Average Spectral Amplification Research Articles

Computation of Ground Motion Amplification Scenario in NCT Delhi for Earthquake Engineering Purposes and Seismic Microzonation

This paper presents a scenario for the spatial variation of the fundamental frequency of the sediment deposits above the basement and the corresponding amplification as well as the average spectral amplification in different frequency bandwidths for the National Capital Territory Delhi (the capital of India). The exposed central quartzite ridge and the Yamuna River channel are responsible for very large spatial variations of the fundamental frequency in the eastern part of the National Capital Territory Delhi. At 20% of the considered sites, a good match is obtained between the fundamental frequency computed numerically using available S-wave velocities to a certain depth and their extrapolation and that obtained experimentally. The computed fundamental and dominant frequencies reveal that both medium-rise (5–10 storey) and high-rise (> 10 storey) buildings in the western part and medium-rise buildings lying in the localities east of or very near to the Yamuna River may suffer heavy to very heavy damage due to the occurrence of the double resonance phenomenon. Furthermore, 1–2-storey buildings lying on the weathered exposed quartzite rock may also suffer heavy damage during local earthquakes because of the occurrence of double resonance. The possible reasons behind the lack of earthquake damage to the Qutab Minar, the tallest brick masonry minaret in the world, over the last 800 years may be the nonoccurrence of double resonance and almost no amplification in the low frequency range. There are two localities in the western part of the National Capital Territory Delhi, namely Kanganheri-Chhawla and Buradi, wherein all sorts of buildings are highly vulnerable to earthquake damage. For the closed Chhatarpur Basin and a semiclosed basin to its northeast, formed due to exposed quartzite rock, three-dimensional (3D) simulations are required to predict the characteristics of basin-generated surface waves and their focusing effects in the Chhatarpur Basin. The average spectral amplification map developed for the 0–10 Hz bandwidth depicts a range of 2.25–4.82 in the National Capital Territory Delhi and may be directly used to transfer the estimated seismic hazard at basement to the free surface.

Local site effect incorporation in probabilistic seismic hazard analysis – A case study from southern peninsular India, an intraplate region

The inclusion of local site effects into seismic hazard analysis is an important issue and has been attempted previously in both deterministic and probabilistic manner. The present study is an attempt to combine the local site response with the standard probabilistic seismic hazard analysis. The site response was computed by performing an equivalent linear analysis in the frequency domain. The input soil profiles for the analysis were taken from the borehole data of the North Kerala region (one of the Southerly states in India). The uncertainty in estimating the shear velocity profile (VS) has been addressed by applying multiple VS–N correlations. The variability in the choice of input motions has been reduced by selecting multiple ground motions representing distinct hazard levels (return period of 50–2000 years). The uniform hazard spectrum developed for the host reference site conditions has been adjusted to the target region and the input motions are scaled accordingly. The analyzed soil profiles were categorized into three distinct soil types namely ‘Sand’, ‘Clay’ and ‘All soil’ based on the predominant soil content. The empirical amplification equation as a function of input rock spectral acceleration (Sar) was developed for each soil type. ‘Sand’ exhibits nonlinear behavior for Sar > 0.1 g whereas ‘clay’ demonstrates sustained amplification at longer periods. The average spectral amplification observed is 3 for ‘All soil’, 5 for ‘clay’ and 3.5 for ‘sand’ in the study region. The regionally developed amplification function aids in transforming a Ground Motion Prediction Equation (GMPE) from generic to site-specific. The modified GMPE is integrated with the regional seismic source model to estimate site-specific probabilistic seismic hazard. The study produces site-specific spectrum and surface hazard maps which can be of direct use to planners and designers in creating a seismic resilient built environment.

A scenario of ground shaking hazard in intracratonic circular basins developed by basin-generated surface waves: an earthquake engineering perspective

This paper presents the comparative scenario of ground motion amplifications in the 2D semi-cylindrical (SC) basin and 3D semi-spherical (SS) intracratonic basin caused by the basin-generated surface (BGS) waves and the associated spatial variations of average spectral amplification, differential ground motion (DGM) and average aggravation factor (AAF). The time-domain seismic responses of both the basins were computed using a recently developed 3D fourth-order accurate viscoelastic finite-difference algorithm based on the well-known GMB-EK rheological model. The analysis of simulated results revealed that AAF and DGM are comparable near the basin-edge in both the basins but the differences are increasing towards the centre of basins due to the focusing of the BGS-waves in the SS-basin. The obtained many-fold increase of 1D/2D-AAFs and DGM at the centre of the SS-basin as compared to the SC-basin reflects the inadequacy of 1D or 2D response of an intracratonic circular basin for the seismic hazard assessment. It may be inferred that the level of damage near the edges of the 2D and 3D circular basins may be comparable but unexpected damage may occur in the central part of a circular basin due to the focusing of the BGS-waves.

Evaluating the effects of ground motion parameters on response spectra in Uttarakhand Himalayas, India

Uttarakhand, a state of India, is located in seismically active Himalayan region and in the proximity of plate boundaries. The effects of important ground motion parameters like magnitude, distance, and local geology and site conditions on acceleration response spectra are examined in Uttarakhand Himalayas in this work. A total of 447 strong ground motion histories (horizontal and vertical) from 42 earthquakes were selected. The results show that the shape of the acceleration response spectra is influenced by the local site conditions and regional geology. The studies are carried out for two categories of sites, i.e., rock sites and soft soil sites. The maximum average horizontal spectral amplification for rock sites is 2.7 at 0.1 s, while for soft soil sites, it is found to be 3.2 at 0.2 s. In the same way, the maximum average vertical spectral amplification for rock is found to be 2.7 at 0.1 s, while for soft soil, it is found to be 2.95 at 0.1 s. The average spectral amplification in vertical component also shifts from low period (rock) to high period (soft soil). The level of spectra increases with decrease in distance for rock sites as well as soft soil sites. When comparing different magnitude earthquakes in different geological conditions, the response spectra are found to follow each other up to 0.04 s, while for period greater than 0.04 s, the spectra of higher magnitude earthquake is observed on the higher side. For soft soil sites, spectra from different magnitude earthquakes are observed to follow each other up to 0.1 s, beyond which they get separated.

Effects of basin parameters on the spatial variation of characteristics of basin generated Rayleigh waves

This paper presents the effects of shape of interface between the sediment and basement rock (SISB), basin-shape-ratio, impedance contrast, sediment-damping and angle of incidence of body waves on the characteristics of basin generated Rayleigh (BGR) waves and associated spatial variations of average spectral amplification (ASA), differential ground motion (DGM) and average aggravation factor (AAF) in the considered 2D basin models. The seismic responses of various basin models were simulated using recently developed viscoelastic P-SV wave fourth-order spatial accurate staggered-grid finite-difference algorithm. It is inferred that the SISB has a major impact on the characteristics of the BGR-waves in basin. The obtained largest and least ASA, DGM and AAF were in the basins with SISB as triangular and trapezoidal, respectively. An increase of ASA, AAF and DGM were obtained with an increase of impedance contrast, sediment quality factor, basin shape-ratio and angle of incidence of body wave. It is also inferred that the generated Rayleigh wave in the rocky area in case of plane wave front with inclination 45° and thereafter their transmission in the basin is responsible for the unexpected AAF of the order of 4.7 in the circular basin.

Quantification of modification of ground motion due to urbanization in a 3D basin using viscoelastic finite-difference modelling

This paper presents the quantification of modification of ground motion due to urbanization in a 3D basin as compared to the free-field motion. The complex interaction effects of basin and city on the ground motion during an earthquake are termed as site–city interaction (SCI) effect in this paper. The cities were developed using 3D building blocks of sixteen-storey (city 1) and eight-storey (city 2) buildings. The analysis, in terms of ground motion perturbation and % reduction in average spectral amplification (ASA) and kinetic energy (KE) as compared to free-field motion, of the simulated responses of the various 3D basin-city models revealed very large role of basin shape, sediment layering, city shape, building type in the city and city density in the SCI effects on the free-field motion. The first spectral amplification peak frequency at the top of the buildings corroborates with the combined fundamental frequency of the building block and sediment deposit in basin. The obtained very large amplification of the order of 49 at the top of a single B8 building may be due to the closeness of the fundamental frequency of the combined basin-building system with the fundamental frequency of the basin and the dominant frequency in the input signal. This was also responsible for the larger % reduction in ASA and KE in city 2 (B8 buildings) as compared to the city 1 (B16 buildings). Based on the analysis of the obtained results, it is concluded that if a city is developed considering into account the building type, city shape and city density as per the basin shape and sediment parameters can be highly beneficial in reducing the earthquake disaster.

Study of Effects of Sediment-Damping, Impedance Contrast, and Size of Semi-Spherical Basin on the Focusing and Trapping of the Basin-Generated Surface Waves

This article presents the effects of sediment-damping, impedance-contrast (IC), and size of semi-spherical (SS) basin on the focusing and trapping of the basin-generated surface (BGS) waves and the spatial-variation of average-spectral-amplification (ASA), differential ground motion (DGM), and average-aggravation-factor (AAF). A frequency-dependent focusing of the BGS-wave is inferred. Increase of ASA, DGM, and AAF with increase of size of the SS-basin with a fixed-shape-ratio revealed that the BGS-wave focusing has counter-balanced the sediment-damping effects. It is concluded that the BGS-wave focusing and trapping in the SS-basin is more sensitive to change of IC as compared to the similar change of sediment-damping.

A Numerical Study of Effects of Valley-Weathering and Valley-Shape-Ratio on the Ground Motion Characteristics

A study of combined effects of valley-weathering and valley-shaperatio on the ground motion characteristics and associated differential ground motion (DGM) is documented in this paper. In order to properly quantify the weathering effects, a forth-order-accurate staggered-grid viscoelastic time-domain finite-difference program has been used for the simulation of SH-wave responses. Simulated results revealed that the defocusing caused by valley is frequency-independent in contrast to the ridge-focusing. A decrease of average spectral amplification (ASA) with an increase of shape-ratio of the non-weathered triangular and elliptical valleys was obtained. Overall, the amplification and de-amplification pattern was larger in case of triangular valleys as compared to the elliptical valleys. It can be concluded that the dwelling within or near the topcorners of weathered valleys may suffer more damage as compared to their surroundings. A weathered triangular valley with large shape-ratio may cause unexpected damage very near its top-corners since both the ASA and DGM are largest.

3D basin-shape ratio effects on frequency content and spectral amplitudes of basin-generated surface waves and associated spatial ground motion amplification and differential ground motion

This paper presents the effects of basin-shape ratio (BSR) on the frequency content and spectral amplitudes of the basin-generated surface (BGS) waves and the associated spatial variation of ground motion amplification and differential ground motion (DGM) in a 3D semi-spherical (SS) basin. Seismic responses were computed using a recently developed 3D fourth-order spatial accurate time-domain finite-difference (FD) algorithm based on the parsimonious staggered-grid approximation of the 3D viscoelastic wave equations. The simulated results revealed the decrease of both the frequency content and the spectral amplitudes of the BGS waves and the duration of ground motion in the SS basin with the decrease of BSR. An increase of the average spectral amplification (ASA), DGM and the average aggravation factor (AAF) towards the centre of the SS basin was obtained due to the focusing of the surface waves. A decrease of ASA, DGM and AAF with the decrease of BSR was also obtained.

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

This paper consists of two parts. The first part of the paper is concerned with developing a 3D staggered grid time-domain finite-difference (FD) code with fourth-order spatial accuracy for simulating the responses of viscoelastic geological models with a continuous variable grid size in all the directions. The 3D FD code is written in Fortran 90. In the developed code, the realistic damping in the time-domain simulation is incorporated based on the generalized Maxwell body rheological model proposed by Emmerich and Korn (GMB-EK) Geophysics 52,1252–1264, 1987 with improvements made by Kristeck and Moczo Bull Seism Soc Am 93, 2273–2280, 2003. The accuracy of implementation of the realistic damping is validated by comparing the numerically computed phase velocity, quality factors and spatial spectral damping with the same based on GMB-EK model and Futterman’s relations. It is also concluded that the grid spacing ratio up to 5.0 can be used unharmed. The second part of the paper presents the application of the developed code to simulate the basement focusing effects on ground motion characteristics in an unbounded medium. The combined effects of sediment damping and the focusing caused by the hemi-spherical (HS) and hemi-cylindrical (HC) synclinal basement topography (SBT) on the ground motion characteristics are studied. The simulated responses and the computed snapshots revealed the SBT focusing and defocusing phenomenon, intense mode conversion and diffractions of the incident waves. A good match of the spectral amplifications caused by the HS and HC basement topography models at their focus with the same computed analytically also reveals the accuracy of the developed FD code. The response of elastic HS and HC basement topography models revealed an increase of spectral amplification with an increase of frequency. Further, an increase of rate of frequency-dependent amplification towards the focus was inferred. The average spectral amplification (ASA) caused by the elastic HS basement topography model at the focus is more than the square of the same caused by the elastic HC basement topography model, and this ratio of ASA is increasing with an increase of sediment damping.

A numerical study of effects of ridge-weathering and ridge-shape-ratio on the ground motion characteristics

A study of combined effects of valley-weathering and valley-shaperatio on the ground motion characteristics and associated differential ground motion (DGM) is documented in this paper. In order to properly quantify the weathering effects, a forth-order-accurate staggered-grid viscoelastic time-domain finite-difference program has been used for the simulation of SH-wave responses. Simulated results revealed that the defocusing caused by valley is frequency-independent in contrast to the ridge-focusing. A decrease of average spectral amplification (ASA) with an increase of shape-ratio of the non-weathered triangular and elliptical valleys was obtained. Overall, the amplification and de-amplification pattern was larger in case of triangular valleys as compared to the elliptical valleys. It can be concluded that the dwelling within or near the topcorners of weathered valleys may suffer more damage as compared to their surroundings. A weathered triangular valley with large shape-ratio may cause unexpected damage very near its top-corners since both the ASA and DGM are largest.

Computation of ground motion amplification in Kolkata megacity (India) using finite-difference method for seismic microzonation

This paper presents the ground motion amplification scenario along with fundamental frequency (F0) of sedimentary deposit for the seismic microzonation of Kolkata City, situated on the world’s largest delta island with very soft soil deposit. A 4th order accurate SH-wave viscoelastic finite-difference algorithm is used for computation of response of 1D model for each borehole location. Different maps, such as for F0, amplification at F0, average spectral amplification (ASA) in the different frequency bandwidth of earthquake engineering interest are developed for a variety of end-users communities. The obtained ASA of the order of 3–6 at most of the borehole locations in a frequency range of 0.25–10.0 Hz reveals that Kolkata City may suffer severe damage even during a moderate earthquake. Further, unexpected severe damage to collapse of multi-storey buildings may occur in localities near Hoogly River and Salt Lake area due to double resonance effects during distant large earthquakes.

Effects of P-Wave and S-Wave Impedance Contrast on the Characteristics of Basin Transduced Rayleigh Waves

Different aspects of body wave amplifications in a basin have been studied in detail in the past. However, the study on amplification of basin-transduced surface waves is very limited, although surface waves are more damaging as compared to body waves. This paper presents the effects of P-wave and S-wave impedance contrast (IC) at the basin-edge on the spectral amplification and complex mode transformation of basin-transduced Rayleigh (BTR) waves. BTR-waves, the acronym for basin-transduced Rayleigh waves, is used in the manuscript. Analysis of simulated results reveals a complex mode transformation of Rayleigh wave after entering the basin. The less dispersed horizontally polarised first mode and highly dispersed vertically polarised fundamental mode of BTR-waves were inferred in the basin. The first mode of BTR-waves is developed in a frequency bandwidth and the frequency content in that is very much dependent on the Poisson’s ratio and fundamental frequency of soil in the basin. An increase of phase velocity of first mode of BTR-waves with Poisson’s ratio is obtained. It is concluded that spectral amplification of BTR-waves depends on both the P-wave IC and S-wave IC at the basin-edge. An increase of the largest and average spectral amplifications of the horizontal component of the BTR-wave is obtained with the increase of both the P-wave IC and S-wave IC. On the other hand, an increase of the largest and average spectral amplification of the vertical component of the BTR-wave is obtained with the increase of P-wave IC, but such a systematic and significant effect is not inferred with the increase of S-wave IC at the basin-edge.

Determination of site amplification in the Los Angeles urban area from inversion of strong-motion records

AbstractThe amplification of strong ground motion at sites in the greater Los Angeles, California, region is determined using the generalized-inverse method of Andrews (1986). Site-amplification estimates are determined at 281 strong-motion sites that provided horizontal-component accelerograms from the 1971 San Fernando, 1987 Whittier Narrows, 1991 Sierra Madre, or 1994 Northridge mainshocks. The estimates are determined relative to the spectral level recorded at a single reference site. In a second inversion, a source-site interaction term is added to Andrews's (1986) model to quantify the effect selected mainshock records have on site-amplification estimates. The source-site interaction term is applied to the San Fernando Valley sites' records of the Northridge earthquake and to three Los Angeles basin sites' records of the Whittier Narrows mainshock.Site-amplification spectra are averaged within two frequency bands: the intermediate-frequency band (IFB) from 0.5 to 1.5 Hz and the high-frequency band (HFB) from 2 to 6 Hz. Results are displayed on maps of surficial geology. Average spectral levels are correlated with average shear-wave velocity in the uppermost 30 m, a geotechnical parameter used by the National Earthquake Hazards Reduction Program (NEHRP) to characterize site amplification. Statistically significant correlation is found in both frequency bands. Average spectral amplification levels for NEHRP class B, C, and D sites in the LA urban area are determined. These averages display an expected increase in spectral amplification with category, with a more pronounced variation in the IFB than in the HFB. Considerable overlap in the one-standard-deviation range of the C and D site levels is found in both IFB and HFB, suggesting that site-specific spectral amplification is influenced by more than just near-surface shear-wave velocity. Average site-amplification levels are compared with those obtained from Northridge aftershock records at 28 collocated sites and are found to be in reasonably good agreement in both frequency bands. Some interesting outliers, that is, sites for which the mainshock- and aftershock-determined amplifications differ significantly, are identified as sites that experienced ground failure during the Northridge mainshock.

Realistic modelling of observed seismic motion in compIex sedimentary basins

Three applications of a numerical technique are illustrated to model realistically the seismic ground motion for complex two-dimensional structures. First we consider a sedimentary basin in the Friuli region, and we model strong motion records from an aftershock of the 1976 earthquake. Then we simulate the ground motion caused in Rome by the 1915, Fucino (Italy) earthquake, and we compare our modelling with the damage distribution observed in the town. Finally we deal with the interpretation of ground motion recorded in Mexico City, as a consequence of earthquakes in the Mexican subduction zone. The synthetic signals explain the major characteristics (relative amplitudes, spectral amplification, frequency content) of the considered seismograms, and the space distribution of the available macroseismic data. For the sedimentary basin in the Friuli area, parametric studies demonstrate the relevant sensitivity of the computed ground motion to small changes in the subsurface topography of the sedimentary basin, and in the velocity and quality factor of the sediments. The relative Arias Intensity, determined from our numerical simulation in Rome, is in very good agreoment with the distribution of damage observed during the Fucino earthquake. For epicentral distances in the range 50 km-100 km, the source location and not only the local soil conditions control the local effects. For Mexico City, the observed ground motion can be explained as resonance effects and as excitation of local surface waves, and the theoretical and the observed maximum spectral amplifications are very similar. In general, our numerical simulations estimate the maximum and average spectral amplification for specific sites, i.e. they are a very powerful tool for accurate micro-zonation