Norwegian National Seismic Network

Technical Report No. 25

Shallow shear wave velocity structure in two sites of Khartoum,

Sudan using methods of seismic dispersion and ambient noise.

Prepared by

Miguel Rodriguez and Jens Havskov

Dept. of Earth Science, University of BergenAllégt.41, N-5007 Bergen, Norway

Tel: +47-55-583600 Fax: +47-55-583660 E-mail: seismo@geo.uib.no

July 2007

Introduction

As part of the cooperation between the University of Bergen, Faculty of Natural Sciences and

research institutions in Sudan, the University of Bergen has allocated funds to initiate the

cooperation and several minor seed projects have been approved (see

www.sudan.mnfa.uib.no). Cooperation in seismology is part of this cooperation.

One of the major problems of Khartoum is to estimate the ground motion amplification and

hence the soil structure. This can be done in several ways, however one simple method used

recently is to use the ambient seismic noise. For this reason, noise data has been collected

recently in Khartoum to be used for testing the method.

Method

A ground motion amplification study requires information on the shear wave velocity

structure of the subsoil. This information allows us to predict the effect of the shallow

stratigraphy on seismic ground motion, or can be used to classify sites based on )30(SV (a

weighted thickness average of the shear wave velocity from the upper 30 meters) values, an

approach currently used in building codes. Traditional seismic prospecting methods face

important difficulties in this task. First, shear-waves are difficult to generate using traditional

sources. Second, in urban sites they may be challenged by severe operational limitations, or

be exceedingly large background noise. For these reasons, methods affected by microtremor

measurements have gained large popularity during recent years.

The microtremor (seismic noise or ambient noise) wavefield is a low level amplitude one,

composed mainly of surface waves, but large enough to be measured with the actual

seismological instrumentation. Since the pioneer work of Aki (1957) much information about

the shallow structure of seismic velocities has been obtained using the dispersion of surface

waves contained in this wavefield. In his method, named Spatial Autocorrelation (SPAC), the

data set is analyzed by computing cross correlations in the frequency domain to estimate the

dispersion curve of the phase velocity. Surface waves at different periods are sensitive to

Earth structure at different depths, with the longer period waves reaching to greater depth.

2

Recent theoretical research has confirmed the conjecture proposed several decades ago and

redacted by Rickett and Claerbout (1999) as: by crosscorrelating noise traces recorded at two

locations at the surface, we can construct the wavefield that would be recorded at one of the

locations if there was a source at the other. Seismic observations confirm the theory using the

ambient noise for recovering coherent and dispersive wave trains of surface waves

propagating between the stations (Shapiro et al. 2005).

In this report, we explore further the applications of the correlation between single stations

pairs to obtain the subsoil structure using the cross correlation in time domain. We used

microtremor data from two sites in Khartoum, Sudan, obtained with the minimum of

equipment: two geophones + a three channels digitizer + a lap-top. We obtain a estimation of

the shallow shear wave velocities in both sites. In one site the results were compared with an

independent estimation of the spectral ratio an obtain a good agreement between the transfer

function. The wavelength range for which the estimated phase and group velocity are reliable

was conditioned by the local velocity structure and the inter-station distances. If the inter-

station distance is too short, there is large correlation between the two stations and no

information can be retrieved. If that distance is too large, the wavelengths may be smaller

than required by the basic sampling theorem, and the π2 ambiguity in the determination of

the phase velocity renders useless the correlation at these distances. In this case, however,

time domains correlations may still be useful, as it is still possible to measure group velocity.

We present the details of the method using the data from the first site and just at the last part

of the report the results for the second site.

Data

Data come from two sites in Khartoum city, Sudan. The first site is located about 50 m from

the Nile in the compound of the Geological Research Authority of Sudan (GRAS) and the

second site on the outskirts of the city.

At both sites ambient noise was recorded using two vertical, 4.5 Hz geophones coupled to a

three channel Sara recorder. This data logger has 24 bit A/D converters for each channel,

which has the same time taken form the PC. At the first site, site 1, the two geophones where

first located with a spacing of 10 m and seismic noise was recorded for approximately 90 sec.

The spacing between geophones was then increased to 30 m and approximately 160 sec were

3

recorded. The spacing was subsequently increased to 50, 60 and 72 meters and recorded,

approximately 170, 140 and 190 sec respectively. The records obtained in the first site are

shown in the Figure 1. We can notice the typical condition of urban site, where peaks of

amplitudes of the seismic noise appears, due to local perturbations, within the stationary

aspect of the entire records.

Figure 1. Microtremors records obtained at Site 1 in Khartum, Sudan. The number shows the inter-station distances. The short st1 and st2 indicate the records for the first and the second geophone. In other distances this presentation remains.

4

The Correlations

The next paragraphs recall the results obtained from the computation of the cross correlation

between two simultaneous traces of ambient noise, recorded at an inter-station distance r. We

deal first with the results for the site 1 in the centre of Khartoum. We consider the

simultaneous and sequential, 10 sec time windows, from the 90 to 180 seconds recorded for

the different inter-stations distance. For each distance these windows were baseline corrected

and cosine tapered over 10% of its length and the normalized time cross correlation between

the signals computed using hamming smoothing (SAC, Goldstein et al., 2003). Then, we

averaged all cross correlation functions computed for these pairs and assign them to the

corresponding inter-station distance. We applied a low-pass, 12 Hz cut filtering allowing us to

eliminate unwanted high frequencies. Figure 2 shows the results as a seismic section.

The resulting cross-correlation contains a surface wave signal coming from opposite

directions along the path linking the stations. We can observe a very clear coherent wave train

in the negative lags (note that the cross-correlation is computed at positive and negative

correlation lag), appearing at increasing time with increasing distance, just as a propagating

signal would appear. A small suggestion of symmetry can be seen in the positive lags. These

two signals appear at positive and negative correlation lags but although the two signals

sample the same structure between a station pair, the noise (source) characteristics in both

directions may be very different, so the spectral content of the cross-correlations may differ

appreciably. At this time any of our cross correlations can be renamed as a seismogram that

would be recorded at one of the stations if in the other would be a source. A superficial

source is an effective one when we try to generate surface waves.

In the seismic section showed at Figure 2, we try to follow a phase between the seismograms,

for example a local maximum, minimum or one zero crossing of each trace in all the section,

but we can not do that for distances, approximately, greater than 30 m. In contrast to that, the

maximum of the envelope can be followed in negatives lags for the whole section, from zero

meters until 72 meters, as a manifestation of the approximate arrival time for Rayleigh waves

(remember that we use the vertical component) in this band of frequencies. In fact, we can

measure 151.7 m/s and we can associate this group speed to the band width of frequencies

near of the predominant frequency of this signal. Now, we proceed to measure the dispersive

properties of these seismograms under the assumption that the different periods are sensitive

5

to different depths. That is, the dispersion curves are a manifestation of the shallow shear

wave structure beneath the site. One way to do that is by using the Multiple Filter Analysis

(MFT) included in software package of Herrmann, (2003).

Figure 2. Seismic section formed with the correlation functions computed for all station pairs measures in site 1 and low pass filtered 12Hz cut. Each trace is plotted at the corresponding inter-station distance. The diagonal line indicates the approximate arrival time for Rayleigh waves in this band.

The Multiple Filter Analysis allows us to estimate the dispersion curve of the group speed.

The manual of MFT96 program in Herrmann (2003), gives the details of the method and of

the operation itself. For all five seismograms we do the MFT analysis and we find a good

agreement of the group speed dispersion structure just for those seismograms associated with

distances grater than 30 m. In Figure 3 shows the group velocity measures from the cross

correlation computed for 72m. The maximum amplitudes were selected by looking in the

maximum amplitude region of the image, which suggests energy which propagates mainly,

6

with group velocities between approximately, 100 and 230 m/s, in agreement with what we

measured using the envelopes of the seismic section. When we are looking at this kind of

images we have in mind the dispersive characteristics of the first three Rayleigh modes for a

single surface layer, also a title of the excellent paper by Mooney and Bolt (1966). These

measurements of group velocity were interpreted as group velocities of the fundamental mode

of Rayleigh wave and were incorporated as data for the inversion to the velocity structure.

Figure 3. Example of dispersion measurements. Right: the cross-correlation computed at negatives lags between the station pair which are separated 72 m at site 1. Middle: MFT diagram in which the white points are the group speed measures interpreted as the dispersion of the fundamental mode of Raleigh waves. The symbols represent the local maximums. The square represent the biggest one, the circle the follow and so subsequently. Left: The amplitudes estimated in the multiple filtering.

7

Not only group velocities estimations can be done from our seismograms. The dispersion

curve of the phase velocity can also be computed from the traces that compose the seismic

section for the site 1. A method to estimate the phase velocity dispersion curve is that

proposed by McMechan and Yedlin (1981) with an adaptation done by Mokhtar et al (1988)

and implemented as POM96 in Herrmann (2003). See the manual for details. The result is an

image in the slowness-frequency domain where are included many phase velocities for each

frequency, see Figure 4. There is a challenge for the analyst to identify the phase velocities

significant in each case. We follow the same idea used in the case of group velocity. Looking

for the region of maximum amplitudes and then choosing the points which describes normal

phase dispersion (phase velocity decreasing with frequency).

Figure 4. Examples of images obtained in the slowness-frequency. The solid squares, in white, show the result of the manual pick and were interpreted as part of the dispersion curve of the phase velocity of the fundamental mode of the Rayleigh wave.

8

As a matter of fact, we used two lines as limits of the region where we must look for. The first

line limits the high frequencies in terms of the sampling theorem, which predicts a line of

constant wavelength through the phase velocity-frequency plane. In the case of the site 1 we

have a minimum inter-station distance of mr 10min = and the high frequency limit is shown in

the Figure 5 as a line of constant wavelength λ = 20 m. Also, we include in Figure 5 the line

of constant wavelength associated a inter-station distance of 30 m. The phase velocity

estimations in the frequency band of 5.2 - 9.5 Hz come mainly from the seismogram

associated with inter-stations distance of 10 meters. While that for frequencies larger than 4.1

Hz and until 5.2 Hz, the significant phase velocities appearing , comes from that of 30 m. It is

clear now that the main contributions to the measures of phase speed are included in the

seismograms associated a inter-station distances computed at 10 and 30 meters. We can

observe in Figure 5 that for frequencies smaller than 4.0 Hz the phase speed estimated has the

shape of the alias manifestation. The frequency of 4.0 is the limit in low frequencies.

Figure 5. Dispersion of phase velocity. Two estimation obtained from the same seismic noise data. The phase velocity was computed from the slowness-frequency and by SPAC method. In terms of the uncertainties offers by the two estimations, and in the band width of frequencies between 4.1 and 8 Hz we observe a good agreement in both curves. Differences are less than 50 m/sec.

9

The amplitude spectra for the seismograms obtained at 72 and 75 m of inter-station distances

for site 1 and the site 2, respectively are shown in the Figure 6. At 72 meters, for the site1, the

energy is concentrated in the frequency range 3.5 and 7.5 Hz. In contrast with the spectrum of

site 1, for 75m at site 2, the maximum is located in the band between 6 and 12 Hz. These

predominant band widths of frequency are forced by the different seismic structure at site 1

and site 2.

Figure 6. Spectral amplitude of the seismograms computed for the 72 and 75 m of inter-station distance. The line between 2 and 10 Hertz identify the dominant width band frequencies.

10

Dispersion curves and the shear wave velocity structure

The inverse problem to estimate a shear wave velocity structure from a dispersion curves is an

old one in seismology. We refer to the Herrmann manual for the adequate use of his SURF96

software which has been used for many years. In this section we discuses the dispersion

curves obtained and present the shear wave velocity structure estimated at both sites. The

estimations of the phase and group velocity obtained from the seismograms generated by the

cross correlations between stations pairs are included in figure 7. These measures are the

basic data used in the inversion to a shear wave velocity structure.

One first check of these results is the comparison between the phase velocity dispersion

curves obtained from the McMechan and Yedlin (1981) procedure obtained here and the

dispersion curve derived from the SPAC method at site 1. See figures 5 and 7. In both

methods, an error bar can be estimated and a very good agreement in the frequency range

from 4.1 – 8.0 Hz can be observed in these terms,. For frequencies less than 4.0 Hz, the

results from both methods are not reliable. For frequencies greater than approximately 10 Hz,

phase velocities from the SPAC method increase with frequency. At these high frequencies,

wavelengths become shorter than 20 m and we approach to the limit imposed by the

fundamental sampling theorem, as is shown by the line of a constant wavelength of 20 m

fixed by the minimum inter-station distance of 10 m in this site. The dispersion curve of phase

speed increase with period, figure 4. At low periods the curve approaches to a, approximately,

constant phase velocity of 200 m/s, at high periods the phase velocity increases until

approximately 450 m/s, in a period of 0.25 s. The phase velocity dispersion curves were

interpreted as a manifestation of the fundamental mode of Rayleigh wave. These measures of

phase velocity dispersion are part of the dispersion data used in the inversion to estimate a

shear wave velocity structure.

Figure 3 shows a complicated dispersion pattern. For the range of periods of 0.15 and 0.5

seconds the estimated values are between the 120 and the 230 m/s. In this range the group

velocity exhibit two minimum, the dominant one is located near of 0.19 s and both have a

similar broad. For periods grater than 0.5 s and until 0.6 s the group velocity increase as it is

expected to reach approximately 450 m/s.

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We have inverted, jointly, the phase velocity dispersion curves and the group velocity

estimates in the range of 0.09 and 0.25 s. See Figure 7. For the inversion of the phase and

group velocity dispersion curves we have fixed arbitrarily the layer thicknesses, small enough

to give flexibility to the inversion, but accepting that our data is insufficient to constrain the

model completely.

Figure 7. Theoretical and observed phase and group velocities for the best-fitting model from Rayleigh waves. Solid lines represent the computed dispersion curves of the phase and group speed for the fundamental mode of Rayleigh waves of the model inverted from the observations.

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The initial model assigned was a shear wave velocity of 0.288 km/sec, density was set to 1.8

gr/cm3 and the Poisson ratio was fixed to 0.25. We inverted exclusively for S-wave velocity

and computed P-wave velocity and density from the Poisson ratio and the density-P wave

velocity relationship. The frequency range where our phase velocity dispersion values are

reliable implies that we are able to constrain the S-wave velocities in, approximately, the

upper 30 m. The solid line in Figure 7 corresponds to the dispersion curves of phase and

group velocity for the fundamental mode of Rayleigh waves computed for the final profile

inverted from the data for this site 1. Table I includes the final seismic structure model

obtained in this inversion. An example of this inversion is shown in Figure 8 for site 1.

Figure 8. Shear-wave velocity profiles inverted from group and phase velocity dispersion curves for the Site 1 The circle and the triangles are observed phase and group velocity respectively. Given the frequencies for which phase dispersion was observed, these profiles are reliable only down to approximately 30 m depth.

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We are interested in site amplification, however, and group and phase velocity dispersion

curves and a model cannot be our final result. In order to compute local amplification, we

have extrapolated the superficial seismic structure obtained from the inversion of group and

phase velocity dispersion curves by assuming and half-space beneath 24 meters depth.

Finally, we computed transfer functions for vertical incidence of shear-waves on the profile

shown in Figure 8 and listed in Table I. The results are given in Figure 9. Maximum

amplification attains about a factor 15 at predominant band frequency of 4-7 Hz. There is a

local maximum with amplification of 10 at 0.75 Hz. In this site has been reported recently a

predominate frequency value of fp=1.3 Hz. by Elkhidir B.A. (2006), however this value can

not be picked from their spectral ratio reported. One first check of these Transfer functions

will be possible when checked first experimental results of predominant frequency be

available for this site.

Figure 9. Transfer functions computed for vertical, plane, P and shear-wave incidence on the velocity profile estimated for site 1 and shown in the preceding figure. Attenuation was neglected.

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In site 2 we follow a similar procedure in the field work and in the data processing as in site 1.

Using the same equipment as in the site 1 we measure the ambient noise in a line with inter-

station distance of each pair of 5, 25, 50, 75, 100, 125, 150, 175 and 200 meters, for

approximately 200 seconds. Additionally we take other measures in the same site but in a

perpendicular direction. The inter-station distances in this case were 5, 22, 47 and 68 meters.

The correlations for all pairs are shown in Figure 10 in a time-distance plot. For inter-station

distances of approximately 5, 20, 50 and 75 meters we can compare the correlation-based

seismograms computed from ambient noise measures in both, perpendicular directions. The

differences of the two seismograms associated to 5 meters are minimal. In 20 meters the

differences are the manifestation of different distances (25 meters in one direction and 22

meters in the other direction), the same can be said for the inter-station distance of 75 meters.

It is not the case for the, approximately, 50 m where the differences are major and cannot be

justified in terms of the distance. Local perturbation can be a cause of this observation. In

general the character of the section is complex and the frequency content is in the band width

of between 5 to 12 Hz. See the spectral content in Figure 6.

The envelope of the traces shows clearly that we can follow some maximums, it is the case of

the solid line included in the Figure 10, which represent a speed of 523 [km/s]. In contrast

with that, once we observe the difficulties for to follow a phase. We can follow a phase just

20 meters as can be noted in the figure 10.

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Figure 10. Seismic section formed with the correlation functions computed for all station pairs measures in site 2. Each trace is plotted at the corresponding inter-station distance. Two traces are presented at inter-station distances of approximately 5, 20, 50and 75 meters, correspond with similar distances used in the two perpendicularly directions. The line represent a group speed of 523 [m/s].

The inversion of the dispersion curves to the shear wave velocity structure was computed in

two ways. First, we have fixed arbitrarily the layer thickness, in the second we fixed the

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depths from a lithology record obtained in a well 16.2 meters depth. Using SURF96 program

and the fixed depths we inverted for two models of S-wave velocity. Finally, we computed

transfer functions for vertical incidence of shear-waves on the models obtained from the

inversion. The results obtained for the two models are given in Figure 11. Maximum

amplification attains about a factor 12 for the first model. The frequency band of the

amplification peaks is 2.5-6.5 Hz. A similar response is obtained in this frequency band for

the second model. In contrast with that, a second local maximum can be observed for the first

model, which has an amplification factor of 6 at frequency of 0.88 Hz. This local maximum

does not appear when the second model was used.

Discussion

The range of observed wavelengths in site 1 was, approximately between 20 and 110 meters.

The sources of the seismic noise, the shear wave velocity structure beneath the site, the

geophones response and the inter-station distances define this range.

The clearest manifestations of the interaction between the microtremores wave field, and the

inter-station distances assigned by us during the experiment are three. The first is that the

wavelengths smaller than 20 m (the smallest wavelength observed), can not be measured

adequately due that the minimum inter-station distance was 10 m. The second is the lack of

spatial coherency of the signal propagating. In figure 5 we can follow a phase at a maximum

inter-stations distance of 50 or 60 meters because the predominate wavelength is

approximately of 64 m (f ≈ 5 Hz; and c ≈ 320 m/s). The third is that the maximum of the

envelope of the seismograms can be follow in the section at distances larger than one

wavelength.

While the ambiguity in the determination of the phase constraints our measurement of phase

speed for inter-station distances grater than, approximately, one wavelength, the main

contribution of the group speed measures to the study of the dispersive characteristics of a

shallow structure is in larger inter-stations distances. For example, the maximum of the

envelope of the seismograms can be follow in the whole extension of the experiment in site

1. This last observation is more relevant in site 2, figure 10, where we can follow a

maximum in the envelope of the seismograms of the section for near of 200 m, however the

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predominant wavelength in this site is approximately 66 m (f ≈ 8 Hz; and c ≈ 523 m/s),

similar to the site 1. Recently, the literature report significant group speed measures, using

cross-correlation of ambient noise at ratios as smallest as (λ/r) = 0.01, between the

predominant wavelength and the inter-station distance. Actually in that conditions between

the predominant wavelength and the inter-station distance, there is not contribution of the

phase. However, a topic of actual research is to predict the phase at ratios as smallest as (λ/r)

= 0.01, searching in the different contributions to the phase of this kind of seismograms

constructed-based from cross-correlation of ambient noise.

The transfer functions computed has not attenuation, then for frequency greater than

approximately 3 Hz., the amplification is over estimated. In fact, we observe for the site 2, a

factor 12 for the maximum between 2.5-6.5 Hz. We can compare this result with an

amplification factor of, approximately 4, at 6.6 Hz obtained from Nakamura method obtained

recently in the same site, Elkhidir (2006). In contrast with that, the amplification factor, about

6, at frequency near of 0.88 Hz. obtained from the transfer function is in excellent agreement

with the H/V results. Their result is reproduced here in the Figure 12.

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Figure 11. Transfer functions computed for vertical, plane, shear-wave incidence on the velocity profil estimated for the site 2. The solid line is the transfer function obtained when the inversion is done having fixed the thickness of the layers. The dashed line correspond with the model obtained when the thickness are assigned from a lithological log. Attenuation was neglected.

In the second site the computed level of amplification is similar to that observed by Elkhidir

(2006) from spectral ratios of ambient noise. If confirmed, it would be a case where the

results of the Nakamura technique can be used not only as a measure of the predominant

frequency but also as estimation of a factor amplification in the site.

The transfer functions show peaks related to the resonance of different layers or that could

result from the contribution of two or more layers. We cannot ascribe a large significance to

the precise frequency of the resonant peaks in Figure 9 and 10 and therefore we do not claim

that that transfer functions reflect faithfully local amplification at both sites. The layering in

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the models is poorly constrained because of the low vertical resolution of surface wave

dispersion. This, plus the impossibility of relating computed amplification to surface geology

makes it very difficult to propose an amplification factors for the sites based on our results.

.

Figure 12. Site Abu Halima. Shows the spectral ration estimated for the site 2, Abu Halima using Nakmura methode. Is the Figure 4 from Elkhidir A. (2006).

We claim that an adequate use of this techniques allow us to predict the effect of the shallow

stratigraphy on seismic ground motion, or can be used to classify sites based on )30(SV .

However, the limitation of the surface waves-based methods of prospecting the shallow shear

wave structure is ineludibly. The poor depth resolution and the limitations in band width of

frequencies of the dispersion curves observed and its effects on the inversion procedure must

be considerate in the correct interpretation of the results. A strategy would be to use the

seismic model and the transfer functions estimated from this method to calibrate a reference

site, where measures of shear wave structure and densities has been reported in a geotechnical

well or measured with another geophysical method. Then a combination of measures of the

traditional H/V ratio, the shear waves shallow structures and transfer function obtained with

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this two station method using ambient noise, can be used for estimate the amplification

factors required in the site effect study that begun at Khartoum, where the different levels of

ground motion amplification must be measured throughout the city. All this information

added to the surficial and shallow geological data will be useful keys in the adequate

interpretation of the future results and the base of a site effect of ground motion study at

Khartoum.

Conclusions

We have presented a site effect study of two sites in the city of Khartoum based on two

simultaneous ambient noise measures and the surface wave dispersion observed in the

correlation-based seismograms. The equipment required was the minimum: two geophones

(4.5 Hz.), coupled to a three channel Sara recorder and a laptop. Single station HVSR

measurements were carried out before at both sites and analyzed using horizontal to vertical

spectral ratios by Elkhidir B.A. (2006). In site 2, our final resonant peaks are in 0.88 and 3-6

Hz. and amplification factor of 6 and 10, respectively. These values are in good agreement

with those reported by Elkhidir B.A. (2006). Our final shear wave velocity results are well

constrained for the upper 30 m, and show surface shear wave velocities between 70 m/s,

increasing to 700 m/s for site 1 and between 200 m/sec, increasing to 900 m/sec in site 2..

This large velocity increase, however, occurs gradually, in several layers, and not across a

single interface.

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Acknowledgements

We tank to GRAS for supporting data collection and the stay of Jens Havskov. The trip to

Khartoum was supported by the Department of Earth Science of the University of Bergen.

Signal processing benefited significantly from the availability of SAC (Goldstein et al.,

2003). MR would like to thank the Department of Earth Science of the University of Bergen

to receive him during part of his sabbatical leave.

References

1. Aki, K. (1957). Space and time spectra of stationary stochastic waves, with special

reference to microtremors, Bull. Earthq. Res. Inst., Tokyo University, 25, 415-457.

2. Rickett and Claerbout (1999). Acoustic daylight imaging via spectral factorization:

Helioseismology and reservoir monitoring. The Leading Edge. August 1999.

3. Shapiro, N.M., M. Campillo, L. Stehly, and M. Ritzwoller (2005). High resolution

surface wave tomography from ambient seismic noise, Science, 307, 1615-1618.

4. Mooney and Bolt (1966).Dispersive Characteristics of the first three Rayleigh modes

for a single surface layer. Bull. Seism. Soc. Am., 56, 43-67.

5. McMechan, G.A., and M.J. Yedlin (1981). Analysis of dispersive waves by wave field

transformation, Geophysics 46, 869-874.

6. Mokhtar, T.A., R.B. Herrmann, and D.R. Russell (1988). Seismic velocity and Q

model for the shallow structure of the Arabian shield from short-period Rayleigh

waves, Geophysics 53, 1379.

7. Herrmann, R.B. and Ch.J. Ammon (2002). Surface waves, Receiver Functions and the

Crust Structure in Computer programs in Seismology, version 3.30.

8. Elkhidir B.A. (2006). Test of site effect estimation usin H/V Nakamura’s Technique.

Technical report. Geological Research Authority of Sudan (GRAS).

9. Goldstein, P., D. Dodge, M. Firpo, Lee Minner (2003). SAC2000: Signal processing

and analysis tools for seismologist and engineers Invited contribution to the IASPEI

International Handbook-1387. of Earthquake and Engineering Seismology. Edited by

WHK Lee, H. Kanamori, P.C. Jennings, and C. Kisslinger. Academic Press. London.

22

TABLE I. Seismic velocity model for site 1

Thickness,

h (km)

Pvelocity,

Vp(km/s)

Svelocity,

Vs(km/s)

Density,

rho(gm/cm3)

0.003 0.378 0.218 1.77 0.003 0.512 0.296 1.88 0.003 0.495 0.286 1.86 0.003 0.426 0.246 1.81 0.003 0.427 0.246 1.81 0.003 0.552 0.319 1.90 0.003 0.799 0.461 2.03

1.144 0.661 2.16

Appendix A

The required data to estimate a model of shear wave velocity in a site are records from the

ambient noise wavefield. The unit, a pair, is two simultaneous records of ambient noise with

inter-station distance of ∆x [m], and a sampling interval of ∆t [sample/sec]. The minimum

duration of the records is approximately 150 sec., better to record 10 minutes of continuous

ambient noise wavefield at each inter-station distance. Our first site example is a five pairs of

records with inter-station distances of 10, 30, 50, 60 and 72 meters. The records duration are

in the range of 150 – 250 second, with ∆t = 200 [sample/sec]. In five pass we can estimate a

model of shear wave shallow structure.

1. Convert data to SAC format. From the field we receive five files in SEISAN format,

each one associated to an inter-station distance. Convert to SAC format using

SACSEI. Insert in the header of the SAC files the variable, ∆t. The output should be

10 files in SAC format.

2. Compute the cross-correlation. In the SAC prompt, a ‘macro’ of SAC,

CORREL.m, receives as arguments the two filenames of the records of ambient noise

associated to a pair. A typical call to CORREL.m macro is:

SAC> m correl.m gras-10.txt_NOI01_SHZ__SAC gras-10.txt_NOI02_SHZ__SAC

The output is a cross-correlation 10 second long

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3. Compute dispersion curve of phase velocity. For to obtain an image with the

dispersion analysis of phase velocity we use the routine POM96 of Herrmann (2003).

The input to POM96 is the five cross-correlations in SAC format with the header

contain information of inter-station distance. Include it to the header. We can use the

cross-correlation in the positives or the negatives lags or both. Try to use in this

example the negatives one by apply to the cross-correlation the follow SAC

commands and rename the cross-correlations as seismograms. From the image which

result of POM96 you must identify the phase velocities curve. In the main text we

describe one way to do that. The phase velocity information will be the input to the

pass five.

4. Compute dispersion curve of group velocity. To compute a group velocity curve of

the cross-correlation = seismograms we applied the Multiple Filter Analysis. See

Herrmann, (2003). This technique is applied on multiply dispersed signals to isolate

group velocities as a function of time using the MFT96 program. The input is one of

the seismograms computed in pass 4 and a typical call to the program is:

5. Inversion of the surface wave dispersion data. The dispersion curves estimated in

pass 3 and 4 will be included in the file disp.d in the required format. Two more files

are required: modl.in, an initial model by the inversion and the control file, obs.d,

which contains control flags used in running the inversion programs. See manual of

SURF96. The inversion procedure iterate until the changes between the observed and

computed curves are small and the analyst judge that the computed dispersion curves

are enough close to the observed segments of the dispersion measures. A model of the

seismic velocity shallow structure is the output of the inversion procedure and the

input to a routine to compute the transfer function of a stratified medium. The

estimated model of shallow structure of seismic velocities is not unique. We suggest

that the evaluation of the model will be made using a comparison between the transfer

function computed with the estimated model and the results at least of H/V technique.

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