RR CM 0310

CSIR Centre for Mathematical Modelling and Computer Simulation

SEISMIC MICROZONATION:METHODOLOGY AND APPROACH

IMTIYAZ A PARVEZ

Research Report CM 0310

NOVEMBER 2003Bangalore 560 037, India

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Seismic Microzonation: Methodology and Approach

Imtiyaz A. Parvez CSIR Centre for Mathematical Modelling and Computer Simulation

NAL Belur Campus, Bangalore 560037

Abstract: The spate of Earthquakes in the country has heightened the sensitivity of

administrators, engineers and even lay people to risks due to earthquakes. Many metropolitan and big cities in India are situated in the severe earthquake hazard threat in the vicinity of Himalayan region and even in peninsular shield. On January 26, 2001, one of the most destructive earthquakes ever to strike India occurred in the Kachchh region of Gujarat in western India. The earthquake was of magnitude 7.7 (Mw) and the damage was spread over a radius of 400 kilometers including major cities like Ahmedabad, Bhavnagar and Surat at a distance of 240 km, 275 km and 350 km respectively. One can not ruled out a similar threat to Delhi the capital from local and probable catastrophic earthquake due in central Himalaya. There are several other cities like Mumbai, Kolkata, Dehradun, Guwahati and many more sitting in thick sedimentary basins along Indo-Gangetic plane and Bramhaputra valley.

To mitigate the seismic hazard, it is necessary to define a correct response in terms of both the peak ground acceleration and spectral amplification. These factors are highly dependent on the local soil conditions and on the source characterization of the expected earthquakes. This is the time to learn a lesson from Bhuj earthquake and to go for a detailed seismic ground motion modeling for microzonation studies in large urban areas and metroplotan cities of India. The present paper will discuss these issues, the methodologies and some example of site-effects in Delhi city.

Key words: seismic microzonation, site effects, megacities, peak ground acceleration.

Introduction:

A quantitative ground motion prediction is a key for assessing and mitigating the earthquake disaster. Three major factors that control the level of strong ground motion are source, path and site effects. Among them, site effects have sometimes played principal role on damage to buildings, as seen from the Mexico, Kobe, Loma Prieta, Izmit and very recently Bhuj earthquakes. It is inevitable to validate the effects of local site for estimating strong motions and mitigating earthquake disaster. For the purpose, it is keenly required to develop the method for characterizing site effects and to understand soil behaviors during strong shaking. As it has been observed from many earthquake scenarios, the major damage to the buildings and man-made structures is mostly found in the area of soft sediments. The constructive interference of incoming waves due to the effect of 2D or 3D geological structure produced very strong ground motions. One of the basic problems associated with the study of seismic zonation/microzonation is to determine the seismic ground motion, at a given site, due to an earthquake with a given magnitude (or moment) and epicentral distance. The ideal solution for such a problem could be to use wide database of recorded strong motions and to group those

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accelerograms that have similar source, path and site-effects. In practice, however, such a database is not available particularly to the country like India. Actually, the number of recorded signals is relatively low and the installation of local arrays in each zone with a high level of seismicity is too expensive an operation that requires a long time interval to gather statistically significant data sets. Alternatively, one has to choose some analytical, empirical or numerical solutions based on theoretical knowledge of seismic waves, their propagation and excitation due to soft sedimentary layers.

Methodology:

There are several methods proposed to investigate the behaviour of soft sedimentary structure to the excitation of seismic waves. The most common procedure, introduced by Borcherdt (1970), and applied by numerous researchers, is to compare the spectra of seismograms of earthquakes with the ones obtained at a nearby reference station located on competent bedrock. The factors of epicentral distance and source radiation, therefore, are practically the same for both neighbouring sites and the differences in the response can be ascribed to the local geological or topographical characteristics of the site. This technique needs the occurrence of earthquakes and to assume that the radiation pattern and epicentral distances for both the sites are similar. Besides it is needed to deploy instruments at all the sites of interest.

Nakamura (1989) developed a simple technique based on the ratio of the spectra of the horizontal to the vertical components of ground motion generated by microtremors or ambient noise. Lermo and Chavez-Garcia (1994) indicate that the method assumes that the surface layers do not amplify the vertical tremor. Besides it is assumed that, for a wide range of frequencies, the ratio of the horizontal to the vertical spectrum at the base of the system, has a value near unity. According to them, this later assumption was experimentally verified by Nakamura using microtremors recorded in a borehole. Thus, Nakamura concluded that the spectral ratio between the horizontal and vertical component of motion in the same site can be used as an estimate of site effects for internal waves.

Despite the apparent appeal of Nakamuras method (source, radiation patterns, directivity and path effects are discarded), the validity of its results and assumptions has not yet been established, especially with complex and deep soft layered structures. Field and Jacob (1993) worked a 3D model in a simpler layer on a half space with microtremors under a random distribution in space and time of forces applied in selected points on top of the layer. By using Green functions, the horizontal and vertical amplitudes were evaluated and compared with the response spectrum at the surface for the incident SH waves to vertical plane. The peak frequency in both the cases was coincident with the resonance natural frequency of the layer for shear waves vertically incident. Lachet and Bard (1995) concluded that Nakamuras technique may be used to determine the natural resonance frequency of a soft layer, but it fails to predict the amplification of surface waves. Moreover, they showed that the natural frequency of the layer obtained with Nakamuras technique and ambient noise simulations is independent of the excitation source, dependent of Poissons ratio and controlled by the polarization

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curve of the Rayleigh waves. However, the method based on the assumption, not always fulfilled, that the propagation of the vertical component of motion is not perturbed by the uppermost surface layers, and can therefore be used to remove source and path effects from the horizontal components. This method produced some unsatisfactory results, as verified in recent severe earthquakes.

As a matter of fact, instead of waiting for data accumulation, either based on the computation of the spectral ratio between the signal recorded at soft soil and nearby bedrock site, or generation of microtremors of ambient noise to be used for H/V ratio technique, it is more wiser to apply the preventive tool given by realistic modeling, based on computer codes developed from the knowledge of the seismic source and of the propagation of seismic waves associated with the given earthquake scenario. With such approach, source, path and site effect are all taken into account and a detailed study of wave field that propagates at large distances from the epicenter is possible. Actually, the realistic modeling of ground motion requires simultaneous knowledge of the geotechnical, lithological, geophysical parameters and topography of the medium, on one side, and tectonic, historical, palaeoseismological, seismotectonic models, on the other, for the best possible definition of the probable seismic source. The initial stage of the realistic modeling is thus devoted to the collection of all available data concerning the shallow geology, and the construction of a three-dimensional structural model to be used in the numerical simulation of ground motion.

A powerful hybrid technique has been developed by Fh et al., 1993a and 1993b which combines the modal summation (Panza, 1985; Panza and Suhadolc, 1987; Florsch et al., 1991; Panza el al., 2001) and Finite-difference scheme (Virieux, 1984; 1986;), exploiting both the methods to their best. However, the most fundamental data like geotechnical information, S-wave velocity structure at a site where a prediction of ground motion is required, are generally insufficient, therefore, the reliability of the modeling of strong ground motion due to 2D/3D structure is highly dependent on the structure of shallow geology over the bed rock. There are several exploration technique used to obtain the S-velocity structure but the conventional seismic methods are difficult or impossible to implement in urban areas or environmental sensitive areas. To overcome this difficulty, recently very popular technique of Microtremor Array Observation is being applied which makes use of microtremors (ambient noise) found in abundance anywhere in the surface of the earth. The Array Measurement of Mirotremors to obtain the S-velocity structure of surface geology, H/V ratio technique and Numerical simulation technique to ground motion simulation will be discussed in the next part.

Array Measurement of Mirotremors

Array observations of the vertical component of microtremors are frequently conducted to estimate subsurface structures as a shear-wave velocity distribution in urban or environmentally sensitive areas. A key technique developed to comply with the desire is the microtremor survey method (Okada, 1998; Okada et al., 1990) which makes use of microtremors found in abundance anywhere on the surface of the earth; that is, the

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frequency-wave number power spectral method (f-k method) (Asten and Henstridge, 1984; Horike, 1985; Matsushima and Okada, 1990; Yamanaka et al., 1999) and the spatial autocorrelation (SPAC) method (Aki, 1957; Henstridge, J.D., 1979; Okada, 1998). In recent years both the methods have become of major interest as a tool that could yield more quantitative information such as shear-wave velocity and thickness of sediments over basement. Both f-k and SPAC methods are based on the assumptions that microtremors are a spatiotemporally stationary stochastic process. The f-k method is an application of the technique developed to detect nuclear explosion using a seismic network with a diameter as large as 200 km. The statistical parameter called the frequency-wavenumber power spectral density (f-k spectrum) played a central role in the detection of nuclear explosions. Its principle is to detect relatively powerful seismic signals from noise and it can separate multimode surface waves as well as body waves, but it requires a seismometers array with sets of stations that are distributed uniformly in azimuth, with a variety of distances between stations to ensure high resolution estimates for the f-k power spectrum. This technique requires large number of stations in the array at least seven for reliable results (Kudo et al., 2002).

Figure 1. A flow of observation and analysis in the SPAC method for estimating S-wave velocity structures using Array observation of microtremors (after Kudo et al., 2002)

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On the other hand, SPAC method requires fewer stations (practically three or four stations as a minimum requirement) and is based on the theory developed by Aki (1957). He gave a theoretical basis of the spatial autocorrelation coefficient defined for microtremors data and developed a method to estimate the phase velocity dispersion of surface waves contained in microtremors using a specially designed circular array. Henstridge (1979) also introduced a licit expression of the relationship between the spatial autocorrelation coefficient and the phase velocity of fundamental-mode Rayleigh waves. Okada (1998) extended it to an exploration method and is currently called the SPAC method. The flow of the observation and analysis in applying the method is shown in figure 1. For a circular array of stations for microtremor observation, let us represent harmonic waves of frequency of microtremors by the velocity wave forms

),,0,0( tu and ),,,( tru observed at the centre of the array )0,0(C and at point ),( rX of the array. The spatial autocorrelation function is defined as

),,,,().,,0,0(),,( trutur = (1)

where )(tu is the average velocity of the wave form in the time domain. The spatial autocorrelation coefficient is defined as the average of the autocorrelation function in all directions over the circular array:

=pi

pi

2

0

),,(),0(.21),( drr (2)

where ),0( is the SPAC function at the centre C(0,0) of the circular array. By integration of equation (2) one can find

= )(),( 0

c

rJr (3)

where J0(x) is the zero-order Bessel function of first kind of x and c( ) is the phase velocity at frequency . The SPAC coefficient ),( r may be obtained in the frequency domain using the Fourier Transform of the observed microtremors:

[ ]=pi

pi

2

0 ),,().(),,(

21),( d

rSSrSR

r

XC

CXe (4)

where )(CS and ),,( rS X are the power spectral densities of microtremors at sites C and X respectively, and ),,( rSCX is the cross spectrum between ground motions at these two sites. Thus the SPAC coefficients may be obtained from averaging normalized coherence function defined as the co-spectrum between point C and X in the direction . From the SPAC coefficients ),( r , the phase velocity is obtained for

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every frequency from the Bessel function argument of equation (3), and the velocity model can be inverted.

By numerical simulations using array of seven stations, as shown in figure 1, Miyakoshi et al., 1996 concluded that the observable maximum wavelength is approximately 10 times the array radius by the SPAC method, independent of the directions of the waves and their numbers; and roughly five times or the less of the array radius by the f-k method in the case of plural wave-propagations. The observable minimum wavelength, which is essentially limited by the spatial aliasing or by the minimum distance between stations, has no significance difference between the SPAC and f-k methods (Okada, 1998)

Nakamura H/V ratio technique for resonance frequency

The other most popular technique of Nakamura (1989) is very widely used to obtain quick Microzonation map of any large urban area with the use of microtremor measurements for the estimation of resonance frequency and site-effects. However, the site amplification obtained by this technique is questionable, as reported in many papers. This technique has been described in several papers and is based on the assumptions for the fundamental characteristics of microtremors.

Usually it is assumed that the transfer functions of surface layers can be given by the ratio

B

ST H

HS =

However, considering the great contribution of Rayleigh wave propagation for the ambient noise, it will be necessary to convert the ratio HS/HB, in order to estimate a transfer function for microtremor measurements. Assuming that the vertical tremor is not amplified by the surface layers (figure 2), the ratio ER defined below should represent the effect of the Rayleigh wave on the vertical motion.

B

SR V

VE =

VS Surface HS LR Soft Layer VB

Substratum HB

Figure 2. Illustration of the simple model assumed for the interpretation of microtremor H/V ratio as defined by Nakamura (1989)

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Assuming that the effect of the Rayleigh wave is equal for vertical and horizontal components, it is possible to define a corrected modified spectral ratio,

BS

BS

R

TM VV

HHESS ==

As a final condition it is assumed that for all frequencies of interest

1=B

B

VH

Thus, an estimate of the transfer function is given by the spectral ratio between the horizontal and the vertical components of the motion at the surface

S

SM V

HS =

Some of the above conditions were already tested, experimentally and theoretically by different authors (Jensen, 2000; Bour et al., 1998; Teves-Costa et al., 1995; Lerno and Chavez-Gacia, 1994; Nakamura, 1989 etc.).

Numerical Simulation of Strong Ground Motion:

Fh et al., (1993a, 1993b) developed a hybrid method that combines the modal summation technique, valid for laterally homogeneous anelastic media, with finite difference that include the lateral heterogeneity of the 2-D subsurface geological structure and optimises the use of the advantage of both methods. The modal summation technique is applied to simulate propagation from the source position to the sedimentary basin or the local irregular feature of interest and the finite difference method is used in the laterally heterogeneous part of the structural model, which contains the sedimentary basin (See Figure 3).

This hybrid approach allows us to calculate the local wavefield from a seismic event, both for small (a few kilometers) and large (a few hundreds of kilometers) epicentral distances. The use of the mode summation method helps to include an extended source, which can be modelled by a sum of point sources appropriately distributed in time and space. This allows the simulation of a realistic rupture process of the fault. The path from the source position to the sedimentary basin or the local heterogeneity can be approximated by a structure composed of flat 1-D homogeneous layers. The finite difference method applied to treat wave propagation in the sedimentary basin, permits to modelling of wave propagation in complicated and rapidly varying 2-D velocity structures. The coupling of the two methods is carried out by introducing the resulting time series obtained with the mode summation method into the finite-difference computations. The ground motion time series computed for the 1-D modal contain all possible body waves and surface waves consistent with the pre-assigned phase velocity and frequency interval. To excite the finite-difference grid, ground motion time series are computed at adjacent points lying on one side of the 2-D part of the model and sampling different depths along two vertical lines that belong to the regular grid used for discretization of the medium (Fh et al., 1990). In this way the seismic wavefield

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generated and propagated in the 1-D medium is used to excite the 2-D part of the structural model.

Figure 3. Schematic diagram of the hybrid (Modal summation and finite difference method).

The anelasticity is treated in the finite difference computations by introducing into the equation of motion a convolution term. This additional term is represented by a system of differential equations that define a low-order rational function. This function approximates the viscoelastic modules of the generalized Maxwell body and is introduced into the stress-strain relation. The solution of this equation developed as a system of n ordinary differential equations of the first order is possible using a numerical algorithm if the quality factor is constant within a defined frequency band. For the SH wave propagation, the computation scheme follows Emmerich and Korn (1987), for P-SV case by Emmerich (1992). Furthermore, the ground agreement of the 1-D analytical and hybrid method results allows establishing to which depth the grid as to be extracted to guarantee the completeness of all the signals introduced into the 2-D model. In this

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way, it is possible to study the wave propagation in 2-D heterogeneous media, as sedimentary basins, with a significant accuracy in computations (Panza et al., 2001)

The initial stage of this work requires collection of all available data concerning the shallow geology, and the construction of cross-sections along which to model the ground motion. It is a multidisciplinary activity by nature, since the required information is obtained from different disciplines, as seismology, history, archaeology, geology and geophysics. Final product is a map of expected ground motions, which in turn constitutes the basis for realistic modeling of ground motion Thus, a complete database in terms of hazard parameters can be constructed immediately, until more experimental evidence and recordings become available. This database would then, naturally be updated continuously by comparison with incoming new experimental data.

Numerical simulation of ground motion for site-effects in Delhi city: an example

Delhi represents a typical example of a megacity, which is under severe seismic threats not only from the local earthquakes but also from the Himalayan earthquakes, located just 200-250 km from the city. The city has already suffered serious damages in the past because of the degraded conditions of the historical built environment, and because of severe local site amplification. In the present scenario, the high density of population and the kind of built environment increase the vulnerability of many parts of this megacity. Such vulnerability may be reduced through the retrofitting of ancient buildings and monuments and through the design of reinforced concrete structures that are able to better resist the high amplitudes of the seismic ground motion. Sound anti-seismic construction requires the knowledge of seismic site response, both in terms of peak ground acceleration and response spectral ratio. Parvez et al., 2002a, 2002b & 2004 have worked on site specific microzonation of Delhi city using hybrid technique discussed above for realistic modeling of ground motion along 2-D structures. They generated synthetic seismograms along two representative geological cross-sections in Delhi City, the NS cross-section runs from ISBT to Sewanagar and another EW cross-section from Tilak Bridge to Punjabibagh. These profiles, initially available up to 30-35 m of depth, have been further extended down, to approximate the bedrock depth level, using Iyengar (2000) data. The details of the material properties of these cross-sections are given in Parvez et al., 2002a, 2002b & 2004.

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Figure 4: The NS Cross section and corresponding synthetic strong motion records computed for 1720 earthquake. The maximum amplitude value in cm/sec2 is also indicated.

The synthetic seismograms (SH- and P-SV-waves) have been computed with the hybrid method for an array of 100 sites regularly spaced, every 100 meters, along the NS cross section for a source of July 15, 1720 (M =7.4). Figure 4 shows the three-component synthetic strong motion accelerograms computed which clearly define the trend of the amplification effects which very well reflect the geometry of the cross section models. Peak acceleration (AMAX) of 1.6 g is estimated in the transverse component at 10.2 km of epicentral distance from the source which is a quite large value and represents a severe seismic hazard, as it can be expected in the epicentral area of an event of magnitude 7.4. We believe that the peak value within 10 km of epicentral distance is saturated for a large event in terms of damage/ground motion like what is observed at the epicenter. Such high values of AMAX are in agreement with the reports of the damage caused by the 1720 earthquake (Iyengar, 2000). The radial components of ground motion exhibit peak values in the range from 0.41 to 0.59 g, and the vertical components reaches similar peak amplitudes, in the range from 0.42 to 0.43 g.

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(14.0, 4.7, 3.6)

(18.0, 2.8, 5.7)

(18.2, 3.6, 6.1)

Figure 5: The NS cross-section and the corresponding plot of response spectra ratio (RSR) versus frequency. The numbers in brackets represent in order the distance in km, frequency in Hz and value of peak RSR, where maximum amplification is found.

The response spectra ratio (RSR), i.e. the response spectra computed from the signals synthesized along the local model normalized by the response spectra computed from the corresponding (same epicentral distance) signals synthesized for the regional bedrock model, is another parameter known as site amplification, relevant for earthquake engineering purposes. The distribution of RSR as a function of frequency and epicentral distance along the profile, up to a maximum frequency of 5 Hz is shown for the three

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components in figure. For each component of motion, the numbers in parenthesis identify the maximum amplification. In order, the distance from the source in km, the frequency in Hz and the value of RSR are given. A 5% damping of the response spectra is considered since reinforced concrete buildings are already or will be built in the area. There are sites, where the amplifications are relevant in all the three components, even if the maximum amplifications are always found in the horizontal components. The RSR is 5 to 10 in the frequency range of 2.8 to 3.7 Hz, for the radial and transverse components of motion. The amplification of the vertical component is large at high frequency (> 4 Hz) whereas it is negligible in lower frequency range.

Acknowledgement: The author is thankful to Dr. Gangan Prathap, Scientist-in-Charge, C-MMACS for his support and permission to publish this article.

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