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Deep Fault Slip Kinematics from Characteristic Microearthquakes

R.M. Nadeau, D.C. Templeton, R. Burgmann, and T.V. McEvilly

Introduction

Analyses of the 14+ years of Parkfield monitoring data have revealed significant and unambiguous departures from stationarity both in the seismicity characteristics and in wave propagation details. Synchronous with these changes have been changes in the repeat times of characteristic microearthquakes sequences, $T_r$, which have been related to slip loading rate variations at depth and which have been used to provide a 4-D image of the evolution of slip rates along the 25 km segment of the San Andreas Fault (SAF) spanning the presumed nucleation region of the next Parkfield M6 earthquake (Nadeau and McEvilly, 1999).

Our ongoing research is showing that this technique is applicable to other faults in Central California, and its more widespread application is revealing unexpected attributes of the kinematics of deformation along these faults and on scales ranging from a few meters to 100's of km.

$T_r$, is also a particularly well constrained observable that can be theoretically related to a variety of physical processes linked to earthquakes, fault structure, and fault deformation (e.g. overall fault strength, stress drops, fault heterogeneity, fault deformation at depth, slip loading of locked segments, fault healing rates, 'in-situ' friction, and event-event triggering). However to provide accurate measurements of these processes in an absolute sense, accurate calibrations between $T_r$ and various constitutive properties within the fault core (e.g. composition, texture, temperature, stress, slip rate and fluid conditions) are needed. Currently such calibrations must be inferred from surface observations, laboratory experiments and seismic behavior. Ideally, however, they would come from 'in situ' measurement of the fault zone-an expensive proposition.

The National Science Foundation, through its EarthScope initiative (SAFOD component), has recently proposed careful scientific drilling into the seismogenic zone of the active San Andreas (SA) fault at Parkfield. Scientific drilling would sample fault zone properties directly and, as proposed, at the site of a repeating earthquake sequence. This effort promises to significantly enhance our understanding of the physics of of this portion of the SAF and to provide the calibration necessary for relating $T_r$ to the constitutive properties and processes responsible for earthquakes and fault deformation at Parkfield.

At the same time EarthScope, through its PBO and InSAR components, has proposed to increase the detail and extent of deformation measurements along a major plate boundary and throughout the country which should greatly improve estimates of fault slip from surface and space based observations. This information, together with the ongoing discovery of widely distributed repeating earthquake sequences in central CA make it feasible to extrapolate (infer) the physical conditions- relative to those found at Parkfield-on 100's of km of fault in central California and elsewhere.

Small repeating earthquakes continue to be discovered in other regions of the world and on other fault types (e.g. convergent boundaries off the coast of Japan (Matsuzawa et al., 2002) and on normal faults in Greece (Dimitrief and McCloskey, 2000). This suggests the possibility of inferring fault conditions elsewhere.

In the U.S., it is conceivable that a collateral benefit of the USARRAY component of EarthScope will be the discovery of a significant number of new repeating earthquake sequences in regions where low magnitude seismicity has not been studied in detail. This has the potential to greatly expand the geographic coverage where inferential methods based on $T_r$ can be applied.

The following subsections summarize the current state of repeating earthquake studies at Berkeley, and give examples of how such studies are already changing our understanding of the kinematics of fault deformation.

East Bay Faults

Method

The method of determining slip rates from earthquake recurrence has been developed in our research program using data from a borehole network along the active San Andreas fault zone at Parkfield, CA.

Studies at very high resolution of microearthquakes at Parkfield, CA since 1987 revealed a systematic organization in space and time, dominated by spatial clustering of nearly identical, regularly recurring microearthquakes ('characteristic events') on small (meters to 10s of meters) wide patches within the fault zone (Nadeau et al., 1994, 1995; Nadeau and McEvilly, 1997). At Parkfield, nearly half of the 5000+ events in the 1987-1998 catalog exhibit this trait. In general, recurrence intervals (0.5 to 3 yr.) scale with the magnitude of the repeating events for the magnitude range available ($M_{w}$ -0.7 to 3). Clusters of these characteristic events occur throughout the slipping fault surface. Scalar seismic moments were estimated for 268 micro-quakes contained in 53 repeating sequences and combined with equivalent estimates from 8 similar but larger event sequences from the Stone Canyon section of the fault and the main Parkfield M6 sequence. These estimates show that seismic moment is being released as a function of time in a very regular manner where repeating earthquakes occur and for a wide range of earthquake magnitude. Measurements of the moment release rate, combined with an assumed tectonic loading rate, lead to estimates of the seismic parameters source area, slip, and recurrence interval. Such parameters exhibit a systematic dependence upon source size over a range of $10^{10}$ in seismic moment, which can be described by simple scaling relationships (Nadeau and Johnson, 1998). What emerges from this analysis of moment release rates is a quantitative description of an earthquake process that is controlled by small strong asperities that occupy less than 1$\%$ of the fault area.

A 26-months period of greatly increased activity during the study interval (M4.2, 4.6, 4.7 and 5.0 events and their aftershocks) accompanied changes exceeding 50$\%$ in previously stable recurrence intervals. Langbein et al. (1999) report on evidence in deformation measurements for a slip rate increase in 1993 at Parkfield. Nadeau and McEvilly (1999) show that it is possible under reasonable assumptions to infer the spatial distribution of variations in slip-rate on the fault surface from the changes in recurrence intervals for the characteristic event sequences. The analysis requires an assumption of constant area for the characteristic repeating sources - one easily supported by the lack of any appreciable change in the seismic moments and waveforms (over the 100 Hz bandwidth) associated with the change in recurrence interval.

Northern Hayward Fault

Along the northern Hayward Fault (HF) using surface short period NCSN catalog data, a prototype study using the micro-quake based deep fault slip technique was compared to an inversion of surface and space based geodetic data for fault slip. The comparison showed a good match between the two data types and formalization of joint inversion of the two data sets is currently underway. Results of our prototype study on the northern HF were encouraging and have been published in Science (Burgmann et al., 2000). We have subsequently found sufficient repeating earthquake activity along the southern HF, Calaveras (CF) and Mission (MF) faults to determine deep fault slip rates on those faults as well.

A long enough time base of waveform data recorded on the deep borehole Hayward Fault Network (HFN) has also now become available which promises to allow practical application of the repeating quake method to repeating sequences of much lower magnitude and consequent greater temporal and spatial resolution.

Southern Hayward, Mission and Calaveras Faults

We have completed our initial and computationally intensive search for characteristic sequences on the southern HF, CF and MF faults, using surface NCSN data and find that seismicity there resembles the clustering found at Parkfield, but at a lower seismicity rate and density. Figure 16.1 shows locations of the NCSN earthquakes that we focused on during the reconnaissance stage of our search for repeaters. This stage of processing characterizes the waveform similarity of all the event pairs separated by 7.5 km or less. Even at reduced catalog completeness (M 1.3) of the NCSN in this area, we see large numbers of highly similar and repeating events (coherency $>$ 0.95) distributed widely on all three faults, indicating the presence of substantial repeating earthquake activity (Figure 16.1). Using NCSN surface data we estimate the fractions of identifiable repeaters to be about 10$\%$ 15$\%$ and 25$\%$, for the northern HF, southern HF, MF and CF segments respectively.

Figure 16.1: Point fault slip rate estimates at depth inferred from recurrence intervals of characteristic micro-earthquakes, superposed on the HypoDD-relocated seismicity along a 120-km-long stretch of the Hayward (HF), Mission (MF) and Calaveras (CF) faults. Locations of characteristically repeating sequences (CS) are shown as large filled (gray) circles. CS and are numerous, widespread and distributed in time and space along these mature actively creeping faults. Rates of slip inferred from the CS recurrence intervals in mm/yr are coded in gray scale as indicated. Black points show locations of non-CS seismicity. Each filled circle represents the average slip rate between time sequential pairs of characteristic events in a sequence. Variations in the rates of repetition are consistent with known variations in slip rate both along strike and through time as determined from surface and space based geodetic methods. For example, sequences NW of Morgan Hill (MH) typically show a steadily decreasing repeat rate with time since the 1984 MH magnitude 6. Left panel shows, in depth section, all slip rate pair estimates and background seismicity for the time period 1984-2002. Second panel shows the same data in map view. Panel three (second from right) shows data in map view for pairs occurring between 1984 to 1992.5, and far left map shows similar data for the period 1992.5 to 2002.2. A time variable slip rate is clear, particularly along the CF where slip rates are high following the 1984 Morgan Hill main shock and slow down significantly afterwards. Slip rate is lowest on the southern HF and MF trends. On these segments, below about 5-6 km, characteristically repeating sequences are absent while background seismicity can clearly be seen. This suggests that the boundary separating the repeating and non-repeating regions delineates the boundary between creeping and non-creeping (locked) fault behavior at depth on this fault system. The locked region of the system, as modeled by Burgmann et al., (2000) shows a reasonable good match to this CS delineated region.
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The lowest fractions are explainable in part by lower slip rates and higher magnitude thresholds, since under these conditions recurrence intervals may be longer than observation times. At Parkfield, where the slip rate is much higher and using NCSN data, the fraction of repeaters is about 48$\%$. In our prototype analysis on the northern HF, we showed that sufficient information was available to resolve spatially varying features of slip using surface NCSN data but that monitoring of short-term temporal variations was not practical with the limited resolution of the surface data on such a slowly moving fault. To the southeast, on the faster moving MF and CF, we are finding sufficient rates of quake repetition to allow us to use NCSN data for monitoring transients (Figure 16.1) as is currently being achieved on the faster slipping SAF to the West (Nadeau and McEvilly, 2002).

East-Bay Fault System

Using NCSN arrival times, we have relocated the seismicity along the HF-MF-CF system using the USGS relocation code HypoDD (Figure 16.1) and are evaluating the more highly resolved spatial and temporal seismicity patterns in relation to surface and spaced based deformation estimates, to the spatial and temporal distribution of repeating earthquake sequences and to the post-seismic period following the 1984 Morgan Hill earthquake. Our preliminary findings indicate that, as at Parkfield and on the creeping section of the SAF, the locations of repeating earthquake sequences are confined to the central portion of seismicity on large faults. However, repeating quakes are not ubiquitous on all faults.

For example our search for characteristic quakes in our study region failed to identify any repeating sequences on the CF fault north of its juncture with the MF trend between Fremont and San Jose (Figure 16.1). Furthermore, along the MF and southern HF, repeating sequences only appear in the shallow portion of the seismogenic zone and appear to delineate the proposed locked region of the Hayward fault which is presumably the generation zone of 1868 M7 type events (Figure 16.1). In addition, their rate of repetition (indicated by their low, very light gray, slip rates) are low relative to the slip rates on the northern HF and CF segments. Since repeating earthquake activity requires repeated loading from the adjacent slipping fault, we interpret the regions of seismically active but non-repeating seismicity to be non-creeping and locked and the low repeat rates of the shallow repeating sequences to be in response to the shielding effect of the deeper locked section of the southern HF and MF.

If this is the case, high resolution relocations of repeating earthquake activity may prove a valuable tool, generally, for delineating locked fault segment boundaries in more detail at depth. Also of note in this regard is the lack of repeating earthquake activity on two splays of transient earthquake activity emanating from the CF south of San Jose. High precision relocations show that these splays were active during the post-seismic period following the Morgan Hill (MH) earthquake of 1984, but in subsequent years these splays have become aseismic (Figure 16.1, map view, 84-92.5 and 92.5 to 2002). It is not yet clear if the lack of repeating sequences on these splays is due to a relatively minor amount of slip release on the faults after MH or to a fundamental instability in the strength properties of earthquake patches on these subsidiary faults.

In addition to the structural features manifest by the relocations and repeating earthquake analyses, temporal variations are also clearly evident. Shown in the right most panels of Figure 16.1 are map views of the repeating sequences, gray scale coded to their slip rate estimates. On the CF during the period 1984-1992.5 repeat rates (and inferred slip rates at depth) are very high in comparison to repeat rates for sequences from 1992.5 to 2002. In addition, repeating events on the southern HF during the 6 years following the Loma Prieta earthquake nearly ceased, which agrees well with diminished surface deformation rates observed on this fault segment (Lienkaemper et al., 1997; Burgmann et al., 1998).

Our ongoing efforts involve the determination of the the kinematics of slip through joint modeling of surface GPS, creep and space based data so that geologic questions regarding the details of slip in the complex of East Bay faults (particularly the Mission cross over region) can be investigated at much higher resolution Schmidt et al., (2002).

San Andreas, Calaveras Juncture

We have also applied similar relocation and repeating earthquake techniques further south in the CF and Quien Sabe fault near the bifurcation of the SAF where little surface or space based deformation data is available.

This juncture of the SAF and the southern CF is a highly complex area where subsurface seismicity does not always follow surface fault traces and where secondary sub-parallel faults, such as the Quien Sabe fault zone, may play an active role in accommodating local shear deformation. The goal of this investigation is to determine the slip rate distribution of these faults at the juncture using repeating earthquake defined subsurface slip rates and surface geodetic measurements.

Currently we are investigating how slip at depth is being partitioned in this complex juncture zone, by determining a lower bound on creep rates at depth using characteristically repeating earthquakes (CREs) and the empirical formula of Nadeau and McEvilly (1999). Essentially, the method treats each CRE sequence as a "creepmeter" at depth, and derives slip from the direct relationship between an event's size and repeat interval relative to those found at Parkfield, CA.

In this region, the seismic structure and repeat rates of the characteristic sequences indicate a very complicated and heterogeneous slip regime apparently reflecting the complex fault geometry at depth, rapid slip transients initiated by moderate earthquakes, and the presence of a significantly greater fraction of locked (i.e. non-creeping) fault behavior (Templeton et al., 2001).

We identified 58 CRE sequences (Figure 16.2). Using the double-difference relocation program HypoDD, we relocated the seismicity to see where in the fault zone the CREs were occurring. On the San Andreas and Calaveras faults, CRE sequences occur along the fault plane on horizontal linear streaks of seismicity. These streaks are more pronounced on the San Andreas than on the Calaveras fault. The smaller Quien Sabe fault zone is much more complex than the more mature San Andreas and Calaveras faults. On the northern end of the fault zone, there is only one CRE sequence which is found on one of three side stepping linear fault strands. On the southern part of the fault zone, fault structures become more complex with several fault strands branching off of the one linear fault strand which hosts most of the CRE sequences found on the Quien Sabe fault zone.

Figure 16.2: San Andreas, Calaveras Fault juncture zone. Location of CREs plotted as filled circles with gray shading scaled to estimated deep slip rates. Grey lines are surface expression of faults and squares indicate location of earthquakes greater than M4.0.
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Some CRE sequences seemed to be influenced by larger nearby earthquakes, especially those found on fault traces that are discontinuous at depth. For example, on the Quien Sabe fault zone, sequences tended to cluster within approximately 3 km of larger earthquakes. Their recurrence intervals tended to be aperiodic and appeared to be influenced by the timing of larger nearby events. On the San Andreas and Calaveras faults, however, both periodically and aperiodically CRE sequences were found within approximately 3 km of larger earthquakes. We believe that aperiodically CRE sequences are indicating changes in the local stress regime due to the redistribution of stress caused by larger nearby earthquakes. We also showed that CRE recurrence intervals on the Calaveras and Quien Sabe fault zone tended to be larger than those on the San Andreas fault. This is due to the fact that the San Andreas fault is slipping at a much greater rate than the Quien Sabe fault zone and hence would have a greater number of earthquakes over the same time interval.

Since only two or three events per CRE sequence were found on the Calaveras and Quien Sabe fault zone, we chose not to average the creep rates at individual sequence locations. Instead we calculated minimum creep rates. As we expected, creep on the Calaveras and Quien Sabe fault zone was lower, between 2.5-6.9 mm/yr, than that found on the San Andreas fault, between 3.2-18.0 mm/yr. We use these creep rates only as lower end members of creep along the fault trace. Interestingly, the smaller Quien Sabe fault zone seems to be creeping about the same amount as the more mature Calaveras fault in this location.

We plan to combine these subsurface creep rates with surface geodetic data to determine the subsurface creep rate distribution along the fault plane using a homogeneous, linear, elastic half-space model.

The SAF: Parkfield to Loma Prieta

As part of a more ambitious exploration of the extent to which characteristically repeating microearthquakes characterize active fault zones, we have applied the methodology developed at Parkfield (Nadeau and McEvilly, 1999) to examine deep slip rate along the San Andreas Fault from South of Parkfield to the Southern extent of rupture of the 1989 Loma Prieta (LP) earthquake from 1984 through 1999 using the NCSN event catalog.

Initial results are fascinating, revealing portions of the fault extending over many tens of kilometers that exhibit coherent pulsing in slip rate. In addition, the pulses appear closely related to the occurrence of the Loma Prieta earthquake in 1989 (Nadeau and McEvilly, 2002).

Relative quiescence on the northern end of the segment is observed prior to LP, after which slip rates increase markedly-the LP locked segment appears to have exerted control on the SAF slip rates at distances greater than 30 km from the termination of its rupture. Also of interest is the fact that LP occurred coincidentally with the initiation of an ongoing pulsing cycle some 40 to 80 km further to the South.

Following LP, the periodic pulsing observed to the South appears to extend northward and shows some correspondence to the occurrence of 3 slow silent quakes in the SJB area. The pulsing observed after LP also appears to be superposed on an exponential decay of slip rate corresponding to aftershock decay in the zone adjacent to and following the LP main event (upper right hand time history panel).

In the middle of the examined fault stretch, quasi-periodic pulsing of slip rates with amplitude variations exceeding 50-100 $\%$ are pronounced with the north central portion repeating with about 3 year periodicity and 1.7 year periodicity in the south central portion.

From 60 to about 20 km northwest of Parkfield, an apparent migration pulse is also observed. On this segment the SAF appears to act as a strain guide for the transference of the tectonic slip-load at a rate of about 25 km/yr. The migration pattern also appears to repeat itself as part of the more frequent (1.7 yr.) pulsing pattern.

To the South at Parkfield, pulsing is more difficult to define, although considerable slip rate change is observed, in accordance with observations of surface slip-rate change in that area (Langbein et al., 1999). Also noteworthy at Parkfield is a distinct reduction in slip rate beginning after 1995 and continuing through 1999 that perhaps indicates a transition to a phase of relative slip quiescence preparatory to occurrence of the anticipated M6-similar to the quiescence observed prior to LP in the North.

Acknowledgements

We appreciate support for this project by the USGS NEHRP through grant numbers 01HQGR0066 and 02HQGR00226.

References

Bryant, W.A., Faults in the southern Hollister area, San Benito counties, California, California Division of Mines and Geology Fault Evaluation Report 164, 1985.

Burgmann, R., E. Fielding and J. Sukhatme, Slip along the Hayward fault, California, estimated from space-based synthetic aperture radar interferometry, Geology, 26, 559-562, 1998.

Burgmann, R., D. Schmidt, R.M. Nadeau, M. d'Alessio, E. Fielding, D. Manaker, T.V. McEvilly, and M.H. Murray, Earthquake Potential along the Northern Hayward Fault, California, Science, 289, 1178-1182, 2000.

Dimitrief, A. and J. McCloskey, A search for Repeating Microearthquakes in Western Greece (abstract), EOS Trans. Am. Geophys. U. 81, F924, 2000.

Langbein, J., R. Gwyther, R. Hart, and M.T. Gladwin, Slip rate increase at Parkfield in 1993 detected by high-precision EDM and borehole tensor strainmeters, Geophys. Res. Lett., 26, 2529-2532, 1999.

Lienkaemper, J.J., J.S. Galehouse, and R.W. Simpson, Creep response of the Hayward fault to stress changes caused by the Loma Prieta earthquake, Science, 276, 2014-2016, 1997.

Matsuzawa, T., T. Igarashi and A. Hasegawa, Characteristic Small-earthquake sequence off Sanriku, northeastern Honshu, Japan, it Geophys. Res. Lett., in press, 2002.

Nadeau, R.M., M. Antolik, P. Johnson, W. Foxall, and T.V. McEvilly, Seismological studies at Parkfield III: microearthquake clusters in the study of fault-zone dynamics, Bull. Seism. Soc. Am. 84, 247-263, 1994.

Nadeau, R.M., W. Foxall, and T.V. McEvilly, Clustering and Periodic Recurrence of Microearthquakes on the San Andreas Fault at Parkfield, California, Science, 267, 503-507, 1995.

Nadeau, R.M. and T. V. McEvilly, Seismological Studies at Parkfield V: Characteristic microearthquake sequences as fault-zone drilling targets, Bull. Seism. Soc. Am., 87, 1463-1472, 1997.

Nadeau, R.M. and L.R. Johnson, Seismological Studies at Parkfield VI: Moment Release Rates and Estimates of Source Parameters for Small Repeating Earthquakes, Bull. Seism. Soc. Am., 88, 790-814, 1998.

Nadeau, R.M. and T.V. McEvilly , Fault slip rates at depth from recurrence intervals of repeating microearthquakes, Science, 285, 718-721, 1999.

Nadeau, R.M. and T.V. McEvilly, Periodic Pulsing of the Tectonic Plate Boundary in Central California, in prep., 2002.

Schmidt, D.A., R. Burgmann, R.M. Nadeau, and M. d'Alessio, Distribution of aseismic slip-rate on the Hayward fault inferred from seismic and geodetic data, J. Geophys. Res., in prep., 2002.

Templeton, D.C., R.M. Nadeau and R. Burgmann, Structure and Kinematics at the Juncture between the San Andreas and Southern Calaveras faults, Eos Trans. AGU, 82, F811, 2001.



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