Paul Spudich

SEA99: A Revised Ground-Motion Prediction Relation for Use in Extensional Tectonic Regimes

We present SEA99, a revised predictive relation for geometric mean horizontal peak ground acceleration and 5%-damped pseudovelocity response spec- trum, appropriate for estimating earthquake ground motions in extensional tectonic regimes, which we demonstrate to have lower ground motions than other tectonic regimes. SEA99 replaces SEA96, a relation originally derived by Spudich et al. (1996, 1997). The data set used to develop SEA99 is larger than that for SEA96, and minor errors in the SEA96 data set have been corrected. In addition, a one-step regression method described by Joyner and Boore (1993, 1994) was used rather than the two-step method of Joyner and Boore (1981). SEA99 has motions that are as much as 20% higher than those of SEA96 at short distances (5-30 km), and SEA99s motions are about 20% lower than SEA96 at longer periods (1.0-2.0 sec) and larger distance (40-100 km). SEA99 dispersions are significantly less than those of SEA96. SEA99 rock motions are on the average 20% lower than motions predicted by Boore et al. (1994) except for short distances at periods around 1.0 sec, where SEA99 motions exceed those predicted by Boore et al. (1994) by as much as 10%. Com- parison of ground motions from normal-faulting and strike-slip events in our data set indicates that normal-faulting horizontal ground motions are not significantly different from extensional regime strike-slip ground motions.

What Can Strong-Motion Data Tell Us about Slip-Weakening Fault-Friction Laws?

We consider the resolution of parameters, such as strength excess, r y r o , and slip-weakening distance, dc, related to fault-constitutive properties, that may be obtained from the analysis of strong-ground motions. We show that wave- form inversion of a synthetic strong-motion-data set from a hypothetical M 6.5 event resembling the 1979 Imperial Valley earthquake cannot uniquely resolve both strength excess and dc. Specifically, we use a new inversion method to find two rupture models, model A having dc 0.3 m and high-strength excess, and model B having dc 1 m and low-strength excess. Both models have uniform initial stress and the same moment-rate function and rupture time distribution, and they produce essentially indistinguishable ground-motion waveforms in the 0-1.6 Hz frequency band. These models are indistinguishable because there is a trade-off between strength excess and slip-weakening distance in controlling rupture velocity. However, fracture energy might be relatively stably estimated from waveform inversions. Our Models A and B had very similar fracture energies. If the stress drop is fixed by the slip distribution, the rupture velocity is controlled by fracture energy. We show that estimates of slip-weakening distance inferred from kinematic in- version models of earthquakes are likely to be biased high due to the effects of spatial and temporal-smoothing constraints applied in such inverse-problem formulations. Regions of high-strength excess are often used to slow or stop rupture in models of observed earthquakes, but our results indicate that regions of long d c and lower strength excess might alternatively explain the slowing of rupture. One way to con- strain dc would be to model ground-motion spectra at frequencies higher than those at which waveform modeling is possible. A second way to discriminate between regions of long dc and large-strength excess might be to assume that dc is long where there are no aftershocks.

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.

Rupture Propagation of the 2004 Parkfield, California, Earthquake from Observations at the upsar

Using a short-baseline seismic array (U.S. Geological Survey Parkfield Dense Seismograph Array [upsar]) about 12 km west of the rupture initiation of the 28 September 2004 M 6.0 Parkfield, California, earthquake, we have observed the movement of the rupture front of this earthquake on the San Andreas fault. The sources of high-frequency arrivals at upsar, which we use to identify the rupture front, are mapped onto the San Andreas fault using their apparent velocity and back azimuth. Measurements of apparent velocity and back azimuth are calibrated using aftershocks, which have a compact source and known location. Aftershock back azimuths show considerable lateral refraction, consistent with a high-velocity ridge on the southwest side of the fault. We infer that the initial mainshock rupture velocity was approximately the Rayleigh speed (with respect to slower side of the fault), and the rupture then slowed to about 0.66 β near the town of Parkfield after 2 sec. The last well-correlated pulse, 4 sec after S, is the largest at upsar, and its source is near the region of large accelerations recorded by strong-motion accelerographs and close to northern extent of continuous surface fractures on the southwest fracture zone. Coincidence of sources with preshock and aftershock distributions suggests fault material properties control rupture behavior. High-frequency sources approximately correlate with the edges of asperities identified as regions of high slip derived from inversion of strong-motion waveforms.

Inferring rate and state friction parameters from a rupture model of the 1995 Hyogo‐ken Nanbu (Kobe) Japan earthquake

We consider the applicability of laboratory-derived rate-and state-variable friction laws to the dynamic rupture of the 1995 Kobe earthquake. We analyze the shear stress and slip evolution of Ide and Takeos [1997] dislocation model, fitting the inferred stress change time histories by calculating the dynamic load and the instantaneous friction at a series of points within the rupture area. For points exhibiting a fast-weakening behavior, the Dieterich-Ruina friction law, with values of dc = 0.01–0.05 m for critical slip, fits the stress change time series well. This range of dc is 10–20 times smaller than the slip distance over which the stress is released, Dc, which previous studies have equated with the slip-weakening distance. The limited resolution and low-pass character of the strong motion inversion degrades the resolution of the frictional parameters and suggests that the actual dc is less than this value. Stress time series at points characterized by a slow-weakening behavior are well fitted by the Dieterich-Ruina friction law with values of dc≥0.01–0.05 m. The apparent fracture energy Gc can be estimated from waveform inversions more stably than the other friction parameters. We obtain a Gc ≈ 1.5×l06 J m−2 for the 1995 Kobe earthquake, in agreement with estimates for previous earthquakes. From this estimate and a plausible upper bound for the local rock strength we infer a lower bound for Dc of about 0.008 m.

Fault zone amplified waves as a possible seismic hazard along the Calaveras Fault in central California

The Calaveras fault lies within a low velocity zone (LVZ) 1-2 km wide near Gilroy, California. Accelerographs G06, located in the LVZ 1.2 km from the Calaveras fault, and G07, 4 km from G06, recorded both the M 6.2 1984 Morgan Hill and the M 6.9 1989 Loma Prieta earthquakes. Comparison of the ground motions shows that a large 0.6-1.0 Hz velocity pulse observed at G06 during the Morgan Hill event may be amplified by focussing caused by the LVZ. Such amplified waves might be a mappable seismic hazard, and the zone of increased hazard can extend as much as 1.2 km from the surface trace of the fault. Finite-difference simulations of ground motions in a simplified LVZ model show a zone of amplified motion similar to the observations.

Rupture characteristics of the three M ∼ 4.7 (1992–1994) Parkfield earthquakes

Slip on the San Andreas fault was determined for three M ∼ 4.7 earthquakes using a tomographic inverse system [Beroza and Spudich, 1988] to invert seismic source time functions (STFs) from S waves. STFs were obtained by deconvolving mainshock accelerograms by those from collocated smaller earthquakes. Accelerograms were from the U.S. Geological Survey Parkfield Small Aperture Array (UPSAR) and from a distributed array of digital accelerometer stations at Parkfield. Eight or nine STFs are used in each of the three inversions. STFs are typically symmetrical pulses with a duration of about 0.3-0.5 s. In the inversion, mainshock rise time was set to 0.05 s, and we allowed the rupture time to vary slightly from a constant rupture velocity of approximately 0.85β. Rupture for all three events, which are located in or close to the Middle Mountain preparation zone or box (MMB), quickly reaches a local maximum in slip and then propagates outward to peaks, ridges, or plateaus in the slip distribution. Slip for the October 20, 1992, event (located just inside the southern edge of the MMB) propagates from an initial spike north and updip along a curving ridge for about 2 km. The initial spike continued to grow in the November 14, 1993, event (located north of the October 20, 1992, event just beneath the hypocenter of the 1966 Parkfield earthquake), which shows little directivity, although there is a smaller patch of slip updip and to the south. In contrast, rupture for the December 20, 1994, event (located just south of the October 20, 1992, event) propagated north and slightly updip, creating a rough plateau in slip a few kilometers wide on a side. Directivity for this event also is to the north. Directivity for all three events points in the approximate direction of the 1966 hypocenter. Small pulses, which comprise a coda, are found on the STFs for several seconds after the initial impulsive event. Several tests based on the assumption that the average of all STFs from UPSAR for each event is an estimate of the true slip at the source suggest that the codas in the STFs are S waves from a long-duration source rather than uncorrected site response. An initiation phase is found on the array average for the November 14, 1993, and December 20, 1994, events. These precursory phases are the result of a spike in slip at the hypocenter. A value of 2.4-4 mm is obtained for D c , the slip-weakening distance, by interpreting the initial spike as a critical patch. The few aftershocks for the October 20, 1992, event are distributed to the north and updip of the mainshock, but the November 14, 1993, event had a strong burst of aftershock activity that propagated to the north of its hypocenter at roughly the same depth. Aftershocks of the December 20, 1994, event are mostly updip. The November 14, 1993, event had the simplest slip distribution, appeared to be the most impulsive, and had the most active aftershock sequence and the greatest depth. If the eventual Parkfield earthquake initiates near the 1966 hypocenter, then the directivity of the three events studied here will have pointed to it. However, it is certainly possible that both the initiation of characteristic Parkfield shocks and the directivity of smaller events are controlled by fault properties on a larger scale such as by fault bends or jogs.

Stability of coda Q in the region of Parkfield, California: View from the U.S. Geological Survey Parkfield Dense Seismograph Array

Many investigators have proposed that changes in the rate at which the coda decays may be an intermediate term precursor to moderate-to-large earthquakes. Parkfield, California, on the San Andreas Fault, is a promising location for studying premonitory changes in coda Q, Qc, because a large earthquake is likely to occur there. We have investigated Qc using recordings from the U.S. Geological Survey Parkfield Dense Seismograph Array, which is a digital array with 14 triaxial sensors and an aperture of about 1 km. For each earthquake we can measure Qc from up to 42 recordings. Their average is more stable than the measurement from a single station. Using clustered seismicity, we have developed criteria for selecting events and reducing scatter in the measurement. The Qc value determined from a seismogram depends on the position and length of the analysis window. Thus Qc should always be measured from the same length window starting at the same lapse time regardless of the source location. In addition, the band-limited signal-to-noise ratio at the end of the analysis window is important. Qc determined in two frequency bands, 4–8 Hz and 8–16 Hz, from a tight cluster of 26 events which occurred between December 1989 and January 1994 has not changed, despite M 4.7 and M 4.6 events in October 1992 and November 1993. Qc measured from local events (Δ < 60 km) in three frequency bands shows larger scatter but has also not changed during this period. For monitoring Qc, observations should include array averaged measurements from a single lapse time. Because Qc measurements made using an analysis window that starts at a constant multiple of the S wave lapse time depend on epicentral distance, a procedure combining the evaluation of the time and distance dependences of Qc also gives stable observations.

Erratum to Observation and Prediction of Dynamic Ground Strains, Tilts, and Torsions Caused by the Mw 6.0 2004 Parkfield, California, Earthquake and Aftershocks, Derived from UPSAR Array Observations

Online Material: Corrected figures and strain, rotation, and displacement gradient time series.

The Effect of Bandwidth Limitations on the Inference of Earthquake Slip-Weakening Distance from Seismograms

Numerous researchers have obtained estimates of slip-weakening distance, Dc , and fracture energy for recent earthquakes. Dc is often observed to be a significant fraction of the total slip and tends to correlate with total slip. Although these observations may well be true of real earthquakes, we show that low-pass filtering of strong-motion seismograms can also produce some of these effects in inverted rupture models. We test the accuracy of Dc estimates by calculating them in low-pass-filtered versions of models A and B of Guatteri and Spudich (2000). Models A and B are two different rupture models for a hypothetical M 6.5 earthquake, and they have nearly identical rupture time, slip, and stress-drop distributions, and nearly identical predicted seismograms, but Dc for model B is about twice that for model A. By low-pass filtering slip models A and B at 1.0 Hz, we simulate the blurring effects of band-limited waveform inversions on these slip models. At each point on a fault, ![Graphic][1] is defined to be the slip at the time of the peak slip speed at that point. Low-pass filtering the slip models causes an upward bias in Dc inferred from stress-slip curves, and it causes an artificial correlation between ![Graphic][2] and the total slip. Low-pass filtering might also bias fracture energy high and radiated energy low. These biases should be considered when interpreting Dc derived from band-limited slip models of real earthquakes. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif