John Boatwright

Frictional constraints on crustal faulting

We consider how variations in fault frictional properties affect the phenomenology of earthquake faulting. In particular, we propose that lateral variations in fault friction produce the marked heterogeneity of slip observed in large earthquakes. We model these variations using a rate- and state-dependent friction law, where we differentiate velocity-weakening behavior into two fields: the strong seismic field is very velocity weakening and the weak seismic field is slightly velocity weakening. Similarly, we differentiate velocity-strengthening behavior into two fields: the compliant field is slightly velocity strengthening and the viscous field is very velocity strengthening. The strong seismic field comprises the seismic slip concentrations, or asperities. The two “intermediate” fields, weak seismic and compliant, have frictional velocity dependences that are close to velocity neutral: these fields modulate both the tectonic loading and the dynamic rupture process. During the interseismic period, the weak seismic and compliant regions slip aseismically, while the strong seismic regions remain locked, evolving into stress concentrations that fail only in main shocks. The weak seismic areas exhibit most of the interseismic activity and aftershocks but can also creep seismically. This “mixed” frictional behavior can be obtained from a sufficiently heterogeneous distribution of the critical slip distance. The model also provides a mechanism for rupture arrest: dynamic rupture fronts decelerate as they penetrate into unloaded complaint or weak seismic areas, producing broad areas of accelerated afterslip. Aftershocks occur on both the weak seismic and compliant areas around a fault, but most of the stress is diffused through aseismic slip. Rapid afterslip on these peripheral areas can also produce aftershocks within the main shock rupture area by reloading weak fault areas that slipped in the main shock and then healed. We test this frictional model by comparing the seismicity and the coseismic slip for the 1966 Parkfield, 1979 Coyote Lake, and 1984 Morgan Hill earthquakes. The interevent seismicity and aftershocks appear to occur on fault areas outside the regions of significant slip: these regions are interpreted as either weak seismic or compliant, depending on whether or not they manifest interevent seismicity.

Hypocenter Locations in Finite-Source Rupture Models

We use a database of more than 80 finite-source rupture models for more than 50 earthquakes ( M w 4.1–8.1) with different faulting styles occurring in both tectonic and subduction environments to analyze the location of the hypocenter within the fault and to consider the correlation between hypocenter location and regions of large slip. Rupture in strike-slip and crustal dip-slip earthquakes tends to nucleate in the deeper sections of the fault; subduction earthquakes do not show this tendency. Ratios of the hypocentral slip to either the average or the maximum slip show that rupture can nucleate at locations with any level of relative displacement. Rupture nucleates in regions of very large slip ( D ≥ 2/3 D max ) in only 16% of the events, in regions of large slip (1/3 D max D D max ) in 35% of the events, and in regions of low slip ( D ≤ 1/3 D max ) in 48% of the events. These percentages significantly exceed the percentages of fault area with very large (∼7%) and large (∼28%) slip. Ruptures that nucleate in regions of low slip, however, tend to nucleate close to regions of large slip and encounter a zone of very large slip within half the total rupture length. Applying several statistical tests we conclude that hypocenters are not randomly located on a fault but are located either within or close to regions of large slip.

The Persistence of Directivity in Small Earthquakes

Abstract We derive a simple inversion of peak ground acceleration (PGA) or peak ground velocity (PGV) for rupture direction and rupture velocity and then test this inversion on the peak motions obtained from seven 3.5≤ M ≤4.1 earthquakes that occurred in two clusters in November 2002 and February 2003 near San Ramon, California. These clusters were located on two orthogonal strike-slip faults so that the events share the same approximate focal mechanism but not the same fault plane. Three earthquakes exhibit strong directivity, but the other four earthquakes exhibit relatively weak directivity. We use the residual PGAs and PGVs from the other six events to determine station corrections for each earthquake. The inferred rupture directions unambiguously identify the fault plane for the three earthquakes with strong directivity and for three of the four earthquakes with weak directivity. The events with strong directivity have fast rupture velocities (0.63 β ≤ v ≤0.87 β ); the events with weak directivity either rupture more slowly (0.17 β ≤ v ≤0.35 β ) or bilaterally. The simple unilateral inversion cannot distinguish between slow and bilateral ruptures: adding a bilateral rupture component degrades the fit of the rupture directions to the fault planes. By comparing PGAs from the events with strong and weak directivity, we show how an up-dip rupture in small events can distort the attenuation of peak ground motion with distance. When we compare the rupture directions of the earthquakes to the location of aftershocks in the two clusters, we find than almost all the aftershocks of the three earthquakes with strong directivity occur within 70° of the direction of rupture.

Regional Estimates of Radiated Seismic Energy

We revise the spectral technique for estimating radiated energy from recordings of large earthquakes at regional distances (Δ 27.5 km from the source, we model the geometrical spreading of the regional wavefield as r – γ where γ = 0.5 for f ≤ 0.2 Hz and γ = 0.7 for f ≥ 0.25 Hz. We fit the spectral falloff with distance using a frequency-dependent attenuation Q = 400( f /1.5)0.6, where Q = 400 for f ≤ 1.5 Hz. There is little directivity apparent in the corrected velocity spectra: the velocity spectra observed to the northwest along strike are amplified by a factor of 2.5 from 0.3 to 1.0 Hz and those to the southeast are amplified by a factor of 1.6 from 0.3 to 0.7 Hz. We group the stations in NEHRP site classes, using average 1-D velocity structures to estimate site amplification as a function of frequency and assuming 0.40 ≤ κ ≤ 0.55 sec for the near-surface attenuation. We increase the amplification of the soft-soil sites from 0.1 to 1.0 Hz by a factor that reaches 1.7 at 0.3 Hz because they are more strongly amplified than the NEHRP-D velocity structure predicts. We combine the 65 single-station estimates of radiated energy using an equal-azimuth weighting scheme that compensates for station distribution and incorporates the observed directivity, yielding a regional estimate of E s = 3.4 ± 0.7 × 1022 dyne cm. This regional estimate of radiated energy corresponds closely to the teleseismic estimate of E s = 3.2 × 1022 dyne cm.

Correlation of Ground Motion and Intensity for the 17 January 1994 Northridge, California, Earthquake

We analyze the correlations between intensity and a set of ground-motion parameters obtained from 66 free-field stations in Los Angeles County that recorded the 1994 Northridge earthquake. We use the tagging intensities from Thywissen and Boatwright (1998) because these intensities are determined independently on census tracts, rather than interpolated from zip codes, as are the modified Mercalli isoseismals from Dewey et al. (1995). The ground-motion parameters we consider are the peak ground acceleration (PGA), the peak ground velocity (PGV), the 5%-damped pseudovelocity response spectral (PSV) ordinates at 14 periods from 0.1 to 7.5 sec, and the rms average of these spectral ordinates from 0.3 to 3 sec. Visual comparisons of the distribution of tagging intensity with contours of PGA, PGV, and the average PSV suggest that PGV and the average PSV are better correlated with the intensity than PGA. The correlation coefficients between the intensity and the ground-motion parameters bear this out: r = 0.75 for PGA, 0.85 for PGV, and 0.85 for the average PSV. Correlations between the intensity and the PSV ordinates, as a function of period, are strongest at 1.5 sec ( r = 0.83) and weakest at 0.2 sec ( r = 0.66). Regressing the intensity on the logarithms of these ground-motion parameters yields relations I ∝ m logθ with 3.0 ≤ m ≤ 5.2 for the parameters analyzed, where m = 4.4 ± 0.7 for PGA, 3.4 ± 0.4 for PGV, and 3.6 ± 0.5 for the average PSV. Manuscript received 15 April 1999.

An Overview of the Global Variability in Radiated Energy and Apparent Stress

A global study of radiated seismic energies E R and apparent stresses T a reveals systematic patterns. Earthquakes with the highest apparent stress occur in regions of intense deformation and rupture strong lithosphere. In oceanic settings, these are strike-slip earthquakes (T a up to 27 MPa) occurring intraplate or at evolving ends of transform faults. At subduction zones and intracontinental settings, these are strike-slip earthquakes with T a up to 7 MPa. Normal-fault earthquakes exhibit a more complex pattern. Higher T a s (up to 5 MPa) are found for intraslab events at depths from 35 to 70 km that occur near zones of intense deformation such as a sharp slab bend or the juncture of colliding slabs. Lower T a s (< 1 MPa) are found for normal-fault earthquakes at the outer rise and outer trench wall or deep in flat warm slabs. The lowest average τ a (0.3 MPa) is found for thrust-fault earthquakes at subduction zones. The variation of average apparent stress with tectonics suggests a relationship with lithospheric strength and fault maturity. Mature faults, such as plate boundaries that have experienced large cumulative slip, appear to have low strength and tend to yield earthquakes with low apparent stresses. Immature faults, in contrast, are stronger and yield high apparent stresses because either they are the result of fresh-rock fracture or at least their cumulative fault slip is quite small. These results have implications of use to the seismic engineering community because E R and its magnitude counterpart M e are reliable indicators of the potential for damaging ground motion.

The Dependence of PGA and PGV on Distance and Magnitude Inferred from Northern California ShakeMap Data

We analyze peak ground velocity (PGV) and peak ground acceleration (PGA) data from 95 moderate (3.5 ≤ M r > 100 km, the peak motions attenuate more rapidly than a simple power law (that is, r -γ ) can fit. Instead, we use an attenuation function that combines a fixed power law ( r -0.7 ) with a fitted exponential dependence on distance, which is estimated as exp(-0.0063 r ) and exp(-0.0073 r ) for PGV and PGA, respectively, for moderate earthquakes. We regress log(PGV) and log(PGA) as functions of distance and magnitude. We assume that the scaling of log(PGV) and log(PGA) with magnitude can differ for moderate and large earthquakes, but must be continuous. Because the frequencies that carry PGV and PGA can vary with earthquake size for large earthquakes, the regression for large earthquakes incorporates a magnitude dependence in the exponential attenuation function. We fix the scaling break between moderate and large earthquakes at M 5.5; log(PGV) and log(PGA) scale as 1.06M and 1.00M, respectively, for moderate earthquakes and 0.58M and 0.31M for large earthquakes.

Triggered Surface Slips in the Salton Trough Associated with the 1999 Hector Mine, California, Earthquake

Surface fracturing occurred along the southern San Andreas, Superstition Hills, and Imperial faults in association with the 16 October 1999 (Mw 7.1) Hector Mine earthquake, making this at least the eighth time in the past 31 years that a regional earthquake has triggered slip along faults in the Salton Trough. Fractures associated with the event formed discontinuous breaks over a 39-km-long stretch of the San Andreas fault, from the Mecca Hills southeastward to Salt Creek and Durmid Hill, a distance from the epicenter of 107 to 139 km. Sense of slip was right lateral; only locally was there a minor (∼1 mm) vertical component of slip. Dextral slip ranged from 1 to 13 mm. Maximum slip values in 1999 and earlier triggered slips are most common in the central Mecca Hills. Field evidence indicates a transient opening as the Hector Mine seismic waves passed the southern San Andreas fault. Comparison of nearby strong-motion records indicates several periods of relative opening with passage of the Hector Mine seismic wave—a similar process may have contributed to the field evidence of a transient opening. Slip on the Superstition Hills fault extended at least 9 km, at a distance from the Hector Mine epicenter of about 188 to 196 km. This length of slip is a minimum value, because we saw fresh surface breakage extending farther northwest than our measurement sites. Sense of slip was right lateral; locally there was a minor (∼1 mm) vertical component of slip. Dextral slip ranged from 1 to 18 mm, with the largest amounts found distributed (or skewed) away from the Hector Mine earthquake source. Slip triggered on the Superstition Hills fault commonly is skewed away from the earthquake source, most notably in 1968, 1979, and 1999. Surface slip on the Imperial fault and within the Imperial Valley extended about 22 km, representing a distance from the Hector Mine epicenter of about 204 to 226 km. Sense of slip dominantly was right lateral; the right-lateral component of slip ranged from 1 to 19 mm. Locally there was a minor (∼1–2 mm) vertical component of slip; larger proportions of vertical slip (up to 10 mm) occurred in Mesquite basin, where scarps indicate long-term oblique-slip motion for this part of the Imperial fault. Slip triggered on the Imperial fault appears randomly distributed relative to location along the fault and source direction. Multiple surface slips, both primary and triggered slip, indicate that slip repeatedly is small at locations of structural complexity.

The Energy Radiated by the 26 December 2004 Sumatra–Andaman Earthquake Estimated from 10-Minute P-Wave Windows

The rupture process of the M W 9.1 Sumatra–Andaman earthquake lasted for approximately 500 sec, nearly twice as long as the teleseismic time windows between the P and PP arrival times generally used to compute radiated energy. In order to measure the P waves radiated by the entire earthquake, we analyze records that extend from the P -wave to the S -wave arrival times from stations at distances Δ >60°. These 8- to 10-min windows contain the PP, PPP , and ScP arrivals, along with other multiply reflected phases. To gauge the effect of including these additional phases, we form the spectral ratio of the source spectrum estimated from extended windows (between TP and TS ) to the source spectrum estimated from normal windows (between TP and TPP ). The extended windows are analyzed as though they contained only the P-pP-sP wave group. We analyze four smaller earthquakes that occurred in the vicinity of the M W 9.1 mainshock, with similar depths and focal mechanisms. These smaller events range in magnitude from an M W 6.0 aftershock of 9 January 2005 to the M W 8.6 Nias earthquake that occurred to the south of the Sumatra– Andaman earthquake on 28 March 2005. We average the spectral ratios for these four events to obtain a frequency-dependent operator for the extended windows. We then correct the source spectrum estimated from the extended records of the 26 December 2004 mainshock to obtain a complete or corrected source spectrum for the entire rupture process (∼600 sec) of the great Sumatra–Andaman earthquake. Our estimate of the total seismic energy radiated by this earthquake is 1.4 × 1017 J. When we compare the corrected source spectrum for the entire earthquake to the source spectrum from the first ∼250 sec of the rupture process (obtained from normal teleseismic windows), we find that the mainshock radiated much more seismic energy in the first half of the rupture process than in the second half, especially over the period range from 3 sec to 40 sec.

Wave Propagation and Site Response in the Santa Clara Valley

Forty-two portable digital instruments were deployed across the Santa Clara Valley from June until early November 1998; this array recorded 14 small and moderate local events and 7 large teleseismic events. We analyze the ground motion from these events to determine station delays and relative site amplification within the Valley. P waves from an event at the southern edge of the valley are early (Δ t > -0.35 sec) at stations over an axial ridge in the basement interface in the middle of the valley, but late (Δ t < 0.20 sec) for stations over the Cupertino and Evergreen basins to either side. The S -wave delays are approximately twice as large. Teleseismic P -waves from an M = 7.0 event beneath the Bonin Islands show a similar pattern in travel-time delays. The P waves are amplified by factors of 1.5-3 for frequencies below 2 Hz at stations within either basin, compared with stations on the axial ridge. The P -wave coda appear enhanced at 2-3 sec, but coda Q estimates at frequencies from 0.2 to 1.1 Hz are not markedly different at stations over the basin compared with stations on the ridge with the possible exceptions of consistently high values over the northern end of the Evergreen Basin. We invert the S -wave spectra for site-specific attenuation and amplification from the 14 local events by assuming a common source spectra for each event, 1/ r geometrical spreading, and constraining the inversion using the 30-m velocity profile at four stations in the array. The largest amplifications occurred in the 1- to 6-Hz band at stations near the northwest edge of the Evergreen basin. While the highest amplifications occur at stations with the lowest S -wave velocities, the scatter obscures the correlation between velocity and amplification. The stations in the basins are characterized by higher attenuation than the stations on the basement ridge. Manuscript received 2 July 2001.