Seismic hazard evaluation for dams in northern Colorado, U.S.A.

A seismic hazard evaluation for three dams in the Rocky Mountains of northern Colorado is based on a study of the historical seismicity. To model earthquake occurrence as a random process utilizing a maximum likelihood method, the catalog must exhibit random space-time characteristics. This was achieved using a declustering procedure and correction for completeness of recording. On the basis of the resulting a- and b-values, probabilistic epicentral distances for a 2 × 10^–5 annual probability were calculated. For a random earthquake of magnitude M _L 6.0–6.5, this distance is 15 km. Suggested ground motion parameters were estimated using a probabilistic seismic hazard analysis. Critical peak horizontal accelerations at the dams are 0.22g if median values are assumed and 0.39g if variable attenuation and seismicity rates are taken into account. For structural analysis of the dams, synthetic acceleration time series were calculated to match the empirical response spectra. In addition, existing horizontal strong motion records from two Mammoth Lakes, California earthquakes were selected and scaled to fit the target horizontal acceleration response spectra.     

Extension of global creepex definition (Ms-mb) to local studies (Md-ML): the case of the Italian region

Creepex, defined as the systematic deviation of the magnitude of a single earthquake from the linear orthogonal regression between local magnitude M_L and coda duration magnitude M_d, calculated for the whole region, is used as a measure of the frequency content of the seismic sources in the Italian region. Predominantly high-frequency events are found in the two areas of Quaternary tectonic shortening in North-Central Italy and in the Calabrian Arc. This result, confirmed by two independent statistical tests, is in agreement with the global pattern obtained from the study of the regression between body-wave magnitude, m_b, and surface-wave magnitude M_s: systematic shift to high frequencies in the energy release of seismic sources located in subduction zones and to low frequencies in zones of spreading. The analysis of the correlation between the patterns of heat flow and of seismic source spectral properties indicates that these source properties, in general, do not reflect thermal conditions in the lithosphere, but rather represent the result of tectonic processes.     

Probabilistic seismic hazard of Pakistan, Azad-Jammu and Kashmir

The seismic hazard study for Pakistan and Azad Jammu and Kashmir has been conducted by using probabilistic approach in terms of peak ground acceleration (PGA) in m/s² and also seismic hazard response spectra for different cities. A new version of Ambraseys et al. (Bull Earthq Eng 3:1–53, 2005) ground acceleration model is used, and parameterization is based on most recent updated earthquake catalogs that consisted of 14,000 events. The threshold magnitude was fixed at M _w 4.8, but seismic zones like northern Pakistan–Tajikistan, Hindukush and northern Afghanistan–Tajikistan border had M _w 5.2. The average normalized ‘a’ and ‘b’ values for all zones are 6.15 and 0.95, respectively. Seismicity of study area was modeled, and ground motion was computed for eight frequencies (0.025, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0, 2.5 s) for different annual exceedance rates of 0.02, 0.01, 0.005, 0.002 and 0.001 (return periods 50, 100, 200, 500 and 1,000 years) for stiff rocks at the gridding of 0.1° × 0.1°. Seismic hazard maps based on computed PGA for 0.02, 0.01 and 0.002 annual exceedance are prepared. These maps indicate the earthquake hazard of Pakistan and surrounding areas in the form of acceleration contour lines, which are in agreement with geological and seismotectonic characteristics of the study area. The maximum seismic hazard values are found at Muzaffarabad, Gilgit and Quetta areas.     

A Bootstrap Test Using Maximum Likelihood Ratio Statistics to Check the Similarity of Two 3-Dimensionally Oriented Data Samples

Comparing three-dimensionally oriented datasets is a problem encountered in various branches of earth science. A simple statistical tool for the comparison of two 3-dimensionally oriented datasets using the bootstrap method in line with the usual nonparametric permutation test is described here. This bootstrap test involves the estimation of maximum likelihood ratio statistic for properly constructed joint frequency tables of the datasets to be compared. This test does not use asymptotic result and will work well even for small sample sizes. Also this test does not make any specific distributional assumptions.     

Seismic hazard assessment under complex source size distribution of mining-induced seismicity

It is well-documented that a variety of factors controlling the rockmass fracturing process in mines often results in a complexity of mining event size distribution. In such cases, the estimation of the probability functions of source size parameterizations, with the use of presently known distribution models, brings about an unacceptable and systematic over- or underestimation of the seismic hazard parameters. It is, therefore, recommended that the non-parametric, kernel estimators of the event size distribution functions, be applied to stationary hazard studies in mining seismicity.These data-driven estimators, adapted to seismic source size characterization, accurately fit all kinds of data underlying distributions, regardless of their complexity. Recently, the non-parametric approach to size characterization was supported by a special method of uncertainty analysis based on resampling techniques. At present, it is a fully developed method, which provides point and interval estimates of size distribution functions and related hazard parameters. Two examples of its use in studying mining seismic data are presented and discussed in this paper. The analyzed data sets were recorded in two different copper mines in Poland. The smoothed bootstrap test for multimodality, which is a specialized tool for investigating the shapes of probability densities, provided highly significant proof that in both cases the probability densities of source size parameterization were complex thus implied the superiority of the non-parametric estimation to the classic, model-based approach in the studied cases. The data were then used to construct non-parametric, kernel estimates of the source size cumulative distribution function (CDF), the exceedance probability and the mean return period. Furthermore, confidence intervals for these quantities were also estimated. The intervals for CDF were narrow, showing that the procedures of non-parametric estimation and resampling based uncertainty analysis were precise. Due to the fact that the mean return period is very sensitive to values of the CDF, in particular for larger events sizes, the uncertainty of the return period estimates was not insignificant but remained manageable. The point and interval estimates of source size CDF and hazard parameters so obtained were compared with the respective point estimates achieved from the inappropriate in the case of complex magnitude distributions, model-based approach.     

Approximate up-scaling of geo-spatial variables applied to deep foundation design

We present a series of simple approximate methods for up-scaling the cumulative distribution function of spatially correlated variables by using an effective number n _e of independent variables. Methods are based on the property of distribution permanence of the gamma and inverse Gaussian distributions under averaging, bootstrap sampling and expansions about the normal and gamma distributions. A stochastic simulation study is used to validate each method, and simple parameters are defined to identify respective ranges of applicability. A practical example is presented where core sample rock strength data are up-scaled to shaft size for probabilistic (risk-based) deep foundation design. Supplemental material is available online.     

On the swelling potential of compacted high plasticity clays

We conducted a study of the spatial distributions of seismicity and earthquake hazard parameters for Turkey and the adjacent areas, applying the maximum likelihood method. The procedure allows for the use of either historical or instrumental data, or even a combination of the two. By using this method, we can estimate the earthquake hazard parameters, which include the maximum regional magnitude Mˆ_max, the activity rate of seismic events and the well-known bˆ value, which is the slope of the frequency-magnitude Gutenberg-Richter relationship. These three parameters are determined simultaneously using an iterative scheme. The uncertainty in the determination of the magnitudes was also taken into consideration. The return periods (RP) of earthquakes with a magnitude M ≥ m are also evaluated. The whole examined area is divided into 24 seismic regions based on their seismotectonic regime. The homogeneity of the magnitudes is an essential factor in such studies. In order to achieve homogeneity of the magnitudes, formulas that convert any magnitude to an M_S-surface scale are developed. New completeness cutoffs and their corresponding time intervals are also assessed for each of the 24 seismic regions. Each of the obtained parameters is distributed into its respective seismic region, allowing for an analysis of the localized seismicity parameters and a representation of their regional variation on a map. The earthquake hazard level is also calculated as a function of the form Θ = (Mˆ_max,RP_6.0), and a relative hazard scale (defined as the index K) is defined for each seismic region. The investigated regions are then classified into five groups using these parameters. This classification is useful for theoretical and practical reasons and provides a picture of quantitative seismicity. An attempt is then made to relate these values to the local tectonics.     

Some source and medium properties of the Vrancea seismic region, Romania

Simple spectral theory of seismic sources was used to determine source parameters directly related to medium properties (stress drop, seismic efficiency and fracture energy) and quality factors of the Vrancea (Romania) seismic region. The results show an increase in maximum static stress drop, maximum seismic efficiency and fracture energy with depth. The seismic efficiency is magnitude independent, but the stress drop is magnitude independent only for events with M_L > 3.8; below this value, the logarithm of stress drop increases quasi-linearly with magnitude. In the depth interval 50–160 km the stress drop increases with a slope of about 2–3 bar/km. The fracture energy per unit area of the fault has values of the order of 10⁵–10⁸ erg/cm².The frequency independent quality factors indicate that the attenuation of P waves is generally higher than that of S waves and that Q_p values are in agreement with recent tectonic models for the Vrancea region: total decoupling of the slab now sinking gravitationally is present only in the southwestern part of the Vrancea region, as suggested by the spatial position of intermediate depth hypocenters.     

Analysis of seismic hazard in landslide-prone regions: criteria and example for an area of Daunia (southern Italy)

In relation to the assessment of earthquake-induced landslide hazard, this paper discusses general principles and describes implementation criteria for seismic hazard estimates in landslide-prone regions. These criteria were worked out during the preparation of a hazard map belonging to the official Italian geological cartography and they are proposed as guidelines for future compilation of similar maps. In the presented case study, we used a procedure for the assessment of seismic hazard impact on slope stability adopting Arias intensity Ia as seismic shaking parameter and critical acceleration a _c as parameter representing slope strength to failures induced by seismic shaking. According to this procedure, after a preliminary comparison of estimated historical maximum values of Ia with values proposed in literature as landslide-triggering thresholds, a probabilistic approach, based on the Newmark’s model, is adopted: it allows to estimate the minimum critical acceleration a _c required for a slope to keep under a prefixed value, the probability of failures induced by seismic shakings expected in a given time interval. In this way, one can prepare seismic hazard maps where seismic shaking is expressed in an indirect way through a parameter (the critical acceleration) representing the “strength” that seismic shakings mobilise in slope materials (strength demand) with a prefixed exceedance probability. This approach was applied to an area of Daunia (Apulia—southern Italy) affected by frequent landslide phenomena. The obtained results indicate that shakings with a significant slope destabilisation potential can be expected particularly in the north-western part of the area, which is exposed to the seismic activity of Apennine tectonic structures.     

Global regression relations for conversion of surface wave and body wave magnitudes to moment magnitude

A homogenous earthquake catalog is a basic input for seismic hazard estimation, and other seismicity studies. The preparation of a homogenous earthquake catalog for a seismic region needs regressed relations for conversion of different magnitudes types, e.g. m _b , M _s , to the unified moment magnitude M _w. In case of small data sets for any seismic region, it is not possible to have reliable region specific conversion relations and alternatively appropriate global regression relations for the required magnitude ranges and focal depths can be utilized. In this study, we collected global events magnitude data from ISC, NEIC and GCMT databases for the period 1976 to May, 2007. Data for m_b magnitudes for 3,48,423 events for ISC and 2,38,525 events for NEIC, M _s magnitudes for 81,974 events from ISC and 16,019 events for NEIC along with 27,229 M _w events data from GCMT has been considered. An epicentral plot for M _w events considered in this study is also shown. M _s determinations by ISC and NEIC, have been verified to be equivalent. Orthogonal Standard Regression (OSR) relations have been obtained between M _s and M _w for focal depths (h < 70 km) in the magnitude ranges 3.0 ≤ M _s  ≤ 6.1 and 6.2 ≤ M _s  ≤ 8.4, and for focal depths 70 km ≤ h ≤ 643 km in the magnitude range 3.3 ≤ M _s  ≤ 7.2. Standard and Inverted Standard Regression plots are also shown along with OSR to ascertain the validation of orthogonal regression for M _s magnitudes. The OSR relations have smaller uncertainty compared to SR and ISR relations for M _s conversions. ISR relations between m _b and M _w have been obtained for magnitude ranges 2.9 ≤ m _b  ≤ 6.5, for ISC events and 3.8 ≤ m _b  ≤ 6.5 for NEIC events. The regression relations derived in this study based on global data are useful empirical relations to develop homogenous earthquake catalogs in the absence of regional regression relations, as the events catalog for most seismic regions are heterogeneous in magnitude types.     

On the validity of time-predictable model for earthquake generation in north-east India

North-east India is seismically very active and has experienced many widelydistributed shallow, large earthquakes. Earthquake generation model for the region was studied using seismicity data [(1906–1984) prepared by National Geophysical Data Centre (NGDC), Boulder Colorado, USA]. For establishing statistical relations surface wave magnitudes (M _s≥5·5) have been considered. In the region four seismogenic sources have been identified which show the occurrences of atleast three earthquakes of magnitude 5·5≤M _s≤7·5 giving two repeat times. It is observed that the time interval between the two consecutive main shock depends on the preceding main shock magnitude (M _p) and not on the following main shock magnitude (M _f) revealing the validity of time predictable model for the region. Linear relation between logarithm of repeat time (T) and preceding main shock magnitude (M _p) is established in the form of logT=cM _p+a. The values ofc anda are estimated to be 0–36 and 1–23, respectively. The relation may be used for seismic hazard evaluation in the region.     

Precursory accelerating seismic crustal deformation in the Northwestern Anatolia Fault Zone

We present the results of a systematic search for the identification of accelerating seismic crustal deformation in the broader northern Aegean area and in northwestern Turkey. We found that accelerating seismic deformation release, expressed by the generation of intermediate magnitude earthquakes, is currently observed in NW Turkey. On the basis of the critical earthquake model and by applying certain constraints which hold between the basic quantities involved in this phenomenon, it can be expected that this accelerating seismic activity may culminate in the generation of two strong earthquakes in this area during the next few years.The estimated epicenter coordinates of the larger of these probably impending earthquakes are 39.7°N–28.8°E, its magnitude is 7.0 and its occurrence time t_c=2003.5. The second strong event is expected to occur at t_c=2002.5 with a magnitude equal to 6.4 and epicenter coordinates 40.0°N–27.4°E. The uncertainties in the calculated focal parameters for these expected events are of the order of 100 km for the epicenter, ±0.5 for their magnitude and ±1.5 years for their occurrence time.     

Magnitude conversion problem for the Turkish earthquake data

Earthquake catalogues which form the main input in seismic hazard analysis generally report earthquake magnitudes in different scales. Magnitudes reported in different scales have to be converted to a common scale while compiling a seismic data base to be utilized in seismic hazard analysis. This study aims at developing empirical relationships to convert earthquake magnitudes reported in different scales, namely, surface wave magnitude, M _S, local magnitude, M _L, body wave magnitude, m _b and duration magnitude, M _d, to the moment magnitude (M _w). For this purpose, an earthquake data catalogue is compiled from domestic and international data bases for the earthquakes occurred in Turkey. The earthquake reporting differences of various data sources are assessed. Conversion relationships are established between the same earthquake magnitude scale of different data sources and different earthquake magnitude scales. Appropriate statistical methods are employed iteratively, considering the random errors both in the independent and dependent variables. The results are found to be sensitive to the choice of the analysis methods.     

Integration and magnitude homogenization of the Egyptian earthquake catalogue

The aim of the present work is to compile and update a catalogue of the instrumentally recorded earthquakes in Egypt, with uniform and homogeneous source parameters as required for the analysis of seismicity and seismic hazard assessment. This in turn requires a detailed analysis and comparison of the properties of different available sources, including the distribution of events with time, the magnitude completeness, and the scaling relations between different kinds of magnitude reported by different agencies. The observational data cover the time interval 1900–2004 and an area between 22°–33.5° N and 25°–36° E. The linear regressions between various magnitude types have been evaluated for different magnitude ranges. Using the best linear relationship determined for each available pair of magnitudes, as well as those identified between the magnitudes and the seismic moment, we convert the different magnitude types into moment magnitudes M _W, through a multi-step conversion process. Analysis of the catalogue completeness, based on the M _W thus estimated, allows us to identify two different time intervals with homogeneous properties. The first one (1900–1984) appears to be complete for M _W ≥ 4.5, while the second one (1985–2004) can be considered complete for magnitudes M _W ≥ 3.     

Atlas of macroseismic maps for French earthquakes with their principal characteristics

The SIRENE macroseismic database has been utilized to draw isoseismal maps for the 140 best-documented French earthquakes, characterized by epicentral intensities of at least V (MSK) and located in all parts of the country. A study of focal depths derived from available local intensity data using an intensity versus distance decay law (Sponheuer) shows that the focal depths of most of the events considered do not exceed about 10 km. Their distribution correlates fairly well with regional dynamic geology features. A relationship is then computed between magnitude, intensity and focal distance, based on 73 instrumenta]ly recorded earthquakes (M _L between 3.3 and 6.3) and on 217 mean radius values (from 2 to 380 km) for isoseismals of intensity VIII to III (MSK). This relationship is applied to historical earthquakes contained in the database SIRENE which are characterised by their intensity only. These results are used in the evaluation as well deterministic as probabilistic of the seismic hazard on the national territory.     

Seismic Hazard and Risk Assessment for Tulbagh,South Africa: Part I – Assessment of Seismic Hazard

In this part of our study the probabilistic seismic hazard analysis (PSHA) for Tulbagh was performed. The applied procedure is parametric and consists essentially of two steps. The first step is applicable to the area in the vicinity of Tulbagh and requires an estimation of the area-specific parameters, which, in this case, is the mean seismic activity rate, , the Gutenberg-Richter parameter, b, and the maximum regional magnitude, m_max. The second step is applicable to the Tulbagh site, and consists of parameters of distribution of amplitude of the selected ground motion parameter. The current application of the procedure provides an assessment of the PSHA in terms of peak ground acceleration (PGA) and spectral acceleration (SA). The procedure permits the combination of both historical and instrumental data. The historical part of the catalogue only contains the strongest events, whereas the complete part can be divided into several subcatalogues, each assumed complete above a specified threshold of magnitude. In the analysis, the uncertainty in the determination of the earthquake was taken into account by incorporation of the concept of `apparent magnitude'. The PSHA technique has been developed specifically for the estimation of seismic hazard at individual sites without the subjective judgement involved in the definition of seismic source zones, when the specific active faults have not been mapped or identified, and where the causes of seismicity are not well understood. The results of the hazard assessment are expressed as probabilities that specified values of PGA will be exceeded during the chosen time intervals, and similarly for the spectral accelerations. A worst case scenario sketches the possibility of a maximum PGA of 0.30g. The results of the hazard assessment can be used as input to a seismic risk assessment.     

Probabilistic seismic and tsunami hazard analysis for design criteria development of a coastal area in the city of Banda Aceh

Both seismic and tsunami hazards design criteria are essential input to the rehabilitation and long-term development of city of Banda Aceh Post Sumatra 2004 (M _w=9.3) disaster. A case study to develop design criteria for future disaster mitigation of the area is presented. The pilot study consists of probabilistic seismic and tsunami hazard analysis. Results of the probabilistic seismic hazard analysis indicates that peak ground acceleration at baserock for 10 and 2% probability of exceedance in 50 years is 0.3 and 0.55 g, respectively. The analysis also provides spectral values at short (T=0.2 s) and long period (T=1.0 s) motions. Some non-linear time-domain earthquake response analyses for soft, medium, and hard site-class were conducted to recommend design response spectra for each site-class. In addition, tsunami inundation maps generated from probabilistic tsunami hazard analysis were developed through tsunami wave propagation analysis and run-up numerical modeling associated with its probability of tsunamigenic earthquake source potential. Both the seismic and tsunami hazard curve and design criteria are recommended as contribution of this study for design criteria, as part of the disaster mitigation effort in the development process of the city. The methodology developed herein could be applied to other seismic and tsunami disaster potential areas.     

First seismic record for intra-arc strike-slip tectonics along the Liquiñe-Ofqui fault zone at the obliquely convergent plate margin of the southern Andes

A temporal seismic network recorded local seismicity along a 130 km long segment of the transpressional dextral strike-slip Liquiñe-Ofqui fault zone (LOFZ) in southern Chile. Seventy five shallow crustal events with magnitudes up to M_w 3.8 and depths shallower than 25 km were observed in an 11-month period mainly occurring in different clusters. Those clusters are spatially related to the LOFZ, to the volcanoes Chaitén, Michinmahuida and Corcovado, and to active faulting on secondary faults. Further activity along the LOFZ is indicated by individual events located in direct vicinity of the surface expression of the LOFZ. Focal mechanisms were calculated using deviatoric moment tensor inversion of body wave amplitude spectra which mostly yield strike-slip mechanisms indicating a NE–SW direction of the P-axis for the LOFZ at this latitude. The seismic activity reveals the present-day activity of the fault zone. The recent M_w 6.2 event near Puerto Aysén, Southern Chile at 45.4°S on April 21, 2007 shows that the LOFZ is also capable of producing large magnitude earthquakes and therefore imposing significant seismic hazard to this region.     

Relationships Between Fundamental Seismic Hazard Parameters for the Different Source Regions in Turkey

Turkey has been divided into eight different seismic regions taking into consideration the tectonic environments and epicenters of the earthquakes to examine relationships of the modal values (a/b), the expected maximum magnitudes (M_max) and the maximum intensities (I_max). For this purpose, the earthquakes for the time period 1900–1992 from the Global Hypocenter Data Base CD-ROM prepared by USGS, and for the time period 1993–2001 from the PDE data and IRIS data are used. Concerning the relationships developed between different magnitude scales and between surface wave magnitudes (M_S) and intensity for different source regions in Turkey, we have constructed a uniform catalog of M_S. We have estimated the values of M_max and I_max using the Gumbel III asymptotic distribution. Highest a-values are observed in the Aegean region and the lowest b-values are estimated for the North Anatolian Fault. Maximum values of a/b, M_max and I_max are related to the eastern and western part of the North Anatolian Fault and the Aegean Arc. The lowest values of all parameters are observed near the Mid Anatolian Fault system. Linear relationships have been calculated between a/b, M_max and I_max using orthogonal regression. If one of the three parameters is computed, two other parameters can be calculated empirically using these linear relationships. Hazard maps of M_max and I_max values are produced using these relationships for a grid of equally spaced points at 1°. It is observed that the maps produced empirically may be used as a measure of seismic hazard in Turkey.     

Computation of the seismic stability of rock wedges

Summary Newmark's concept of computing the permanent displacement under seismic loads has been combined with the conventional limit equilibrium analysis to compute the displacements of a rock wedge. The rock wedge formed by the intersecting planes may or may not have a tension crack in the upper slope surface. As the static analysis of a rock wedge is available from the literature, only the seismic problem is treated theoretically in more details.A computer program has been developed to compute the displacements from the digitised input data of the acceleration-time-history. The program can take into account the water pressure on the intersecting planes and on the planes of the tension crack. The effect of rock anchors if present is also taken care of in addition to static surcharge loads. The program calculates the conventional static factor of safety, remaining resistance against sliding, the critical acceleration, exciting force, relative velocity with time and the cumulative displacements.Two model examples are presented: one with simple sinusoidal acceleration and the other one with actual earthquake data considering the different systems of forces acting on the wedge. The results are critically discussed with respect to the different parameters e. g. anchor forces, water pressure and cohesion influencing the magnitude of displacements under seismic loads. It is shown that the critical acceleration is a better index for the seismic stability than the conventional factor of safety.The critical acceleration presented in this paper serves as a very handy tool for a site engineer to get the first hand information about the stability of the wedge for a given acceleration-time-history without going into the details of dynamic analysis.Notations A, B Inclined intersecting planes - C, D Geometric points on the intersection ofA andB - a _cr Critical acceleration - a _h Horizontal acceleration - a _v Vertical acceleration - a _r Relative acceleration of the wedge - DF Driving force - DF _dyn Dynamic driving force - DF _st Static driving force - FS Factor of safety - g Acceleration due to gravity - m Mass of the wedge - RF Resisting force - RF _dyn Dynamic resisting force - RF _st Static resisting force - RS Remaining resisting force against sliding - RS _dyn Total seismic induced force - RS _st Remaining static resisting force against sliding - s _r Cumulative relative displacement of the wedge - TRS Total remaining resisting force against sliding - v _r Relative velocity of the wedge - W Weight of the wedge - W _A ,W _B Weight of the wedge in the planeA andB - Dip of line of intersection of the planesA andB - Average friction angle - _A , _B Friction angle of planeA andB - I, II, III, IV Points in the curve shown in Fig. 6