Downhole Instrument Orientations and Near Surface Q Analysis From the SMART 2 Array Data

Installation of the SMART2 downhole array in Da-Han Industrial School was completed in May 1992. This array contains one free surface station and three downhole accelerometers down to 200 m · depth. Thirteen events recorded by this downhole array are used to study the orientations of the downhole instruments by cross -correlation method. The results show the longitudinal direction of the instruments at SO m, 100 m, and 200 m depths of downhole accelerometers are N3°E, N91°E, and N75°E, respectively. The near surface Q value is calculated by using the records of three events. The result of Q(0=9.SSf 1.o6 was obtained from the smoothed power spectrum ratios. The surface ground motions of two events are simulated from the observed downhole records and Q value we obtained by using the Haskell method. The results confirm the downhole instrument orientations and near surface Q value that we derived in this study.


INTRODUCTION
There are several studies about finding Q value near the surface in California by com paring the downhole ground motion with the surface ground motion.including Hauksson et al (1987) (Qb=25 average between 1500 m and.420 m depth), Malin et al. (1988) (Qb=9 between 0 and 500 m depth), Seale and Archuleta (1989) (Qb=lO between 0 and 166 m depth), Gibbs and Roth (1989) (Q=4 between 57 and 102 m depth).Fletcher et al. (1990) (Qb=8 at one and 11 at the others in the upper 50 m) and Archuleta et al. (1992) (Q=12 in the upper 200 m), they all found very low Q values near the surface.Recently.Wang (1993) reviewed Q values in Taiwan and pointed out that the Q values of the sediments can be made for further studies.Chang and Yeh (1983) using strong motion data found Q(f)=98fi.o in the upper 11 km and Q(f)=225fl.1 in the upper 80 km for northeMt Taiwan.The only study of the near surface Q in Taiwan wu done by using the SMARTl arr ay data in the Lotung area (Shieh, 1992).The SMART2 array (Chiu and Yeh, 1991) is located in the Hualien area.Three downhole accelerometers are installed in the Da-Han Industrial School at depths of 50 m, 100 m, and 200 m.This downhole array gives us an opportunity to study the near surface Q value in the Hualien area.The orientations of the downhole instruments are not measured since the installation.Before doing the Q value study, we must solve the problem of the downhole instrument orientations.Several methods had been used to check the downhole instrument orientation, for example, polarization method (Vidale, 1986) and cross-correlation method (Yamazaki et al., 1992).In this study, we used the cross-correlation method to estimate the instrument orient�tions of the downhole array.To check the estimated value of instrument orientation and Q value, we used the Haskell method to simulate surface ground motion by using the downhole record as input motion.From the similarity between the synthesiz, ed results and the observed records, we can show the exactness of the instrument orientations and near surface Q value we obtained.

DOWNHOLE ARRAY AND DATA
The SMART2 downhole array is located in the Da-Han Industrial School in the Hualien area.This arr ay consists of one free surface and 3 downhole accelerometers whose depths are 50 m, 100 m, and 200 m.The four FBA sensors are connected to two 6-chann el SSR-1 digital recorders.Each recorder has 16 bits resolution and the sampling rate is 200 points/sec.
An Omega clock timing system provides one ms accuracy and continuously synchronizes the clock to standard time.
The SMART2 downhole array began operating on May 6, 1992.From this date through Sep. 1, 1992, thirteen earthquakes were recorded by this downhole array (Table 1).These events are used to calculate the instrument orientations of the downhole array.Figure 1 shows the location of the downhole array and epicenters.Most of the records are too weak to do the near surface Q and simulation study, but fi ve of them were strong enough for our study.In these five events, the ML are larger than 4.5 and the peak ground accelerations of their EW and NS components are larger than 5 .0gals for the station at depths of 200 m.
On the basis of the in situ soil boring and downhole velocity logging (Chung-Chi Technical Consultant Co. 1991), the average shear wave velocity profiles as well as the geological columnar sections are shown in Figure 2. The geological profile includes four layers.The first consists of brown medium-coarse sand with small gravel, the second is gravel and gray mud with some medium-coarse sand, the third is sand with thin clay and small gravel, and the fourth layer includes rock, pebble gravel and medium-coarse sand.

DOWNHOLE INST RUMENT ORIENTATIONS
The problem of downhole instrument orientation is solved by using the maximum cross correlation method.This is a four-dimensional problem, include three components and time lag, as Yamazaki et aL (1992)   where a is the angle waited to be solved.
( 1) (2) If we want to decide the angle a:, a reference .stationwith known instrument orientation is necessary.For the next calculation, we consider a ground motion at the reference point x(t)=[x1 (t),x2(t)].If the reference point and the checking point are not far apart, within a few hundred meters, the existence of coherently propagating waves between the points can be assumed.The orientation difference angle a: between reference station (x) and checking point (y) can be estimated by the maximum cross-correlation coefficient between x(t) and z(t) in the time domain.Since there only two horizontal components in these vectors are used, a sum of two cross-covariance function is considered (3) i=l i=l where E[.] means the ensemble average and T is the time lag between x(t) and z(t).Substi tuting equation (1) into equation (3) results in where tii is the element of the transformation matrix T in equation (1) and Rx;y; (r) is defined as ( 5) In evaluating equations (4) and (5) for the sample processes of x(t) and y(t), the temporal average is used instead of the ensemble average for convenience.Then equation ( 5) is replaced by and where n is the number of discretized steps. At

Q VALUE 373
Frequency dependent Q was found by Aki and Chouet (1975) from studying the coda wave of earthquake in California and Japan.A relationship that Q grows with frequency proportionally as rn was suggested by many authors (e.g., Der and McElfresh, 1977;Tsujiura, 1978;Rautian and Khalturin, 1978;Aki, 1980;Console and Rovelli, 1981;and Rodriguez et al. , 1983).For studying the Q value, we calculate the power spectra of the recorded accelerograms and take a smoothing procedure.A power spectrum is estimated by where A*(w) is the complex conjugate of A(w), and A(w) is the Fourier spectrum of the acceleration time history a(t).In this study, we use the time domain moving window method to smooth the power spectrum.The degree of smoothing depends on the window length.A shorter window length will result in a smoother spectrum (Bath, 1979).The window we use is cosine window, shown as in Figure 5, and the form is : w (t) = 0.5 (1 -cos ( 27r(t -t1 )/tw)) where t1 and t2 are low and high roll-off time, the window length tw equal to (t2-t1) and the window shift length 18 is given as tw/2.In this study, the Q value is defined as Q8, so we rotated the horizontal components into tangential and radial components with the angle obtained by previous section.The power spectrum of a seismic wave, generated from seismic source, propagated through a dispersive medium and received by j-th station with epicentral distance R; can be represented as (Aki and Chouet, 1975;Console and Rovelli, 1981) S;(f,R;) where O(f) is the source spectrum, F(R;) represents the geometric spreading function, v is the group velocity of the wave in medium, and Q(f) stands for quality factor of the path.
Considering the Q between two stations (in this study it is from 200 m depth to ground surface), the power spectrum ratio can be represented as: where subscripts 1 and 2 stand for surface and 200 m deep stations, respectively, � R=R 1 -

R2•
The 200 m distance compared to hypocentral distance is very small, so F(R1)/F(R2) can be assumed equal to 1 and f1RJv equals the known time leg T. Then the spectrum ratio can be represented as: and the Q(f) can be represented as ( 14) where a and b are constants.
Before calculating the value of S1 (f)/S2(f) for obtaining the Q(f), we must consider the effects of amplification in the ground motions.Amplification due to the impedance contrast between two materials is a result of the conservation of energy (Carter et al., 1984).
Assuming complete transmission, the amplification factor for a plane wave traveling from medium 1 into medium 2 is A= � V P2V2 (1 5) where v and p are velocity and density respectively.
Using the velocities and densities obtained from in situ geotechnical survey (Chung-Chi Technical Consultant Co., 1991), the amplification factor between 200 m and ground surface layer can be calculated and was equal to 3. The free surface record was corrected by this amplification factor and free surface effect.The corrected record and the record at 200 m depth were used to calculate the near surface Q value.Figure 6 depicts the Q(f) values by different smoothing window length .From this figure, we can see that a shorter window length results in more convergence Q value at the higher frequency part.The Q values oscillated from 7 Hz to 40 Hz at the window length of 1 second (Figure 6a), and the oscillations decreased as the window length became shorter.More consistent results were obtained in the low frequency part for different window lengths.Through several tests, we selected 0.05 second time window for smoothing, and the least-square fit also shown in Figure 6d, and the result is Q( f)= 9. 55 f 1 •06• From Figure 6d we can see that the results of Qo from event 10, 12, and 11 have become smaller.The magnitude of events 10, 12, and 11 are 5.1, 4.8, and 4.6, and the hypocentral depths are 30.0,15.7, and 11.7 km, respectively.Theoretically, the spectral ratio can delete the source effect, but it may not remove it completely.This effect can include the standard deviation.If we use more events, it may show in the same error band.Comparing the hypocentral depths of these three events, we can see .that the deeper event (event 10) has larger Q0 value.One possible rell$0fl is that the seismic wave from a deeper event will incident more vertically than that from a shallow event.So, the attenuation effect for the vertical incident wave will be smaller.This means that the Qo value will be larger.Since this study has only three events, it does not prove this result.If we have more events we can do deeper discussion of this problem.

SIMULATION OF SURFACE GROUND MOTION
The exactness of the results of the downhole instrument orientations and the near sur• face Q(f) can be checked by using the downhole records •as input motion to synthesize the surface ground motion through the Haskell method.On the basis of the directions we got, Comparing the synthetic and observed seismograms, we can see that the results by using the record at 50 m depths as input motion are better than those using deeper reeords.The simulation results for event 13 are better than those for event 5; that is because event 5 has more high frequency signals and not considers the free surf ace reflection wave as shown  clearly in the records of event 5 (Figure 7).From Figure 8 we can see that although the later phase has a little shift, the amplitude still has yery good fit.These simulation results show that the downhole instrument orientations and the frequency dependent Q obtained in this study are suitable for use.

CONCLUSION AND DISCUSSIONS
Since the installation of the SMART2 downhole array in Dan-Han Industrial School in the Hualien area, we have no idea about the downhole instrument orientations.In this study, we use the earthquake records to solve this problem and calculate the Q value through the spectral ratio method.
On the basis of in situ geotechnical survey, the four•dimensional cross -corre lation method was simplified to a two dimensional problem.This simple cross•correlation method was used to study the orientation of each downhole instrument by fi nding the maximum correlation coefficient from a different rotated angle in respect to the ground surf ace station.The results show the longitudinal directions of the downhole accelerometers at depths of 50 m, 100 m, and 200 ma re N3°±7°E, N91°±10°E, and N75°±10°E, respectively.
Frequency dependent Q was calculated after the orientation correction, and the result of Q(f)=9.55f 1 •06 was obtained from the smoothed power spectrum ratio.Shieh (1992) obtained Q=55.11 ±15.10 average from 1to 22 Hz for Pleistocene sediment layer under the SMARTl array area.When frequency equal to 10 Hz, the Q value is 132.0 in SMART2 downhole array area.The Q value in Da•Han downhole array area is higher than that in Lotung area (SMARTI area).The geology and velocity logging data shows that the alluvium layer under the SMARTI array is softer than the gravel layer beneath the SMART2 downhole area, so, the higher Q value is reasonable.
The one-dimensional Haskell method was used to check the accuracy of the instrument orientations and Q value we obtained.The surface motions were simulated by using downhole records at depths of 50 m, 100 m, and 200 mas input motion.The results were good enough to prove the accuracy of instrument orientations and Q(f) value obtained in this study.

Fig. 3 .
Fig. 3. Cross-correlation coefficient at different angles for the records of the sta tion pairs between (a) surface and 50 m, (b) surface and 100 m, and (c) 100 m and 200 m depths.

Fig. 4 .
Fig. 4. Examples of the velocity waveforms of event 5 after the orientation angle correction.

Table 1 .
Event parameters recorded by the SMART2 downhole arr ay.