't -2

120 240 360

A z i m u t h (degrees)

1

Love W a v e s

/ -~-; ~ . ~ ~ . ~ /

O0 120 240 360

r-" k ~ : , , ~ , ~ ~ i

o _1 . T = 2 5 0 ~ 0l . [ ~ . ~ ._~ ~o ~. . =o

5 _ ~ ~ >=' - =

1

[~ • , ' ' , , •

0 120 240 360

Azimuth (degrees)

FIG. 12. Moment tensor inversion results from simultaneous Rayleigh- and Love-wave inversions for periods of 200 and 250 sec. In this case, the DS Q model and the LP source velocity model were used. Note the satisfactory fit to the observed spectra, and the stability of the Love wave observations.


0.5

0.3

0.1

-0.1

-0.3

-0.5

0.5

0.3

0.1

-0.1

-0.3

-0 .5

M o m e n t Tensor for Loma Prieta Model ; Rayleigh Wave Inver s ion

_~ T [

.il ii!

I T

Q Models Rayleigh Wave (Q):

• Q=DS I • Q = MG •

Mxy Myy-Mxx Myy+MXx My z Mxz

M o m e n t Tensor for Loma Prieta Model : Love and Rayleigh Wave Inve r s ion

T

Ill/~ll

•ill

Mxy Myy-Mxx Myy+M~o( Myz* Mxz

O Models Love Wave: QL = PREM

Rayleigh Wave (Q):

• Q = MG • Q = PREM

M o m e n t Tensor for Excitat ion Func t ions : Love and Rayleigh Wave I n v e r s i o n

0.5 ,..~. Q Models:

Q=DS

0,1 Excitation Function.s:

.... it; 1 - 0.1 RA-yo

~m~o PREM

- 0 . 3 • LP

-0.5 I Mxy Myy-Mx~ Myy+Mxx Myz* Mxz

FIG. 13. Es t imates of the moment tensor components for the Loma Prieta ear thquake using various Q and source s t ructure models. (Top) Moment tensors for Rayleigh waves alone with the LP model and varying Q models. (Middle) Moment tensors for s imultaneous inversions of Rayleigh and Love waves for the LP model and varying Q models for Rayleigh waves. (Bottom) Moment tensors for s imultaneous inversions of Rayleigh and Love waves for various source models, wi th fixed Q models.

1640 T.C. WALLACE E T A L .

inversion from this article (Fig. 14a), with the inversions for the LP model for each of the different global Q models (Fig. 14b to d). Note tha t the major double couple is near ly in exact agreement with the body-wave solution for all of the Q models. The best double couple solution from the joint surface-wave inversion using the LP s t ructure and the DS Q model is strike = 129" +_ 2 °, dip = 69 ° _+ 3" and rake = 134" +_ 4". The seismic moment is 3.3 + 0.5 × 1019 Nm ( M w =

7.0). The minor double couple varies from 3 to 14% for the different Q models, comparable to the var ia t ion found when the source depth is varied by + 5 km about the optimal depth for a given combination of source and Q models. This indicates tha t the long-period waves do not require, but can accommodate, some variat ion from a pure double couple point source. This means tha t the surface waves are not incompatible with the finite-source body-wave inversions that indicate substantial var ia t ion in rake along the fault, as long as this gives a consistent average mechanism.

DIscussioN

The s tandard seismological procedure for invest igat ing large earthquakes, which we have followed in this study, is to derive independent source models based on various wavetypes. The overall source process is then inferred by merging the results. As in the present case, the source models are often inconsistent in some respects. Here there appears to be a "frequency-dependent" signature: The long-period surface wave analysis results in large seismic moment, longer source duration, and deeper centroid depth than corresponding body-wave analysis. In other cases, the fault ing mechanisms are also different. There is little doubt tha t for some events such discrepancies reflect a real phenomenon. When body-wave analysis is conducted on data recorded on nar- rowband ins t rumentat ion, such as the WWSSN, it is difficult to resolve the long-period spectral component of large sources, but modern broadband data like those used in this study have much bet ter resolution of the source. It has

(a) N (b) N

S s (c) N (d) N

S S

FIG. 14. Lower hemisphere projections of the moment tensor solutions and associated major double couples for the body-wave inversion (a), and simultaneous Rayleigh and Love wave inversions using the LP model with global Q models of (b) Dziewonski and Steim (1982), (c) Masters and Gilbert (1983), and (d) PREM.


been documented that there are "slow" ear thquakes and that some events have significant "aseismic" (at least in the frequency band required to generate body waves) slip, in which case even the broadband data may not resolve the long-period radiation.

Understanding the discrepancy between short-period and long-period source models is essential for understanding fault mechanics. At present, a popular conceptualization of the faulting process is of a series of "patches" of large displacement surrounded by regions of much less slip. This view is largely based on finite-source body-wave studies and conflicts somewhat with geodetic measurements , which can be fit using uniform slip distributions. Do the "patches" fail with rapid rupture, producing high-frequency body-wave radiation, while the surrounding regions slip slowly, thus only having a long-period signature? Another view is that the deeper centroid depth and larger moment from surface-wave studies may represent slow slip in the lowermost crust or the uppermost mantle, where there is a transit ion in rheological properties. High strain rates during rupture in the shallow region can induce co-seismic failure on the down-dip extension of the fault. Differences in grain size and thermal state of the deeper fault may then cause differences in rupture particle velocity that affect the spectrum of seismic radiation.

The Loma Prieta ear thquake provides an unusual ly well-controlled test case to determine whether a single broadband seismic model can explain the entire faulting process. Careful analysis of assumptions used in the modeling is needed to assess the significance of the period-dependent source parameters. It is clear that propagation corrections and the choice of global at tenuat ion model can have significant effects of the centroid depth and source duration determined by the inversion of surface waves. Although our analysis does not achieve exact agreement between the body- and surface-wave inversions, we believe that model uncertainties are large enough to plausibly account for the discrepancies in these parameters.

The seismic moment discrepancy is more difficult to resolve. It is possible to adjust the at tenuat ion and shear modulus used in the body wave modeling such that the moment is increased. For teleseismic signals, we assumed t* equal to 0.9 and 3.6 sec for P and SH waves, respectively. If we assume that the actual value of t* is 0.6 and the value for shear modulus, ~, should be 6.0 × 1011 dyne/cm 2, ra ther than 3.0 × 1011 dyne/cm 2, then the body-wave moment can be increased to 3.0 × 1019 N-m. In our opinion, these values for t* and ~ are unreasonable for the Loma Prieta earthquake. At regional distances, we assume that Q~ = 1000 and Q~ = 500. These are fairly high values for Q and may bias the moment downward; taken alone, the regional distance waveforms give a moment of 2.3 x 1019 N-m, less than the combined teleseismic and regional distance moment. Lower Q values for the regional phases are not unreasonable given the tectonic region traversed by most paths, but the best choice of Q values is not well determined.

If the surface-wave moment is t ruly larger than the body-wave moment, then we must account for the additional slip somewhere along the fault. Two possibilities for the additional slip include (1) unmodeled slip that occurred beyond the 8-sec t ime window of the body-wave moment rate function, or (2) a long-period component of slip that is unmodeled in the body-wave analysis. We tested the hypothesis that the slip occurred beyond the time window of the body-wave inversion by repeating the inversion with varying window lengths.

1642 T. C. W A L L A C E E T A L .

Our original choice for the teleseismic t ime window was 25 sec for P waves and 40 sec for S H waves. We repeated the inversion with P-wave windows of 20, 25, 30, 35, and 50 sec. Figure 15 shows the seismic moment determined in each inversion. For windows longer than 30 sec, the moment increases slightly, but the rms fit decreases due to unmodeled and nonsystematic waveform features. The conclusion is that no high-frequency radiation occurred after about 10 sec unless the mechanism was very different. The results of the time-dependent moment tensor inversion seems to rule out the lat ter possibility.

The concept of a long-period slip component is in part based on a heteroge- neous fault zone model (Kanamori, 1981) in which patches of the fault are too strong to fail except during a large earthquake. The material surrounding these patches is weaker and can slip either aseismic or seismically. Strong ground motion models for the Loma Prieta ear thquake suggest that slip is concentrated in two patches (e.g., Beroza, 1991; Hartzell et al., 1991; Wald et al., 1991). These two patches of high slip occurred on regions of the fault that had little or no aftershock activity. The slip in these patches was as large as 3.0 m. The percentage of the fault area that can be described as "high strength patches" is roughly 30%. The remainder of the fault had slip on the order of 0.5 to 1.5 m. Geodetic modeling by Lisowski et al. (1990) suggests that the average slip on the fault is approximately 2.8 m using the geodetically determined fault plane. The seismic moment is inferred to be 3.0 to 3.5 × 1019 N-m, consistent with the surface-wave analysis. This implies that the material surrounding the high strength patches may have slipped to a final value that is larger than that inferred from high-frequency body waves. One possible way to account for this slip is to assume that it had a much longer rise time that the slip on the high

S e i s m i c m o m e n t vs t i m e w i n d o w

0

Z

t O

0

.o

o

20 I

25 I I' I

30 3.5 40 T i m e w i n d o w for P w a v e i n v e r s i o n

i

45 I

5O

FIG. 15. Es t imates of total seismic momen t determined from inversion of teleseismic P waves us ing various source-time function window lengths. The preferred window length is 25 sec.

BROADBAND INVESTIGATION OF DEEP SLOW SLIP 1643

strength patches. Beck and Ruff (1985) have assumed this is the case for very large subduction zone events and have used an ad hoc procedure of adding a "smooth" component of long duration to the time function (moment release rate) to account for the missing seismic moment.

We tested the hypothesis that slow slip could account for the Loma Prieta ear thquake moment release by adding moment to the body-wave time function with a series of slowly varying time functions. Figure 16 summarizes this analysis. The very broadband instrumentat ion makes it nearly impossible to account for a significant increase in moment unless the process time is 30 sec or longer. It is possible to remove the moment discrepancy with these ad hoc t ime functions, and, because the moment release is small, it does not have much effect on the source duration derived from the surface-wave inversion. Such a slow-slip mechanism has not been observed in the laboratory, so it is difficult to assess whether it is real, or merely the result forcing a fit to other unmodeled signal energy.

The aftershock distribution from the Loma Prieta ear thquake suggests that the faulting was complex. Geodetic measurements (Plafker and Galloway, 1989; Lisowski et at., 1990), and strong motion studies (Beroza, 1991; Hartzell et al., 1991; Wald et al., 1991) indicate that most slip during the event was concentrated between 18 and 5 km depth. Aftershocks below 10 km define a plane dipping 65 ° to 70 °, which is consistent with the seismic focal mechanism (Dietz and Ellsworth, 1990). Above 10-kin depth, the aftershock distribution is diffuse, and no single plane is defined (Schwartz and Nelson, !991). This suggests that

ARL Synthetic

_f

max amp. (xlO 3) 1.49

Time Function 1.96

1.83

1.58 ~ ~ ~ ' ~ 1.49

/- , ,

o 20

FIG. 16. The effect of a "slow" component of slip on the synthetic P-wave broadband ground displacement for a representative teleseismic station, ARU.

1644 T. C. W A L L A C E E T A L .

deep slip occurred on a steeply dipping fault, while shallow slip occurred on numerous faults, perhaps parti t ioning motion between the San Andreas and the Sargent faults. The nature of the shallow slip during the Loma Prieta earthquake is extremely important for assessing the likelihood of future ear thquakes in the region. On the basis of our modeling, the slip history of the Loma Prieta event was fairly simple. If there was slip on faults that had different geometries than that indicated by the mainshock focal mechanism, the moment release must have been quite small. Based on the hypocentral depth of nearly 18 km and the centroid depth of 10 to 12 km, the slip was probably concentrated between 8 and 15 km depth. It is unknown why the slip did not continue to the surface, but it is possible that that intersection of the rupture with shallow faults terminated the rupture.

CONCLUSIONS

The Loma Prieta ear thquake has very well-determined average faulting orientation, consistent for different seismic wavetypes and among many different investigations. There is, however, some period dependence in the estimates of centroid depth, total rupture duration, and seismic moment. This study has explored both the stability of the focal mechanism parameters for periods ranging from 1 to 300 sec, and the model assumptions that may account for the apparent period dependence of the source properties. The source parameter estimates from the long-period surface waves are influenced by choice of propagation model, a t tenuat ion mode, and source velocity structure. The variation in results for a suite of reasonable models indicates that it is premature to place too much emphasis on the period-dependent discrepancies in the seismic models, but a full resolution of the inconsistencies is not yet in hand. The physically plausible interpretat ion that the discrepancies actually reflect an anomalous slow-slip component of the source process warrant further investigation, as this would have significance for our understanding of the faulting process and the transition to the ductile deformation regime below the britt le failure zone. Improved propagation and at tenuat ion models are required for this level of source analysis, and the importance of this source process problem provides strong motivations for the development of such second generation earth models.

ACKNOWLEDGMENTS

This research was supported by the U.S. Geological Survey (USGS), Depar tment of the Interior, under USGS award to UCSC 14-08-0001-G1843, and by the W. M. Keck Foundation. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily represent ing the official policies, e i ther expressed or implied, of the U.S. government. We wish to t h a n k David Wald and John Vidale for helpful discussions on the strong ground motion resul ts and 'Susan Schwartz for helpful discussions concerning the aftershocks and apparent faul t ing complexity. Reviews by Ralph Archel ta and Tom Hanks improved the manuscr ipt considerably. We also wish to t h a n k Michelle Wallace for her comments on the manuscript . Contr ibution number 123 of the Ins t i tu te of Tectonics and the C. F. Richter Seismological Laboratory.

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BROADBAND INVESTIGATION OF DEEP SLOW SLIP 1645

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DEPARTMENT OF GEOSCIENCES UNIVERSITY OF ARIZONA TUCSON, ARIZONA 85721

(T.C.W.)

RICHTER SEISMOLOGICAL LABORATORY AND ~NSTITUTE OF TECTONICS UNIVERSITY OF CALIFORNIA, SANTA CRUZ SANTA CRUZ, CALIFORNIA 95064

(A.V., J.Z., T.L.)

Manuscript received 15 March 1991

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