Geology topics

D.M. Boore

Publications and source records attributed to D.M. Boore.

At least 19 recordsLinked to original sources

USGS2011

Regional correlations of V S 30 averaged over depths less than and greater than 30 meters

Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m ( V S 30 ), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m ( V Sz , with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that V Sz is systematically larger for a given V Sz than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating V S 30 to V Sz for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate V S 30 from V Sz for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in log V S 30 of ±1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to V S 30 uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that V S 30 is correlated with V Sz for z as great as 400 m for sites of the KiK-net network, providing some justification for using V S 30 as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m.

Bulletin of the Seismological Society of America↗

USGS2011

Modifications to existing ground-motion prediction equations in light of new data

We compare our recent ground-motion prediction equations (GMPEs) for western North America (WNA; Boore and Atkinson, 2008 [BA08]) and eastern North America (ENA; Atkinson and Boore, 2006 [AB06]; Atkinson, 2008 [A08]) to newly available ground-motion data. Based on these comparisons, we suggest revisions to our GMPEs for both WNA and ENA. The revisions for WNA affect only those events with M ≤ 5:75, while those for ENA affect all magnitudes. These are simple modi[1]fications to the existing GMPEs that bring them into significantly better agreement with data. The wealth of new data clearly demonstrates that these modifications are warranted; we therefore recommend the use of the updated equations for seismic hazard analyses and other applications. More detailed studies are under way by many investigators (including ourselves) to develop a new generation of ground-motion models in both WNA and ENA from scratch, through a comprehensive reevaluation of source, path, site, and modeling issues. In time, those more complete models will replace those proposed in this study. However, as the new models will be several years in development, we recommend using the modified models proposed herein, labeled BA08′ (for WNA), AB06′ (for ENA), and A08′ (for ENA, to replace A08), as interim updates to our existing models. The proposed models are in demonstrable agreement with a rich database of ground motions for moderate-magnitude earthquakes in both WNA and ENA and are constrained at larger magnitudes by the BA08 magnitude and distance scaling.

Bulletin of the Seismological Society of America↗

USGS2010

High-frequency filtering of strong-motion records

The influence of noise in strong-motion records is most problematic at low and high frequencies where the signal to noise ratio is commonly low compared to that in the mid-spectrum. The impact of low-frequency noise (<1 Hz) on strong-motion intensity parameters such as ground velocities, displacements and response spectral ordinates can be dramatic and consequentially it has become standard practice to low-cut (high-pass) filter strong-motion data with corner frequencies often chosen based on the shape of Fourier amplitude spectra and the signal-to-noise ratio. It has been shown that response spectral ordinates should not be used beyond some fraction of the corner period (reciprocal of the corner frequency) of the low-cut filter. This article examines the effect of high-frequency noise (>5 Hz) on computed pseudo-absolute response spectral accelerations (PSAs). In contrast to the case of low-frequency noise our analysis shows that filtering to remove high-frequency noise is only necessary in certain situations and that PSAs can often be used up to 100 Hz even if much lower high-cut corner frequencies are required to remove the noise. This apparent contradiction can be explained by the fact that PSAs are often controlled by ground accelerations associated with much lower frequencies than the natural frequency of the oscillator because path and site attenuation (often modelled by Q and κ, respectively) have removed the highest frequencies. We demonstrate that if high-cut filters are to be used, then their corner frequencies should be selected on an individual basis, as has been done in a few recent studies.

Bulletin of Earthquake Engineering↗

USGS2010

Determination of stress parameters for eight well-recorded earthquakes in eastern North America

We determined the stress parameter, Δσ , for the eight earthquakes studied by Atkinson and Boore (2006), using an updated dataset and a revised point-source stochastic model that captures the effect of a finite fault. We consider four geometrical-spreading functions, ranging from 1/ R at all distances to two- or three-part functions. The Δσ values are sensitive to the rate of geometrical spreading at close distances, with 1/ R 1.3 spreading implying much higher Δσ than models with 1/ R spreading. The important difference in ground motions of most engineering concern, however, arises not from whether the geometrical spreading is 1/ R 1.3 or 1/ R at close distances, but from whether a region of flat or increasing geometrical spreading at intermediate distances is present, as long as Δσ is constrained by data that are largely at distances of 100 km–800 km. The simple 1/ R model fits the sparse data for the eight events as well as do more complex models determined from larger datasets (where the larger datasets were used in our previous ground-motion prediction equations); this suggests that uncertainty in attenuation rates is an important component of epistemic uncertainty in ground-motion modeling. For the attenuation model used by Atkinson and Boore (2006), the average value of Δσ from the point-source model ranges from 180 bars to 250 bars, depending on whether or not the stress parameter from the 1988 Saguenay earthquake is included in the average. We also find that Δσ for a given earthquake is sensitive to its moment magnitude M , with a change of 0.1 magnitude units producing a factor of 1.3 change in the derived Δσ .

Bulletin of the Seismological Society of America↗

USGS2009

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↗

USGS2009

A guide to differences between stochastic point-source and stochastic finite-fault simulations

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control observed ground motions.

Bulletin of the Seismological Society of America↗

USGS2008

Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s

This paper contains ground-motion prediction equations (GMPEs) for average horizontal-component ground motions as a function of earthquake magnitude, distance from source to site, local average shear-wave velocity, and fault type. Our equations are for peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped pseudo-absolute-acceleration spectra (PSA) at periods between 0.01 s and 10 s. They were derived by empirical regression of an extensive strong-motion database compiled by the 'PEER NGA' (Pacific Earthquake Engineering Research Center's Next Generation Attenuation) project. For periods less than 1 s, the analysis used 1,574 records from 58 mainshocks in the distance range from 0 km to 400 km (the number of available data decreased as period increased). The primary predictor variables are moment magnitude (M), closest horizontal distance to the surface projection of the fault plane (RJB), and the time-averaged shear-wave velocity from the surface to 30 m (VS30). The equations are applicable for M=5-8, RJB<200 km, and VS30= 180-1300 m/s. ?? 2008, Earthquake Engineering Research Institute.

Earthquake Spectra↗

USGS2008

Comparisons of shear-wave slowness in the Santa Clara Valley, California using blind interpretations of data from invasive and noninvasive methods

Many groups contributed to a blind interpretation exercise for the determination of shear-wave slowness beneath the Santa Clara Valley. The methods included invasive methods in deep boreholes as well as noninvasive methods using active and passive sources, at six sites within the valley (with most investigations being conducted at a pair of closely spaced sites near the center of the valley). Although significant variability exists between the models, the slownesses from the various methods are similar enough that linear site amplifications estimated in several ways are generally within 20% of one another. The methods were able to derive slownesses that increase systematically with distance from the valley edge, corresponding to a tendency for the sites to be underlain by finer-grained materials away from the valley edge. This variation is in agreement with measurements made in the boreholes at the sites.

Bulletin of the Seismological Society of America↗

USGS2008

Strong-motion data from the two Pingtung, Taiwan, earthquakes of 26 December 2006

1016 strong-motion records at 527 free-field stations and 131 records at 42 strong-motion arrays at buildings and bridges were obtained for the Pingtung earthquake doublet from the Taiwan Central Weather Bureau's dense, digital strong-motion network. We carried out standard processing of these strong-motion records at free-field stations. A data set, including the originally recorded files, processed data files, and supporting software and information, is archived online http:// tecdc.earth.sinica.edu.tw/data/EQ2006Pingtung/. We have not yet completed the processing of the strong-motion array data at buildings and bridges. However, some preliminary results and the strong-motion array data recorded at the second nearest instrumented building to the Pingtung earthquake doublet are shown. This paper is intended to document our data processing procedures and the online archived data files, so that researchers can efficiently use the data. We also include two preliminary analyses: (1) a comparison of ground motions recorded by multiple accelerographs at a common site, the TAP 117 station in Taipei, and (2) attenuation of the horizontal ground motions (peak acceleration and response spectra at periods of 0.2, 1.0, and 3.0 s) with respect to distance. Our comparison study of multiple recordings at TAP 117 indicates that waveform coherence among 20- and 24-bit accelerograph records is much higher as compared to records from 16-bit or 12-bit accelerographs, suggesting that the former are of better quality. For the 20- and 24-bit accelerographs, waveform coherence is nearly 1 over the frequency range 1 to 8 Hz for all components, and is greater than about 0.9 from 8 to 20 Hz for the horizontal component, but only from 8 to 12 Hz for the vertical component. Plots of pseudo-acceleration response spectra (PSA) as a function of distance, however, show no clear indication for a difference related to the performance level of the accelerographs. The ground-motions of the first event (Mw = 7.0) are comparable, or even somewhat lower, than those from the smaller second event (Mw = 6.9), consistent with the relative difference of the local magnitudes (ML = 6.96 and 6.99 for the first and second events, respectively). The ground motions from the first event are generally lower than those predicted from equations based on other in-slab subduction earthquakes, whereas the ground motions from the second event are closer to the predictions. Ground-motions for soil sites are generally larger than those from rock sites.

Terrestrial, Atmospheric and Oceanic Sciences↗

USGS2007

On using surface-source downhole-receiver logging to determine seismic slownesses

We present a method to solve for slowness models from surface-source downhole-receiver seismic travel-times. The method estimates the slownesses in a single inversion of the travel-times from all receiver depths and accounts for refractions at layer boundaries. The number and location of layer interfaces in the model can be selected based on lithologic changes or linear trends in the travel-time data. The interfaces based on linear trends in the data can be picked manually or by an automated algorithm. We illustrate the method with example sites for which geologic descriptions of the subsurface materials and independent slowness measurements are available. At each site we present slowness models that result from different interpretations of the data. The examples were carefully selected to address the reliability of interface-selection and the ability of the inversion to identify thin layers, large slowness contrasts, and slowness gradients. Additionally, we compare the models in terms of ground-motion amplification. These plots illustrate the sensitivity of site amplifications to the uncertainties in the slowness model. We show that one-dimensional site amplifications are insensitive to thin layers in the slowness models; although slowness is variable over short ranges of depth, this variability has little affect on ground-motion amplification at frequencies up to 5 Hz.

Soil Dynamics and Earthquake Engineering↗

USGS2007

Beyond SaGMRotI: Conversion to SaArb, SaSN, and SaMaxRot

In the seismic design of structures, estimates of design forces are usually provided to the engineer in the form of elastic response spectra. Predictive equations for elastic response spectra are derived from empirical recordings of ground motion. The geometric mean of the two orthogonal horizontal components of motion is often used as the response value in these predictive equations, although it is not necessarily the most relevant estimate of forces within the structure. For some applications it is desirable to estimate the response value on a randomly chosen single component of ground motion, and in other applications the maximum response in a single direction is required. We give adjustment factors that allow converting the predictions of geometric-mean ground-motion predictions into either of these other two measures of seismic ground-motion intensity. In addition, we investigate the relation of the strike-normal component of ground motion to the maximum response values. We show that the strike-normal component of ground motion seldom corresponds to the maximum horizontal-component response value (in particular, at distances greater than about 3 km from faults), and that focusing on this case in exclusion of others can result in the underestimation of the maximum component. This research provides estimates of the maximum response value of a single component for all cases, not just near-fault strike-normal components. We provide modification factors that can be used to convert predictions of ground motions in terms of the geometric mean to the maximum spectral acceleration (SaMaxRot) and the random component of spectral acceleration (SaArb). Included are modification factors for both the mean and the aleatory standard deviation of the logarithm of the motions.

Bulletin of the Seismological Society of America↗

USGS2006

Surface waves in the western Taiwan coastal plain from an aftershock of the 1999 Chi-Chi, Taiwan, earthquake

Significant surface waves were recorded in the western coastal plain (WCP) of Taiwan during the 1999 Chi-Chi, Taiwan, earthquake and its series of aftershocks. We study in detail the surface waves produced by one aftershock (20 September 1999, 18hr 03m 41.16sec, M 6.2) in this paper. We take the Chelungpu-Chukou fault to be the eastern edge of the WCP because it marks a distinct lateral contrast in seismic wave velocities in the upper few kilometers of the surface. For many records from stations within the WCP, body waves and surface waves separate well in both the time domain and the period domain. Long-period (e.g., >2 sec) ground motions in the plain are dominated by surface waves. Significant prograde Rayleigh wave particle motions were observed in the WCP. The observed peak ground velocities are about 3-5 times larger than standard predictions in the central and western part of the plain. Observed response spectra at 3 sec, 4 sec, and 5 sec at the center of the plain can be 15 times larger than standard predictions and 10 times larger than the predictions of Joyner (2000) based on surface wave data from the Los Angeles basin. The strong surface waves were probably generated at the boundary of the WCP and then propagated toward the west, largely along radial directions relative to the epicenter. The geometry of the boundary may have had a slight effect on propagation directions of surface waves. Group velocities of fundamental mode Rayleigh and Love waves are estimated using the multiple filter analysis (MFA) technique and are refined with phase matched filtering (PMF). Group velocities of fundamental mode surface waves range from about 0.7 km/sec to 1.5 km/sec for the phases at periods from 3 sec to 10 sec. One important observation from this study is that the strongest surface waves were recorded in the center of the plain. The specific location of the strongest motions depends largely on the period of surface waves rather than on specific site conditions or plain structures. Accordingly, we conjecture that surface waves could be generated in a wide area close to boundaries of low-velocity sedimentary wave guides. In the case studied in this article the area can be as wide as 30 km (from the Chelungpu fault to the center of the plain). Surface waves converted by P and S waves at different locations would overlap each other and add constructively along their propagation paths. As a result, the surface waves would get stronger and stronger. Beyond a certain distance to the boundary, no more surface waves would be generated. Consequently, no more local surface waves would be superimposed into the invasive surface waves, and the surface waves would tend to decay in amplitude with distance.

Bulletin of the Seismological Society of America↗

USGS2006

Orientation-independent measures of ground motion

The geometric mean of the response spectra for two orthogonal horizontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of ground-motion intensity could differ for the same actual ground motion. This dependence on sensor orientation is most pronounced for strongly correlated motion (the extreme example being linearly polarized motion), such as often occurs at periods of 1 sec or longer. We propose two new measures of the geometric mean, GMRotDpp, and GMRotIpp, that are independent of the sensor orientations. Both are based on a set of geometric means computed from the as-recorded orthogonal horizontal motions rotated through all possible non-redundant rotation angles. GMRotDpp is determined as the ppth percentile of the set of geometric means for a given oscillator period. For example, GMRotDOO, GMRotD50, and GMRotD100 correspond to the minimum, median, and maximum values, respectively. The rotations that lead to GMRotDpp depend on period, whereas a single-period-independent rotation is used for GMRotIpp, the angle being chosen to minimize the spread of the rotation-dependent geometric mean (normalized by GMRotDpp) over the usable range of oscillator periods. GMRotI50 is the ground-motion intensity measure being used in the development of new ground-motion prediction equations by the Pacific Earthquake Engineering Center Next Generation Attenuation project. Comparisons with as-recorded geometric means for a large dataset show that the new measures are systematically larger than the geometric-mean response spectra using the as-recorded values of ground acceleration, but only by a small amount (less than 3%). The theoretical advantage of the new measures is that they remove sensor orientation as a contributor to aleatory uncertainty. Whether the reduction is of practical significance awaits detailed studies of large datasets. A preliminary analysis contained in a companion article by Beyer and Bommer finds that the reduction is small-to-nonexistent for equations based on a wide range of magnitudes and distances. The results of Beyer and Bommer do suggest, however, that there is an increasing reduction as period increases. Whether the reduction increases with other subdivisions of the dataset for which strongly correlated motions might be expected (e.g., pulselike motions close to faults) awaits further analysis.

Bulletin of the Seismological Society of America↗

USGS2006

Earthquake ground-motion prediction equations for eastern North America

New earthquake ground-motion relations for hard-rock and soil sites in eastern North America (ENA), including estimates of their aleatory uncertainty (variability) have been developed based on a stochastic finite-fault model. The model incorporates new information obtained from ENA seismographic data gathered over the past 10 years, including three-component broadband data that provide new information on ENA source and path effects. Our new prediction equations are similar to the previous ground-motion prediction equations of Atkinson and Boore (1995), which were based on a stochastic point-source model. The main difference is that high-frequency amplitudes (f ??? 5 Hz) are less than previously predicted (by about a factor of 1.6 within 100 km), because of a slightly lower average stress parameter (140 bars versus 180 bars) and a steeper near-source attenuation. At frequencies less than 5 Hz, the predicted ground motions from the new equations are generally within 25% of those predicted by Atkinson and Boore (1995). The prediction equations agree well with available ENA ground-motion data as evidenced by near-zero average residuals (within a factor of 1.2) for all frequencies, and the lack of any significant residual trends with distance. However, there is a tendency to positive residuals for moderate events at high frequencies in the distance range from 30 to 100 km (by as much as a factor of 2). This indicates epistemic uncertainty in the prediction model. The positive residuals for moderate events at < 100 km could be eliminated by an increased stress parameter, at the cost of producing negative residuals in other magnitude-distance ranges; adjustment factors to the equations are provided that may be used to model this effect.

Bulletin of the Seismological Society of America↗

USGS2006

Report of the workshop on Extreme Ground Motions at Yucca Mountain, August 23-25, 2004

This Workshop has its origins in the probabilistic seismic hazard analysis (PSHA) for Yucca Mountain, the designated site of the underground repository for the nation's high-level radioactive waste. In 1998 the Nuclear Regulatory Commission's Senior Seismic Hazard Analysis Committee (SSHAC) developed guidelines for PSHA which were published as NUREG/CR-6372, 'Recommendations for probabilistic seismic hazard analysis: guidance on uncertainty and the use of experts,' (SSHAC, 1997). This Level-4 study was the most complicated and complex PSHA ever undertaken at the time. The procedures, methods, and results of this PSHA are described in Stepp et al. (2001), mostly in the context of a probability of exceedance (hazard) of 10-4/yr for ground motion at Site A, a hypothetical, reference rock outcrop site at the elevation of the proposed emplacement drifts within the mountain. Analysis and inclusion of both aleatory and epistemic uncertainty were significant and time-consuming aspects of the study, which took place over three years and involved several dozen scientists, engineers, and analysts.

Open-File Report↗

USGS2005

Processing of strong-motion accelerograms: Needs, options and consequences

Recordings from strong-motion accelerographs are of fundamental importance in earthquake engineering, forming the basis for all characterizations of ground shaking employed for seismic design. The recordings, particularly those from analog instruments, invariably contain noise that can mask and distort the ground-motion signal at both high and low frequencies. For any application of recorded accelerograms in engineering seismology or earthquake engineering, it is important to identify the presence of this noise in the digitized time-history and its influence on the parameters that are to be derived from the records. If the parameters of interest are affected by noise then appropriate processing needs to be applied to the records, although it must be accepted from the outset that it is generally not possible to recover the actual ground motion over a wide range of frequencies. There are many schemes available for processing strong-motion data and it is important to be aware of the merits and pitfalls associated with each option. Equally important is to appreciate the effects of the procedures on the records in order to avoid errors in the interpretation and use of the results. Options for processing strong-motion accelerograms are presented, discussed and evaluated from the perspective of engineering application. ?? 2004 Elsevier Ltd. All rights reserved.

Soil Dynamics and Earthquake Engineering↗

USGS2005

On pads and filters: Processing strong-motion data

Processing of strong-motion data in many cases can be as straightforward as filtering the acceleration time series and integrating to obtain velocity and displacement. To avoid the introduction of spurious low-frequency noise in quantities derived from the filtered accelerations, however, care must be taken to append zero pads of adequate length to the beginning and end of the segment of recorded data. These padded sections of the filtered acceleration need to be retained when deriving velocities, displacements, Fourier spectra, and response spectra. In addition, these padded and filtered sections should also be included in the time series used in the dynamic analysis of structures and soils to ensure compatibility with the filtered accelerations.

Bulletin of the Seismological Society of America↗

USGS2004

Can site response be predicted?

Large modifications of seismic waves are produced by variations of material properties near the Earth's surface and by both surface and buried topography. These modifications, usually referred to as "site response", in general lead to larger motions on soil sites than on rock-like sites. Because the soil amplifications can be as large as a factor of ten, they are important in engineering applications that require the quantitative specification of ground motions. This has been recognised for years by both seismologists and engineers, and it is hard to open an earthquake journal these days without finding an article on site response. What is often missing in these studies, however, are discussions of the uncertainty of the predicted response. A number of purely observational studies demonstrate that ground motions have large site-to-site variability for a single earthquake and large earthquake-location- dependent variability for a single site. This variability makes site-specific, earthquake-specific predictions of site response quite uncertain, even if detailed geotechnical and geological information is available near the site. Predictions of site response for average classes of sites exposed to the motions from many earthquakes can be made with much greater certainty if sufficient empirical observations are available.

Journal of Earthquake Engineering↗