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Prediction of earthquake response spectra
We have developed empirical equations for predicting earthquake response spectra in terms of magnitude, distance, and site conditions, using a two-stage regression method similar to the one we used previously for peak horizontal acceleration and velocity. We analyzed horizontal pseudo-velocity response at 5 percent damping for 64 records of 12 shallow earthquakes in Western North America, including the recent Coyote Lake and Imperial Valley, California, earthquakes. We developed predictive equations for 12 different periods between 0.1 and 4.0 s, both for the larger of two horizontal components and for the random horizontal component. The resulting spectra show amplification at soil sites compared to rock sites for periods greater than or equal to 0.3 s, with maximum amplification exceeding a factor of 2 at 2.0 s. For periods less than 0.3 s there is slight deamplification at the soil sites. These results are generally consistent with those of several earlier studies. A particularly significant aspect of the predicted spectra is the change of shape with magnitude (confirming earlier results by McGuire and by Irifunac and Anderson). This result indicates that the conventional practice of scaling a constant spectral shape by peak acceleration will not give accurate answers. The Newmark and Hall method of spectral scaling, using both peak acceleration and peak velocity, largely avoids this error. Comparison of our spectra with the Nuclear Regulatory Commission's Regulatory Guide 1.60 spectrum anchored at the same value at 0.1 s shows that the Regulatory Guide 1.60 spectrum is exceeded at soil sites for a magnitude of 7.5 at all distances for periods greater than about 0.5 s. Comparison of our spectra for soil sites with the corresponding ATC-3 curve of lateral design force coefficient for the highest seismic zone indicates that the ATC-3 curve is exceeded within about 7 km of a magnitude 6.5 earthquake and within about 15 km of a magnitude 7.5 event. The amount by which it is exceeded for the 7.5 event is largest in the period range from 0.5 to 2.0 s.
The design earthquake and earthquake response spectra
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Comparison of earthquake source spectra and attenuation in eastern North America and southeastern Australia
The paucity of ground-motion data in stable continental regions (SCRs) remains a key limitation when developing relations that seek to predict effects of strong ground shaking from large damaging earthquakes. It is desirable to combine data from more than one SCR to increase database size, but this raises questions as to whether the source and attenuation properties of the SCRs are equivalent. We compare recently compiled spectral-amplitude databases from small to moderate events (moment magnitudes, 2.0 ??? M ??? 5.0) in both southeastern Australia and eastern North America (ENA). Both are SCRs but are widely separated, spatially and in tectonic history. We statistically compare ground motions by plotting mean and standard deviations of spectral amplitudes for data grouped in magnitude and distance bins. These comparisons show that the source and attenuation properties of the two regions are very similar, in particular, at shorter hypocentral distances R (i.e., R < 70 km). At larger distances, regional attenuation differences are observed that may be attributed to differences in crustal structure. We conclude that it is valid to combine the Australian and ENA ground-motion datasets in the development of ground-motion prediction equations, with some limitations in frequency and distance ranges. These ground-motion relations may serve as generic functions for SCRs around the world.
Empirical improvements for estimating earthquake response spectra with random‐vibration theory
The stochastic method of ground‐motion simulation is often used in combination with the random‐vibration theory to directly compute ground‐motion intensity measures, thereby bypassing the more computationally intensive time‐domain simulations. Key to the application of random‐vibration theory to simulate response spectra is determining the duration ( D rms ) used in computing the root‐mean‐square oscillator response. Boore and Joyner (1984) originally proposed an equation for D rms , which was improved upon by Liu and Pezeshk (1999) . Though these equations are both substantial improvements over using the duration of the ground‐motion excitation for D rms , we document systematic differences between the ground‐motion intensity measures derived from the random‐vibration and time‐domain methods for both of these D rms equations. These differences are generally less than 10% for most magnitudes, distances, and periods of engineering interest. Given the systematic nature of the differences, however, we feel that improved equations are warranted. We empirically derive new equations from time‐domain simulations for eastern and western North America seismological models. The new equations improve the random‐vibration simulations over a wide range of magnitudes, distances, and oscillator periods.
Fault healing promotes high-frequency earthquakes in laboratory experiments and on natural faults
Faults strengthen or heal with time in stationary contact and this healing may be an essential ingredient for the generation of earthquakes. In the laboratory, healing is thought to be the result of thermally activated mechanisms that weld together micrometre-sized asperity contacts on the fault surface, but the relationship between laboratory measures of fault healing and the seismically observable properties of earthquakes is at present not well defined. Here we report on laboratory experiments and seismological observations that show how the spectral properties of earthquakes vary as a function of fault healing time. In the laboratory, we find that increased healing causes a disproportionately large amount of high-frequency seismic radiation to be produced during fault rupture. We observe a similar connection between earthquake spectra and recurrence time for repeating earthquake sequences on natural faults. Healing rates depend on pressure, temperature and mineralogy, so the connection between seismicity and healing may help to explain recent observations of large megathrust earthquakes which indicate that energetic, high-frequency seismic radiation originates from locations that are distinct from the geodetically inferred locations of large-amplitude fault slip
Surface seismic measurements of near-surface P-and S-wave seismic velocities at earthquake recording stations, Seattle, Washington
We measured P - and S -wave seismic velocities to about 40-m depth using seismic-refraction/reflection data on the ground surface at 13 sites in the Seattle, Washington, urban area, where portable digital seismographs recently recorded earthquakes. Sites with the lowest measured V s correlate with highest ground motion amplification. These sites, such as at Harbor Island and in the Duwamish River industrial area (DRIA) south of the Kingdome, have an average V s in the upper 30 m (V¯ s30 ) of 150 to 170 m/s. These values of V¯ s30 place these sites in soil profile type E (V¯ s30 < 180 m/s). A “rock” site, located at Seward Park on Tertiary sedimentary deposits, has a V¯ s30 of 433 m/s, which is soil type C (V¯ s30 : 360 to 760 m/s). The Seward Park site V¯ s30 is about equal to, or up to 200 m/s slower than sites that were located on till or glacial outwash. High-amplitude P - and S -wave seismic reflections at several locations appear to correspond to strong resonances observed in earthquake spectra. An S -wave reflector at the Kingdome at about 17 to 22 m depth probably causes strong 2-Hz resonance that is observed in the earthquake data near the Kingdome.
Microearthquake spectra from the Anza, California, seismic network: Site response and source scaling
We analyzed spectra of local microearthquakes recorded by the Anza, California, seismic network to isolate the effects of site response and to investigate the scaling of source parameters for small earthquakes. Spectra of microearthquakes (M < 2; Mo < 1019 dyne-cm) at Anza have shapes characteristic of the receiver sites and are generally independent of the source region. Thus, the site response is a major conditioner of the observed spectral shape. To remove the effects of site response from the spectra of a M ∼ 3 event and isolate its source spectrum, we divided by the spectra of an adjacent aftershock used as an empirical Green's function event. The spectral ratios indicate that the apparent corner frequencies of small earthquakes (Mo < 1019dyne-cm) observed at even the high-fmax stations on hard rock are much lower than the source corner frequencies. The spectral ratios are consistent with stress drop remaining constant with decreasing seismic moment, for events with moments as small as 1018 dyne-cm. The spectral ratios display remarkable agreement between sites which showed vast differences in their original spectra, indicating that the spectral division effectively removed the site response. The source spectrum of the M ∼ 3 event has a high-frequency spectral fall-off of about ω−2. An apparent dependence of high-frequency fall-off with seismic moment in the original spectra can also be explained by the effects of site response. The difference between the P- and S-wave corner frequencies and high-frequency roll-offs in the observed spectra for these events is the result of the site response and is not a source property. The shapes of the spectra of microearthquakes at Anza can largely be explained by attenuation at shallow depth with a frequency-independent Q. For some sites, near-surface resonances are also apparent in the spectra of microearthquakes. It is indicated by t* values determined for each site that Qp ∼ Qs for the shallow low-Q layer. Further evidence of low near-surface Q is observed in the anomalous spectra of an unusually shallow earthquake (source depth ∼ 1 km) in the network. The spectra from this shallow event are depleted in high-frequency energy at most stations, relative to those of deeper events. This observation can be explained by a low-Q surficial zone. For stations of the network situated on alluvium, this low-Q layer has a maximum thickness of about 3 km and maximum P- and S-wave Q values of 30 to 50.
Does earthquake stress drop increase with depth in the crust?
We combine earthquake spectra from multiple studies to investigate whether the increase in stress drop with depth often observed in the crust is real, or an artifact of decreasing attenuation (increasing Q ) with depth. In many studies, empirical path and attenuation corrections are assumed to be independent of the earthquake source depth. We test this assumption by investigating whether a realistic increase in Q with depth (as is widely observed) could remove some of the observed apparent increase in stress drop with depth. We combine event spectra, previously obtained using spectral decomposition methods, for over 50,000 earthquakes (M0 to M5) from 12 studies in California, Nevada, Kansas and Oklahoma. We find that the relative high-frequency content of the spectra systematically increases with increasing earthquake depth, at all magnitudes. By analyzing spectral ratios between large and small events as a function of source depth, we explore the relative importance of source and attenuation contributions to this observed depth dependence. Without any correction for depth-dependent attenuation, we find a systematic increase in stress drop, rupture velocity, or both, with depth, as previously observed. When we add an empirical, depth-dependent attenuation correction, the depth dependence of stress drop systematically decreases, often becoming negligible. The largest corrections are observed in regions with the largest seismic velocity increase with depth. We conclude that source parameter analyses, whether in the frequency or time domains, should not assume path terms are independent of source depth, and should more explicitly consider the effects of depth-dependent attenuation.
Acceleration spectra for subduction zone earthquakes
We estimate the source spectra of shallow earthquakes from digital recordings of teleseismic P wave groups, that is, P + p P + s P , by making frequency dependent corrections for the attenuation and for the interference of the free surface. The correction for the interference of the free surface assumes that the earthquake radiates energy from a range of depths. We apply this spectral analysis to a set of 12 subduction zone earthquakes which range in size from M S = 6.2 to 8.1, obtaining corrected P wave acceleration spectra on the frequency band from 0.01 to 2.0 Hz. Seismic moment estimates from surface waves and normal modes are used to extend these P wave spectra to the frequency band from 0.001 to 0.01 Hz. The acceleration spectra of moderate subduction zone earthquakes, that is, earthquakes whose seismic moments are less than 10 27 dyn cm, exhibit ω-square or Brune-type spectra, while the acceleration spectra of large subduction zone earthquakes, that is, earthquakes whose seismic moments are greater than 10 27 dyn cm, exhibit intermediate slopes where ü(ω) ∝ ω 5/4 for frequencies from 0.005 to 0.05 Hz. For this set of earthquakes, spectral shape appears to be a discontinuous function of seismic moment. Using reasonable assumptions for the phase characteristics, we transform the spectral shape observed for large earthquakes into the time domain to fit Ekström's (1987) moment rate functions for the M S = 8.1 Michoacan earthquake of September 19, 1985, and the M S = 7.6 Michoacan aftershock of September 21, 1985.
Determination of Δσ and κ0 from response spectra of large earthquakes in Greece
We fit an ω −2 model to response spectra from eight recent Greek earthquakes ranging in size from M = 5.8 to M = 6.9. The diminution parameter κ 0 was determined for each site, with a value near 0.06 for a typical soil site. The stress parameter (Δσ) showed little variation from earthquake to earthquake and had a mean value of 56 bars over all earthquakes. Predictions of peak velocity, peak acceleration, rupture duration, and fault length using the derived stress parameters are consistent with observations. Frequency-dependent site amplifications were included in all estimates; the combined effect of amplification and attenuation had a maximum value close to a factor of 2.5 for a typical soil site, relative to the motions at the surface of a perfectly elastic uniform half-space composed of materials near the source. The results form the foundation for predictions of strong motions in Greece for distances and magnitudes other than those for which data are available.
Damping scaling factors for elastic response spectra for shallow crustal earthquakes in active tectonic regions: "average" horizontal component
Ground motion prediction equations (GMPEs) for elastic response spectra are typically developed at a 5% viscous damping ratio. In reality, however, structural and nonstructural systems can have other damping ratios. This paper develops a new model for a damping scaling factor (DSF) that can be used to adjust the 5% damped spectral ordinates predicted by a GMPE for damping ratios between 0.5% to 30%. The model is developed based on empirical data from worldwide shallow crustal earthquakes in active tectonic regions. Dependencies of the DSF on potential predictor variables, such as the damping ratio, spectral period, ground motion duration, moment magnitude, source-to-site distance, and site conditions, are examined. The strong influence of duration is captured by the inclusion of both magnitude and distance in the DSF model. Site conditions show weak influence on the DSF. The proposed damping scaling model provides functional forms for the median and logarithmic standard deviation of DSF, and is developed for both RotD50 and GMRotI50 horizontal components. A follow-up paper develops a DSF model for vertical ground motion.
The ShakeOut Scenario: Meeting the needs for construction aggregates, hot mix asphalt, and ready mix concrete
An M w 7.8 earthquake as described in the ShakeOut Scenario would cause significant damage to buildings and infrastructure. Over 6 million tons of newly mined aggregate would be used for emergency repairs and for reconstruction in the five years following the event. This aggregate would be applied mostly in the form of concrete for buildings and bridges, asphalt or concrete for pavement, and unbound gravel for applications such as base course that goes under highway pavement and backfilling for foundations and pipelines. There are over 450 aggregate, concrete, and asphalt plants in the affected area, some of which would be heavily damaged. Meeting the increased demand for construction materials would require readily available permitted reserves, functioning production facilities, a supply of cement and asphalt, a source of water, gas, and electricity, and a trained workforce. Prudent advance preparations would facilitate a timely emergency response and reconstruction following such an earthquake.
Maximum spectral demands in the near-fault region
The Next Generation Attenuation (NGA) relationships for shallow crustal earthquakes in the western United States predict a rotated geometric mean of horizontal spectral demand, termed GMRotI50, and not maximum spectral demand. Differences between strike-normal, strike-parallel, geometric-mean, and maximum spectral demands in the near-fault region are investigated using 147 pairs of records selected from the NGA strong motion database. The selected records are for earthquakes with moment magnitude greater than 6.5 and for closest site-to-fault distance less than 15 km. Ratios of maximum spectral demand to NGA-predicted GMRotI50 for each pair of ground motions are presented. The ratio shows a clear dependence on period and the Somerville directivity parameters. Maximum demands can substantially exceed NGA-predicted GMRotI50 demands in the near-fault region, which has significant implications for seismic design, seismic performance assessment, and the next-generation seismic design maps. Strike-normal spectral demands are a significantly unconservative surrogate for maximum spectral demands for closest distance greater than 3 to 5 km. Scale factors that transform NGA-predicted GMRotI50 to a maximum spectral demand in the near-fault region are proposed. ?? 2008, Earthquake Engineering Research Institute.
The behavior of the Salesforce Tower, the tallest building in San Francisco, California inferred from earthquake and ambient shaking
The newly constructed tallest building designed in conformance with performance-based design procedure in San Francisco, California is a 61-story building equipped with an accelerometric array that recorded the January 4, 2018 M4.4 Berkeley earthquake. The building is designed with concrete core shear walls and perimeter gravity steel columns. The earthquake records as well as on-demand recorded ambient responses of the building are studied to determine its dynamic characteristics and building-specific behavior. At the level of shaking of either the earthquake or ambient excitation, the frequencies and low modal damping ratios (<2%) are similar. The building exhibits torsional behavior most likely due to abrupt asymmetrical changes in the size of the core shear wall. The translational and torsional modes during the earthquake are closely coupled, which leads to a beating effect, the period of which is calculable. Due to the relatively low-amplitude shaking during the earthquake, the drift ratios were small and did not cause any damage. It is expected that during stronger shaking levels, these characteristics may change.
Before and after retrofit behavior and performance of a 55-story tall building inferred from distant earthquake and ambient vibration data
A sparsely instrumented 55-story building in Osaka, Japan had recorded unprecedented, severe and long-duration long-period resonating responses during the March 11, 2011 M9.0 Tohoku earthquake that occurred at 767 km distance. Thereafter, studies of the records resulted in implementation of a significant retrofit design, comprising dampers and buckling restrained braces (BRBs). The responses of the retrofitted building were also recorded during the April 24, 2016 M7.3 Kumamoto earthquake that occurred at 478 km. The earthquake and on-demand acquired ambient response data are analyzed in this study to assess the impact of this rare, retrofitted and instrumented tall building subjected to long period strong shaking from events originating at far distances. As expected, the fundamental frequency and critical damping ratio of the building increased, albeit small, after the retrofit as compared to before the retrofit. Increase of damping percentage is a positive finding and indicates that even larger percentages may be attained under shaking stronger than the 2016 event. The records indicate that the building still experiences significant resonance, torsion, as well as a beating effect.
Earthquake stress drop, source spectra from laboratory experiments, and the apparent unsteadiness of frictional slip
Over a range of co-seismic total energy release, high sample rate slip, stress, and slip velocity measurements were made during frictional failure to determine seismic source properties. The near-field measurements were used to estimate stress drops using spectral approaches that are analogous to the standard seismological moment-corner determined Δσ and acceleration amplitude Δσ arms stress drops. Rapid frictional sliding produces slip velocity amplitude spectra that vary with frequency -1 so long as the energy dissipated by friction approaches the total energy release. Under these conditions Δσ and Δσ arms are similar in size. Since these are nearly direct measurements of fault slip velocity and because they produce flat acceleration spectra between the corner and an apparent fmax, friction in these experiments seems to produce dynamic acceleration and deceleration at all resolved frequencies. The physical origin of this unsteady motion is not known exactly but likely reflects rapid dynamic variations in fault strength or applied stress. On the other hand, when the total energy stored prior to failure is artificially made somewhat larger relative to that which can be dissipated by friction the velocity spectra vary with frequency -2 immediately below the corner. At these conditions Δσ and Δσ arms diverge. The excess stored energy is preferentially partitioned into radiated energy upon failure. Collectively the experiments imply that to produce unsteady, white noise accelerations that are observed for natural earthquakes, requires that at least 95% of the energy released does not escape the source region to be radiated to the far-field.
Damping scaling of response spectra for shallow crustal earthquakes in active tectonic regions
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