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A glossary for rotational seismology

Some common terms for rotational seismology are compiled from contributions by many authors, including R. DeSalvo, J. R. Evans, E. F. Grekova, C. R. Hutt, H. Igel, C. A. Langston, B. Lantz, E. Majewski, R. Nigbor, J. Pujol, P. Spudich, R. Teisseyre, M. D. Trifunac, R. J. Twiss, and Z. Zembaty. In addition, some glossary terms about earthquakes are excerpted from Aki and Lee (2003), Lee and Wu (2009), and others for the benefit of readers who are not seismologists. It is a first attempt to compile a glossary for rotational seismology (including some terms for continuum mechanics), and it is by no means complete. Several iterations will be required to reach a satisfactory glossary, and this compilation is just a start.

Bulletin of the Seismological Society of America↗

Suggested readings in continuum mechanics and earthquake seismology

Rotational seismology is a newly emerging field of interest to scientists from widely differing disciplines. We compile here some suggested readings for those wishing to become familiar with disciplines relevant to rotational seismology and its engineering applications. These readings are not exhaustive but contain a number of basic references with occasional annotations. We concentrate on two areas: continuum mechanics and earthquake seismology. Continuum mechanics is the branch of mechanics that deals with the deformation and motion of materials, including various elasticity theories. Although classical elasticity works well for studying earthquakes in the far field, there are alternate elasticity theories that may be more appropriate for studying earthquakes in the near field. The readings in continuum mechanics are intended for seismologists and include (1) fundamental textbooks, (2) intermediate to advanced books, (3) heteromodular theories, and (4) Cosserat theory. A brief introduction to continuum mechanics for seismologists is included as an appendix. In addition, because we wish to attract workers in other disciplines to rotational seismology, we include a short list of suggested readings in earthquake seismology.

Bulletin of the Seismological Society of America↗

Introduction to the special issue on rotational seismology and engineering applications

Because of a lack of suitable instruments, rotational ground motions have not been observed until the last decade. Rotational measurements in the near field of earthquakes in Japan ( Takeo, 1998 ) indicate that rotational ground motions are many times larger than expected from the classical elasticity theory. After failing to obtain useful rotational ground motions (using similar rotational sensors as Takeo did), we deployed a far more sensitive rotational velocity sensor (R-1) at the HGSD station in eastern Taiwan. From 7 December 2004 to 12 November 2006, several hundreds of earthquakes were recorded during our Phase 1 operation. This was mostly a learning exercise to solve field operation problems; Phase 1 operations ended when our two R-1 sensors ceased to operate. A K2+R1 instrument was deployed in the spring of 2007 to start our Phase 2 operation. From 8 May 2007 to 17 February 2008, we observed 52 local earthquakes with good rotational velocity signals (with signal-to-noise ratio >∼5), together with excellent translational acceleration signals (with signal-to-noise ratio >∼10). Unfortunately, field operation was interrupted due to flooding of the HGSD station site in mid-February 2008; we just resumed normal operation in June 2008.

Bulletin of the Seismological Society of America↗

The puzzle of the 1996 Bárdarbunga, Iceland, earthquake: no volumetric component in the source mechanism

A volcanic earthquake with M w 5.6 occurred beneath the Bárdarbunga caldera in Iceland on 29 September 1996. This earthquake is one of a decade-long sequence of events at Bárdarbunga with non-double-couple mechanisms in the Global Centroid Moment Tensor catalog. Fortunately, it was recorded well by the regional-scale Iceland Hotspot Project seismic experiment. We investigated the event with a complete moment tensor inversion method using regional long-period seismic waveforms and a composite structural model. The moment tensor inversion using data from stations of the Iceland Hotspot Project yields a non-double-couple solution with a 67% vertically oriented compensated linear vector dipole component, a 32% double-couple component, and a statistically insignificant (2%) volumetric (isotropic) contraction. This indicates the absence of a net volumetric component, which is puzzling in the case of a large volcanic earthquake that apparently is not explained by shear slip on a planar fault. A possible volcanic mechanism that can produce an earthquake without a volumetric component involves two offset sources with similar but opposite volume changes. We show that although such a model cannot be ruled out, the circumstances under which it could happen are rare.

Bardarbunga↗

Geodetically inferred coseismic and postseismic slip due to the M 5.4 31 October 2007 Alum Rock earthquake

On 31 October 2007 the M 5.4 Alum Rock earthquake occurred near the junction between the Hayward and Calaveras faults in the San Francisco Bay Area, producing coseismic and postseismic displacements recorded by 10 continuously operating Global Positioning System (GPS) instruments. The cumulative postseismic displacements over the four months following the earthquake are linearly related to the cumulative number of aftershocks and are comparable in magnitude to the coseis mic displacements. The postseismic signal suggests that, in addition to afterslip at seismogenic depths, localized right-lateral/reverse slip occurred on dipping shallow fault surfaces southwest of the Calaveras. The spatial distribution of slip inferred by inverting the GPS data is compatible with a model in which moderate Calaveras fault earthquakes rupture locked patches surrounded by areas of creep, afterslip, and microseismicity (Oppenheimer et al., 1990). If this model and existing Calaveras fault slip rate estimates are correct, a slip deficit remains on the 2007 Alum Rock rupture patch that may be made up by aseismic slip or slip in larger earthquakes. Recent studies (e.g., Manaker et al., 2005) suggest that at depth the Hayward and central Calaveras faults connect via a simple continuous surface illuminated by the Mission Seismic Trend (MST), implying that a damaging earthquake rupture could involve both faults (Graymer et al., 2008). If this geometry is correct, the combined coseismic and postseismic slip we infer for the 2007 Alum Rock event predicts static Coulomb stress increases of ???0:6 bar on the MST surface and on the northern Calaveras fault ???5 km northwest of the Alum Rock hypocenter.

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A California statewide three-dimensional seismic velocity model from both absolute and differential times

We obtain a seismic velocity model of the California crust and uppermost mantle using a regional-scale double-difference tomography algorithm. We begin by using absolute arrival-time picks to solve for a coarse three-dimensional (3D) P velocity (V P ) model with a uniform 30 km horizontal node spacing, which we then use as the starting model for a finer-scale inversion using double-difference tomography applied to absolute and differential pick times. For computational reasons, we split the state into 5 subregions with a grid spacing of 10 to 20 km and assemble our final statewide V P model by stitching together these local models. We also solve for a statewide S-wave model using S picks from both the Southern California Seismic Network and USArray, assuming a starting model based on the V P results and a V P =V S ratio of 1.732. Our new model has improved areal coverage compared with previous models, extending 570 km in the SW-NE directionand 1320 km in the NW-SE direction. It also extends to greater depth due to the inclusion of substantial data at large epicentral distances. Our V P model generally agrees with previous separate regional models for northern and southern California, but we also observe some new features, such as high-velocity anomalies at shallow depths in the Klamath Mountains and Mount Shasta area, somewhat slow velocities in the northern Coast Ranges, and slow anomalies beneath the Sierra Nevada at midcrustal and greater depths. This model can be applied to a variety of regional-scale studies in California, such as developing a unified statewide earthquake location catalog and performing regional waveform modeling.

Bulletin of the Seismological Society of America↗

Comparing stochastic point-source and finite-source ground-motion simulations: SMSIM and EXSIM

Comparisons of ground motions from two widely used point-source and finite-source ground-motion simulation programs (SMSIM and EXSIM) show that the following simple modifications in EXSIM will produce agreement in the motions from a small earthquake at a large distance for the two programs: (1) base the scaling of high frequencies on the integral of the squared Fourier acceleration spectrum; (2) do not truncate the time series from each subfault; (3) use the inverse of the subfault corner frequency for the duration of motions from each subfault; and (4) use a filter function to boost spectral amplitudes at frequencies near and less than the subfault corner frequencies. In addition, for SMSIM an effective distance is defined that accounts for geometrical spreading and anelastic attenuation from various parts of a finite fault. With these modifications, the Fourier and response spectra from SMSIM and EXSIM are similar to one another, even close to a large earthquake (M 7), when the motions are averaged over a random distribution of hypocenters. The modifications to EXSIM remove most of the differences in the Fourier spectra from simulations using pulsing and static subfaults; they also essentially eliminate any dependence of the EXSIM simulations on the number of subfaults. Simulations with the revised programs suggest that the results of Atkinson and Boore (2006), computed using an average stress parameter of 140 bars and the original version of EXSIM, are consistent with the revised EXSIM with a stress parameter near 250 bars.

Bulletin of the Seismological Society of America↗

Effects of 3D random correlated velocity perturbations on predicted ground motions

Three-dimensional, finite-difference simulations of a realistic finite-fault rupture on the southern Hayward fault are used to evaluate the effects of random, correlated velocity perturbations on predicted ground motions. Velocity perturbations are added to a three-dimensional (3D) regional seismic velocity model of the San Francisco Bay Area using a 3D von Karman random medium. Velocity correlation lengths of 5 and 10 km and standard deviations in the velocity of 5% and 10% are considered. The results show that significant deviations in predicted ground velocities are seen in the calculated frequency range (≤1 Hz) for standard deviations in velocity of 5% to 10%. These results have implications for the practical limits on the accuracy of scenario ground-motion calculations and on retrieval of source parameters using higher-frequency, strong-motion data.

Bulletin of the Seismological Society of America↗

The influence of maximum magnitude on seismic-hazard estimates in the Central and Eastern United States

I analyze the sensitivity of seismic-hazard estimates in the central and eastern United States (CEUS) to maximum magnitude (m max ) by exercising the U.S. Geological Survey (USGS) probabilistic hazard model with several m max alternatives. Seismicity-based sources control the hazard in most of the CEUS, but data seldom provide an objective basis for estimating m max . The USGS uses preferred m max values of moment magnitude 7.0 and 7.5 for the CEUS craton and extended margin, respectively, derived from data in stable continental regions worldwide. Other approaches, for example analysis of local seismicity or judgment about a source's seismogenic potential, often lead to much smaller m max . Alternative models span the m max ranges from the 1980s Electric Power Research Institute/Seismicity Owners Group (EPRI/SOG) analysis. Results are presented as haz-ard ratios relative to the USGS national seismic hazard maps. One alternative model specifies m max equal to moment magnitude 5.0 and 5.5 for the craton and margin, respectively, similar to EPRI/SOG for some sources. For 2% probability of exceedance in 50 years (about 0.0004 annual probability), the strong m max truncation produces hazard ratios equal to 0.35-0.60 for 0.2-sec spectral acceleration, and 0.15-0.35 for 1.0-sec spectral acceleration. Hazard-controlling earthquakes interact with m max in complex ways. There is a relatively weak dependence on probability level: hazardratios increase 0-15% for 0.002 annual exceedance probability and decrease 5-25% for 0.00001 annual exceedance probability. Although differences at some sites are tempered when faults are added, m max clearly accounts for some of the discrepancies that are seen in comparisons between USGS-based and EPRI/SOG-based hazard results.

Bulletin of the Seismological Society of America↗

Evidence for a twelfth large earthquake on the southern hayward fault in the past 1900 years

We present age and stratigraphic evidence for an additional paleoearthquake at the Tyson Lagoon site. The acquisition of 19 additional radiocarbon dates and the inclusion of this additional event has resolved a large age discrepancy in our earlier earthquake chronology. The age of event E10 was previously poorly constrained, thus increasing the uncertainty in the mean recurrence interval (RI), a critical factor in seismic hazard evaluation. Reinspection of many trench logs revealed substantial evidence suggesting that an additional earthquake occurred between E10 and E9 within unit u45. Strata in older u45 are faulted in the main fault zone and overlain by scarp colluviums in two locations.We conclude that an additional surfacerupturing event (E9.5) occurred between E9 and E10. Since 91 A.D. (??40 yr, 1??), 11 paleoearthquakes preceded the M 6:8 earthquake in 1868, yielding a mean RI of 161 ?? 65 yr (1??, standard deviation of recurrence intervals). However, the standard error of the mean (SEM) is well determined at ??10 yr. Since ~1300 A.D., the mean rate has increased slightly, but is indistinguishable from the overall rate within the uncertainties. Recurrence for the 12-event sequence seems fairly regular: the coefficient of variation is 0.40, and it yields a 30-yr earthquake probability of 29%. The apparent regularity in timing implied by this earthquake chronology lends support for the use of time-dependent renewal models rather than assuming a random process to forecast earthquakes, at least for the southern Hayward fault.

Bulletin of the Seismological Society of America↗

Rupture directivity of moderate earthquakes in northern California

We invert peak ground velocity and acceleration (PGV and PGA) to estimate rupture direction and rupture velocity for 47 moderate earthquakes (3.5≥M≥5.4) in northern California. We correct sets of PGAs and PGVs recorded at stations less than 55–125 km, depending on source depth, for site amplification and source–receiver distance, then fit the residual peak motions to the unilateral directivity function of Ben-Menahem (1961). We independently invert PGA and PGV. The rupture direction can be determined using as few as seven peak motions if the station distribution is sufficient. The rupture velocity is unstable, however, if there are no takeoff angles within 30° of the rupture direction. Rupture velocities are generally subsonic (0.5β–0.9β); for stability, we limit the rupture velocity at v=0.92β, the Rayleigh wave speed. For 73 of 94 inversions, the rupture direction clearly identifies one of the nodal planes as the fault plane. The 35 strike-slip earthquakes have rupture directions that range from nearly horizontal (6 events) to directly updip (5 events); the other 24 rupture partly along strike and partly updip. Two strike-slip earthquakes rupture updip in one inversion and downdip in the other. All but 1 of the 11 thrust earthquakes rupture predominantly updip. We compare the rupture directions for 10 M≥4.0 earthquakes to the relative location of the mainshock and the first two weeks of aftershocks. Spatial distributions of 8 of 10 aftershock sequences agree well with the rupture directivity calculated for the mainshock.

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Localized surface disruptions observed by InSAR during strong earthquakes in Java and Hawai'i

Interferometric Synthetic Aperture Radar data spanning strong earthquakes on the islands of Java and Hawai‘i in 2006 reveal patches of subsidence and incoherence indicative of localized ground failure. Interferograms spanning the 26 May 2006 Java earthquake suggest an area of about 7.5 km 2 of subsidence (~2 cm) and incoherence south of the city of Yogyakarta that correlates with significant damage to housing, high modeled peak ground accelerations, and poorly consolidated geologic deposits. The subsidence and incoherence is inferred to be a result of intense shaking and/or damage. At least five subsidence patches on the west side of the Island of Hawai‘i, ranging 0.3–2.2 km 2 in area and 3–8 cm in magnitude, occurred as a result of a pair of strong earthquakes on 15 October 2006. Although no felt reports or seismic data are available from the areas in Hawai‘i, the Java example suggests that the subsidence patches indicate areas of amplified earthquake shaking. Surprisingly, all subsidence areas in Hawai‘i were limited to recent, and supposedly stable, lava flows and may reflect geological conditions not detectable at the surface. In addition, two ‘a‘ā lava flows in Hawai‘i were partially incoherent in interferograms spanning the earthquakes, indicating surface disruption as a result of the earthquake shaking. Coearthquake incoherence of rubbly deposits, like ‘a‘ā flows, should be explored as a potential indicator of earthquake intensity and past strong seismic activity.

Bulletin of the Seismological Society of America↗

Fundamental questions of earthquake statistics, source behavior, and the estimation of earthquake probabilities from possible foreshocks

Estimates of the probability that an M L 4.8 earthquake, which occurred near the southern end of the San Andreas fault on 24 March 2009, would be followed by an M 7 mainshock over the following three days vary from 0.0009 using a Gutenberg–Richter model of aftershock statistics (Reasenberg and Jones, 1989) to 0.04 using a statistical model of foreshock behavior and long‐term estimates of large earthquake probabilities, including characteristic earthquakes (Agnew and Jones, 1991). I demonstrate that the disparity between the existing approaches depends on whether or not they conform to Gutenberg–Richter behavior. While Gutenberg–Richter behavior is well established over large regions, it could be violated on individual faults if they have characteristic earthquakes or over small areas if the spatial distribution of large‐event nucleations is disproportional to the rate of smaller events. I develop a new form of the aftershock model that includes characteristic behavior and combines the features of both models. This new model and the older foreshock model yield the same results when given the same inputs, but the new model has the advantage of producing probabilities for events of all magnitudes, rather than just for events larger than the initial one. Compared with the aftershock model, the new model has the advantage of taking into account long‐term earthquake probability models. Using consistent parameters, the probability of an M 7 mainshock on the southernmost San Andreas fault is 0.0001 for three days from long‐term models and the clustering probabilities following the M L 4.8 event are 0.00035 for a Gutenberg–Richter distribution and 0.013 for a characteristic‐earthquake magnitude–frequency distribution. Our decisions about the existence of characteristic earthquakes and how large earthquakes nucleate have a first‐order effect on the probabilities obtained from short‐term clustering models for these large events.

Bulletin of the Seismological Society of America↗

Tsunami simulations of the 1867 Virgin Island earthquake: Constraints on epicenter location and fault parameters

The 18 November 1867 Virgin Island earthquake and the tsunami that closely followed caused considerable loss of life and damage in several places in the northeast Caribbean region. The earthquake was likely a manifestation of the complex tectonic deformation of the Anegada Passage, which cuts across the Antilles island arc between the Virgin Islands and the Lesser Antilles. In this article, we attempt to characterize the 1867 earthquake with respect to fault orientation, rake, dip, fault dimensions, and first tsunami wave propagating phase, using tsunami simulations that employ high-resolution multibeam bathymetry. In addition, we present new geophysical and geological observations from the region of the suggested earthquake source. Results of our tsunami simulations based on relative amplitude comparison limit the earthquake source to be along the northern wall of the Virgin Islands basin, as suggested by Reid and Taber (1920) , or on the carbonate platform north of the basin, and not in the Virgin Islands basin, as commonly assumed. The numerical simulations suggest the 1867 fault was striking 120°–135° and had a mixed normal and left-lateral motion. First propagating wave phase analysis suggests a fault striking 300°–315° is also possible. The best-fitting rupture length was found to be relatively small (50 km), probably indicating the earthquake had a moment magnitude of ∼7.2. Detailed multibeam echo sounder surveys of the Anegada Passage bathymetry between St. Croix and St. Thomas reveal a scarp, which cuts the northern wall of the Virgin Islands basin. High-resolution seismic profiles further indicate it to be a reasonable fault candidate. However, the fault orientation and the orientation of other subparallel faults in the area are more compatible with right-lateral motion. For the other possible source region, no clear disruption in the bathymetry or seismic profiles was found on the carbonate platform north of the basin.

Bulletin of the Seismological Society of America↗

LiDAR-Assisted identification of an active fault near Truckee, California

We use high-resolution (1.5-2.4 points/m2) bare-earth airborne Light Detection and Ranging (LiDAR) imagery to identify, map, constrain, and visualize fault-related geomorphology in densely vegetated terrain surrounding Martis Creek Dam near Truckee, California. Bare-earth LiDAR imagery reveals a previously unrecognized and apparently youthful right-lateral strike-slip fault that exhibits laterally continuous tectonic geomorphic features over a 35-km-long zone. If these interpretations are correct, the fault, herein named the Polaris fault, may represent a significant seismic hazard to the greater Truckee-Lake Tahoe and Reno-Carson City regions. Three-dimensional modeling of an offset late Quaternary terrace riser indicates a minimum tectonic slip rate of 0.4 ?? 0.1 mm/yr.Mapped fault patterns are fairly typical of regional patterns elsewhere in the northern Walker Lane and are in strong coherence with moderate magnitude historical seismicity of the immediate area, as well as the current regional stress regime. Based on a range of surface-rupture lengths and depths to the base of the seismogenic zone, we estimate a maximum earthquake magnitude (M) for the Polaris fault to be between 6.4 and 6.9.

Bulletin of the Seismological Society of America↗

Short baseline variations in site response and wave-propagation effects and their structural causes: Four examples in and around the santa clara valley, California

Ground motion records of local and regional events from a portable array are used to investigate the structural causes of variations in ground motion over distances of a few hundred meters to a few kilometers in the sedimentary basin environment of the Santa Clara Valley, California, and its margins. Arrays of portable seismic stations are used to target four study areas with different ground motion patterns: (1) an edge of the alluvial basin extending up onto a marginal ridge (Blossom Hill), (2) a Cenozoic basin with a nearly flat bottom (Cupertino Basin), (3) a long, narrow Cenozoic basin with a steep V profile (Evergreen Basin), and (4) a line perpendicular to the trace of the Hayward fault. Average peak velocities on Blossom Hill from local earthquakes are a factor of 2.5 times higher than nearby valley sites. Three-dimensional (3D) modeling is used to conclude that the majority of the amplification is due to lower shear-wave velocities along a local fault zone (Shannon–Berrocal). Site amplification over the Cupertino Basin in the frequency band 0.5–4 Hz is generally low (less than 2.0 relative to a Mesozoic rock site) and spatially uniform. This response is attributed to the shallow, flat-bottomed shape of the basin and the uniform, flat-laying sedimentary fill. In contrast, site amplification in the Evergreen Basin generally exceeds 3.0 and is attributed to the deep, V-shaped geometry of the basin and younger sedimentary fill. 3D waveform modeling shows the elongated shape of the Evergreen Basin causes more efficient trapping of long-period waves for sources along the long axis of the basin. A low-velocity zone is postulated along the Hayward fault with a width between 100 and 200 m, based on elevated site response along the fault trace and 4.5-Hz fault zone guided waves on the horizontal components of stations near the fault.

California↗

Seismotectonics and fault structure of the California Central Coast

I present and interpret new earthquake relocations and focal mechanisms for the California Central Coast. The relocations improve upon catalog locations by using 3D seismic velocity models to account for lateral variations in structure and by using relative arrival times from waveform cross-correlation and double-difference methods to image seismicity features more sharply. Focal mechanisms are computed using ray tracing in the 3D velocity models. Seismicity alignments on the Hosgri fault confirm that it is vertical down to at least 12 km depth, and the focal mechanisms are consistent with right-lateral strike-slip motion on a vertical fault. A prominent, newly observed feature is an ~25 km long linear trend of seismicity running just offshore and parallel to the coastline in the region of Point Buchon, informally named the Shoreline fault. This seismicity trend is accompanied by a linear magnetic anomaly, and both the seismicity and the magnetic anomaly end where they obliquely meet the Hosgri fault. Focal mechanisms indicate that the Shoreline fault is a vertical strike-slip fault. Several seismicity lineations with vertical strike-slip mechanisms are observed in Estero Bay. Events greater than about 10 km depth in Estero Bay, however, exhibit reverse-faulting mechanisms, perhaps reflecting slip at the top of the remnant subducted slab. Strike-slip mechanisms are observed offshore along the Hosgri–San Simeon fault system and onshore along the West Huasna and Rinconada faults, while reverse mechanisms are generally confined to the region between these two systems. This suggests a model in which the reverse faulting is primarily due to restraining left-transfer of right-lateral slip.

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