Joe B. Fletcher

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.

Mapping Apparent Stress and Energy Radiation over Fault Zones of Major Earthquakes

Using published slip models for five major earthquakes, 1979 Imperial Valley, 1989 Loma Prieta, 1992 Landers, 1994 Northridge, and 1995 Kobe, we produce maps of apparent stress and radiated seismic energy over their fault surfaces. The slip models, obtained by inverting seismic and geodetic data, entail the division of the fault surfaces into many subfaults for which the time histories of seismic slip are determined. To estimate the seismic energy radiated by each subfault, we measure the near-fault seismic-energy flux from the time-dependent slip there and then multiply by a function of rupture velocity to obtain the corresponding energy that propagates into the far-field. This function, the ratio of far-field to near-fault energy, is typically less than 1/3, inasmuch as most of the near-fault energy remains near the fault and is associated with permanent earthquake deformation. Adding the energy contributions from all of the subfaults yields an estimate of the total seismic energy, which can be compared with independent energy estimates based on seismic-energy flux measured in the far-field, often at teleseismic distances. Estimates of seismic energy based on slip models are robust, in that different models, for a given earthquake, yield energy estimates that are in close agreement. Moreover, the slip-model estimates of energy are generally in good accord with independent estimates by others, based on regional or teleseismic data. Apparent stress is estimated for each subfault by dividing the corresponding seismic moment into the radiated energy. Distributions of apparent stress over an earthquake fault zone show considerable heterogeneity, with peak values that are typically about double the whole-earthquake values (based on the ratio of seismic energy to seismic moment). The range of apparent stresses estimated for subfaults of the events studied here is similar to the range of apparent stresses for earthquakes in continental settings, with peak values of about 8 MPa in each case. For earthquakes in compressional tectonic settings, peak apparent stresses at a given depth are substantially greater than corresponding peak values from events in extensional settings; this suggests that crustal strength, inferred from laboratory measurements, may be a limiting factor. Lower bounds on shear stresses inferred from the apparent stress distribution of the 1995 Kobe earthquake are consistent with tectonic-stress estimates reported by Spudich et al. (1998), based partly on slip-vector rake changes. Manuscript received 21 February 2001.

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.

Maximum Slip in Earthquake Fault Zones, Apparent Stress, and Stick-Slip Friction

The maximum slip, observed or inferred, for a small patch within the larger fault zone of an earthquake is a remarkably well-constrained function of the seismic moment. A large set of maximum slips, mostly derived from slip models of major earthquakes, indicate that this parameter increases according to the cube root of the seismic moment. Consistent with this finding, neither the average slip rate for the patches of maximum slip nor the apparent stresses of earthquakes show any systematic dependence on seismic moment. Maximum average slip rates are several meters per second independent of moment and, for earthquakes in continental crustal settings, the apparent stress is limited to about 10 MPa. Results from stick-slip friction experiments in the laboratory, combined with information about the state of stress in the crust, can be used to predict, quite closely, the maximum slips and maximum average slip rates within the fault zones of major earthquakes as well as their apparent stresses. These findings suggest that stick-slip friction events observed in the laboratory and earthquakes in continental settings, even with large magnitudes, have similar rupture mechanisms. Manuscript received 24 February 2003.

Moment Tensor Inversion of Ground Motion from Mining-Induced Earthquakes, Trail Mountain, Utah

A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop ground-motion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes M c. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 × 105 to 2.4 × 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

Near-Fault Peak Ground Velocity from Earthquake and Laboratory Data

We test the hypothesis that peak ground velocity (pgv) has an upper bound independent of earthquake magnitude and that this bound is controlled primarily by the strength of the seismogenic crust. The highest pgvs, ranging up to several meters per second, have been measured at sites within a few kilometers of the causative faults. Because the database for near-fault pgv is small, we use earthquake slip models, laboratory experiments, and evidence from a mining-induced earthquake to investigate the factors influencing near-fault pgv and the nature of its scaling. For each earthquake slip model we have calculated the peak slip rates for all subfaults and then chosen the maximum of these rates as an estimate of twice the largest near-fault pgv. Nine slip models for eight earthquakes, with magnitudes ranging from 6.5 to 7.6, yielded maximum peak slip rates ranging from 2.3 to 12 m/ sec with a median of 5.9 m/sec. By making several adjustments, pgvs for small earthquakes can be simulated from peak slip rates measured during laboratory stick- slip experiments. First, we adjust the pgv for differences in the state of stress (i.e., the difference between the laboratory loading stresses and those appropriate for faults at seismogenic depths). To do this, we multiply both the slip and the peak slip rate by the ratio of the effective normal stresses acting on fault planes measured at 6.8 km depth at the KTB site, Germany (deepest available in situ stress measurements), to those acting on the laboratory faults. We also adjust the seismic moment by replacing the laboratory fault with a buried circular shear crack whose radius is chosen to match the experimental unloading stiffness. An additional, less important adjustment is needed for experiments run in triaxial loading conditions. With these adjustments, peak slip rates for 10 stick-slip events, with scaled moment magnitudes from −2.9 to 1.0, range from 3.3 to 10.3 m/sec, with a median of 5.4 m/sec. Both the earthquake and laboratory results are consistent with typical maximum peak slip rates averaging between 5 and 6 m/sec or corresponding maximum near-fault pgvs between 2.5 and 3 m/sec at seismogenic depths, independent of magnitude. Our ability to replicate maximum slip rates in the fault zones of earthquakes by adjusting the corresponding laboratory rates using the ratio of effective normal stresses acting on the fault planes suggests that the strength of the seismogenic crust is the important factor limiting the near-fault pgv.

Development of Ground-Motion Prediction Equations Relevant to Shallow Mining–Induced Seismicity in the Trail Mountain Area, Emery County, Utah

To provide a basis for assessing the seismic hazard to the Joes Valley Dam due to future coal mining in the nearby Cottonwood Tract, central Utah, we developed ground-motion prediction relations using data recorded by a seismic network, established and operated by the University of Utah Seismograph Stations. The network was centered on the Trail Mountain coal mine, located adjacent to the Cottonwood Tract. From late 2000 until early 2001, this network recorded numerous mining-induced events with magnitudes as large as 2.17. The ground motion from these events, recorded at hypocentral distances ranging from about 500 m to approximately 10 km, were well suited to developing new ground-motion prediction relations, especially when augmented by data from a M 4.2 earthquake in the Willow Creek mine, about 50 km north of Trail Mountain. Using a two-stage regression analysis, we determined prediction relations for peak acceleration, peak velocity, and pseudovelocity response spectra, at 5% damping, for periods of 0.1, 0.2, 0.5, 1.0, and 2.0 s. To illustrate the potential seismic hazard at the Joes Valley dam, we used these ground-motion relations to predict a peak velocity of 6.8 cm/s due to an earthquake with the probable maximum magnitude of 3.9, at a hypocentral distance of 1 km, recorded at a rock site typical for this region. This result does not take into account the site response at the dam.

Laboratory-based maximum slip rates in earthquake rupture zones and radiated energy

Laboratory stick-slip friction experiments indicate that peak slip rates increase with the stresses loading the fault to cause rupture. If this applies also to earthquake fault zones, then the analysis of rupture processes is simplified inasmuch as the slip rates depend only on the local yield stress and are independent of factors specific to a particular event, including the distribution of slip in space and time. We test this hypothesis by first using it to develop an expression for radiated energy that depends primarily on the seismic moment and the maximum slip rate. From laboratory results, the maximum slip rate for any crustal earthquake, as well as various stress parameters including the yield stress, can be determined based on its seismic moment and the maximum slip within its rupture zone. After finding that our new equation for radiated energy works well for laboratory stick-slip friction experiments, we used it to estimate radiated energies for five earthquakes with magnitudes near 2 that were induced in a deep gold mine, an M 2.1 repeating earthquake near the San Andreas Fault Observatory at Depth (SAFOD) site and seven major earthquakes in California and found good agreement with energies estimated independently from spectra of local and regional ground-motion data. Estimates of yield stress for the earthquakes in our study range from 12 MPa to 122 MPa with a median of 64 MPa. The lowest value was estimated for the 2004 M 6 Parkfield, California, earthquake whereas the nearby M 2.1 repeating earthquake, as recorded in the SAFOD pilot hole, showed a more typical yield stress of 64 MPa.