The Calculation of Local Magnitude from the Simulated Wood-Anderson Seismograms of the Short-Period Seismograms in the Taiwan Area

The attenuation function, logA0(�.), used in the calculation of local magnitude is derived for the Taiwan area. The simulated Wood-Anderson seismograms are con­ structed by using digital three-components short-period seismogram of the Central Weather Bureau Seismic Network, (CWBSN). The decay of peak amplitude with dis­ tance is the attenuation characteristic of seismic energy. Also, it essentially represents the distance correction term, log Ao (A), after a proper normalization. Considering the focal depth of earthquakes in the Taiwan area, the logA0(6.) functions are: {-0.00716R logR 0.39 (0 km < 6.:::; 80 km) l ogAo(.6.) = -0.00261R 0.83 logR 1.07 (80 km< A) for shallow earthquakes (focal depth, h :::; 35 km) and logAo(.6.) = -0.00326R 0.83 logR 1.01 for deep earthquakes (h > 35 km) where 6. is epicentral distance, R( = ../ 6. 2 + h 2 ) is the hypocentral distance. Results also show that the local magnitude of a deep earthquake is underestimated by using the Richter's logA0(6.) values (1935, 1958) with comparison to the ML value obtained from the revised logAo(A) values of this study. By applying the revised attenuation function, a compatible local magnitude can be calculated from the strong motion data. The conversion of duration magnitude, Mn which is currently used in the Taiwan area, to ML is in the form: ML = l.12Mn + 0.03 ± 0.21 1 Central Weather Bureau, 64, Kung Yuan Road, Taipei, Taiwan, R.O.C.


INTRODUCTION
The local magnitude. ML· popularly used by local seismic network was formulated by Richter (1935Richter ( , 1958 as : where A is the maximum amplitude in millimeters recorded on the standard Wood-Anderson torsion seismograph with static magnification of 2800, natural period of 0.8 second, and damping factor of 0.8 at an epicentral distance L.\, Ao which describes the lo� of energy with respect to distance such as geometrical spreading, anelastic attenuation. and wave scattering is distant dependent. These effects depend on the characteristics of the crust and upper mantle of applied area. The logAo function is of more interesting in engineering seismology and seismology. The ML formulation was originally designed for the region of southern California where the function of logA0(L.\) was empirically detennined. However, equation (1) is also used in the other seismic network to determined local magnitude as the Richter's southern California I og Ao is used with the assum ption of similar characteristics of the crust and upper mantle. On the other hand, a number of studies (Yeh et al., 1982;Bakun and Joyner, 1984;Chavoz and Priestley, 1985), reconstructed the logA0 function for the applied area by using synthetic Wood-Anderson seismogram from strong motion or short period seismogram.
In this paper, I use short period digital seismograms to simulate Wood-Anderson seismo grams. To study the attenuation of seismic wave, a new logA0(.6.) curve can be developed for Taiwan area and calibrated so that logAo(lOO) = -3. The variety of logA0(L.\) for earthquake occurr ing at different focal depths is taken into account. It is due to the wide range of focal depths in Taiwan area. This gives le� Lg wave excitation (Campillo et al. 1983) for earthquake occurri ng beneath the crust.

DATA
Since 1991, the Central Weather Bureau (CWB) has upgraded the seismic network, named as Central Weather Bureau Seismic Network (CWBSN). The local station of new system is installed with a three-component short-period digital seismographs while a real time operation is performed in the center. The seismograph is the velocity type sensor, S13, and has adjustable natural frequency of from 0.75 Hz to 1.1 Hz. The signal is digitized locally by a 12-bit ND converter with 100 samples per second, and then transmitted through the dedicated phone line of 4800 baud rate. The network consists of 68 stations. including 43 digital stations belonging to the CWB and 25 one-component short-period stations of the Taiwan Telemeter{!d Seismograph Network (TISN). which is operated by the Institute of Earth Sciences (JES). Academia Sinica since 1973. The telemetry of TISN is analog transmission. The signal is digitized with the same sample rate as CWB 's signal at the center of CWBSN. The system is well calibrated by using weight lift and 1 Hz harmonic current feed technique. The normalized instrument responses for three instrumental type are shown in Figure 1. The sensitivity factor as well as station parameters are listed in Table 1. The last column of Table 1 is the instrumental type : 1 for S-13 sensor with analog transmission; 2 for L-4C sensor with analog transmission; 3 for S-13 sensor with digital transmission whose response curves are shown in Figure 1. The nwnber written near by curve denotes the instrument type as listed. in the last column of Table 1. At each of the 43 digital stations, a strong motion accelerograph, A800 (Teledyne), is also installed. The instrwnent is a triggered type and the triggered level is generally set up at 2% of the full scale (lg). The local accelerograph is connected to dial-up phone line for data retrieval, calibration, and timing synchronization.
The current local magnitude is calculated from the simulated Wood-Anderson seismo gram from the short-period digital seismogram while the Richter's logA0(Ll) curve (1935, 1958) is used. The uncertainty of local magnitude may be caused by the use of logA0(Ll) which is essentially valid for southern California. Moreover, the Richter's logA0(Ll) func tion (1935,1958) is of depth-independence since almost all earthquakes in southern California are shallow. But, it is not so for earthquakes in Taiwan.
In order to derive a proper logA0(Ll) function which is suitable for the Taiwan area, the ray path of selected earthquakes should be able to sample the whole area. Totally, 224 earthquakes occurring in the period of Sept. 1991 to Feb. 1992 with wide range of focal depth from shallow to 120 km are selected in this study on the basis of the following criteria : (1) The event was recorded by at least 10 digital stations, without clipped amplitude (2048 counts) on horizontal components; and (2) The distance from the nearest station to the farthest one under condition (1) must be greater than 150 km. Figure 2 is a location map to show all events used in this study.

DATA ANALYSIS AND RESULTS
The value of the amplitude of seismic wave at epicentral distance Ll, denoted as A ( Ll ), it is the combined results of material attenuation and geometrical spreading. The A( Ll) can be written as  where 'Y and n are the attenuation and geometrical spreading coefficients respectively; which is affected by site effects and varies with station's magnification. Equation (2) can be related to the function A0(d) shown in equation (1) as long as A(d) = 1 mm at d = 100 km.
The synthetic Wood-Anderson seismogram (SWAS) can be constructed from the short period seismogram. The processing is explained as follows: First. the short-period seis mogram is transformed into frequency domain; Second, the instrument response is removed to have ground displacement spectrum; then multiplied by a Wood-Anderson instrument re sponse in frequency domain; Finally, the spectrum is transformed back into the time domain. To fit all measured peak amplitudes of SWAS (Z, Hl, or H2) into equation (2) individually, I adopt the multiple linear regression analysis method by taking logarithm on both sides of equation (2) as ( 3) The reduced amplitude in the left hand side of equation (3) has linear relationship with hypocentral distance R. In order to resolve C and S terms which both are constants representing different physical meanings, I applied an iteration technique. The term S is initialized as unit. The S tenn of each station is calculated by taking the averaged ratio of the observed value to the theoretical value after first iteration. Then. it can be used for the next iteration of regression analysis. The processing will be stopped by checking the ratio values as they approach 1 or the multiplication of all averaged ratio values approaching 1. Usually, it takes 3 or 4 iterations to make one of two conditions satisfied. The function A0(.6.) is then formed by adjusting C to fit the scale used by Richter's (1935Richter's ( , 1958. Ass wning n=0.833 for the Lg wave propagation, Figure 4 shows the data points of reduced amplitude versus distance after 3 iterations of regression analysis. It is worth noting that a single linear equation can not fit the data points, especially at the shon distance (.6: ::=; 80 km). The result indicates that the dominant wave is changed at different distance ranges. It is believed that shear wave has large amplitude at shon distance while Lg wave is conspicuous at regional distance. It is consistent with the other observations (Bouchon, 1982;Hasegawa, 1983;Dwyer et al., 1983;Campillo et aL, 1984;Shin and Herrmann, 1987). Considering this result and the depth distribution of earthquakes in the Taiwan area, the regression analysis is performed by three cases (1) Shallow earthquakes (h ::; 35 km) and long distance range (.6. > 80 km); (2) shallow earthquakes (h ::; . 35 km) and shon distance range (.6. ::; 80 km); and ( Totally, 102 earthquakes are used in this case. Each event has at least 10 recordings in the required distance range which is greater than 150 km. Using n=0.833 and H 1 to perfonn regression analysis, Figure 5 displays the data points of reduced amplitude vs. distance before (as open circles) and after (as solid circles) regression analysis. The linearity is more remarkable as regression is applied. The slope of 0.00261 is essentially implying the atten uation effects of the area. Therefore, the slope can be converted to have 1 = 0.0061 km-1 .
To realize the variation of 1 caused by using different kinds of peak amplitude, the data of H2 and Z are also taken for regression analysis. Figure 6 shows the distribution of reduced amplitude of H2 (as open circles) and Z (as solid triangles) individually.
The 1 values of 0.006 km-1 and 0.0059 km-1 are obtained respectively. The same / value tells that the propagation of seismic wave is similarly attenuated on the horizontal and vertical components. Results show that the log A0 ( .6.) function can be expressed as -0.00261R -0.83 log R -1.07.

Case 2
Using recordings within short distance range, at least 4 recordings are required and the distance range greater than 50 km. There are 84 earthquakes meeting the requirement.
Assuming n=l .O of body wave propagation and H 1 used, Figure 7 is the distribution of reduced amplitude with respect to the distance before (open circles) aild after (solid circles) regression analysis respectively. The slope of 0.00716 is equal to 'Y = 0.0165 km-1• The same values are obtained as using either H2 or Z peak amplitude. Using the 1 value, lo9Ao(.6.) is in the form of-0.00716R -log R -0.38 in this case.

Case 3
There are 53 deep earthquakes (h > 35 km) which are taken into account. For each of them, there are at least 10 recordings in the distance range greater than 150 km. Using n=0.833 and Hl, Figure 8 is the reduced amplitude distribution before (open circles) and

DISCUSSION AND CONCLUSIONS
Applying the multiple regression analysis for SWAS, a revised distance correction term for local magnitude is derived. The new logA0(.6. ) function can be expressed as followings: {-0.00716R -logR -0.39 (0 km < 6. ::;; 80 km) l ogA o (A) = -0.00261R -0.83 logR -1.07 (80 km< A) for shallow earthquakes ( h ::;; 35 km), and logAo(A) = -0.00326R -0.83 logR -1.01 for deep earthquakes (h > 35 km) Figure 9 shows the comparison of logAo(A) curves. The circles represent the Richter's curve for southern California. The squares are the attenuation function obtained by Yeh et aL (1982) by SWAS of strong motion data of Taiwan area. The line is obtained in this study of assuming focal depth at 10 km representing the attenuation curve of shallow earthquakes. The results indicate that the attenuation of seismic waves at short distance in Taiwan area is greater than those in southern California, but slightly less at long distance. The result from Yeh et al. (1982) is only for reference since the selected strong motion data are too few to  (1935,1958). The squares are the results of Yeh et aL (1984). The solid line is from this study assuming h = 10 km.

165
sample the whole area. Therefore, their attenuation curves cannot represent the full charac teristics of the Taiwan area.
The attenuation coefficient ('y) can be related to the sesimic quality factor, Q, if the form Q = 7r f / / U, where f is the frequency of the wave, and U is its velocity. Thus, the 1 value obtained from case 1 can be used to estimate the Q for Lg in the Taiwan area. The Lg-:-Q is about 190 by assuming U=3.5 km/sec and /=l.25 Hz (the natural frequency of Wood-Anderson seismograph). Similarly, the shear wave Q of 165 can be calculated by assuming the shear velocity of 3.3 km/sec. All these results are consistent with the average Q values obtained by previous works for the Taiwan area (Chang and Yeh, 1983;Wang, 1988;Wang and Liu, 1990;).
Using the log Ao( .6.) curve developed in this study, the local magnitudes are recom puted by using Hl denoted as ML(Hl), H2 as ML(H2), Z as ML(Z) of SWAS for 224 earthquakes. Figures lOa and lOb show the comparison of ML ( H 1) versus ML ( H 2) and ML(Hl) versus ML (Z) respectively. It appears that the same magnitude values are obtained no matter the H 1 or H 2 used. On the other hand, the local magnitude calculated from Z is smaller than those from Hl or H2 by a factor of 0.5 magnitude unit. It turns out that the average ratio of horizontal peak amplitude to vertical peak amplitude is approximately

3.
The difference of local magnitude calculation by applying the Richter's log A 0 ( .6.) (ML(old)) and the logAo(.6.) of this study (ML(new)) is shown as open circles in Figure   11. The data points include all events occurring in the Taiwan area from Sep. 1991 to Feb. ML = 0.94Mv + 1.04 ± 0.28 (6) It is noted that ML in equation ( 6) was determined from the I og A0 ( i:l) values obtained by Yeh et al. (1982). In order to establish a unique magnitude scale, it is necessary to compare the Mn with the ML of this study. Using the same data set, there are 221 earthqualces whose duration magnitudes were determined by the TTSN. Figure 12 shows the data points of ML vs Mn. The relationship is in the form ML = 1.12Mv + 0.03 ± 0.21 (7) and shown by a solid line in the figure. The dashed line is from equation (6). Obviously, equation (6) gives an overestimated ML values comparing to equation (7), especially for the magnitude of earthquakes smaller than 5.6.  (new)) and Richter's logA0 (denoted as ML(old)) (1935,1958). The open circles are the magnitude calculated from 224 earthquakes, the solid circles belong to shallow earthquakes only.