Download - AReal-Time Processing of Seismic Intensity

Transcript
Page 1: AReal-Time Processing of Seismic Intensity

� �� 60� (2008)

� 2 �243�252�

������� ��

���������������� � � ��� � ��� � !� " # ��$ % &

A Real-Time Processing of Seismic Intensity

Takashi KJCJ<>, Shin AD>, Hiromitsu N6@6BJG6, Hiroyuki FJ?>L6G6,

and Nobuyuki MDG>@6L6

Independent Administrative Institution, National Research Institute for Earth Scienceand Disaster Prevention, 3�1, Tennodai, Tsukuba, Ibaraki 305�0006, Japan

(Received August 16, 2007; Accepted January 8, 2008)

A new calculation method is proposed for a real-time seismic intensity indicator (Ir), whoseconcept is similarly to the JMA seismic intensity (IJMA) defined by Japan Meteorological Agency. Withthe increasing requirements of earthquake early warning (EEW) system, it is much more obvious thatIJMA has a real-time delay since the IJMA needs a filtering operation in frequency domain. In order toimprove the real-time calculation suitable for the EEW system, a new real-time seismic intensityindicator, Ir (real-time seismic intensity), is defined by using an approximating filter in time domaininstead of the original filter in frequency domain. This indicator, Ir, can be calculated as a time serieson real-time and its maximum value, Ia (approximate seismic intensity), corresponds to an approxi-mate value of IJMA. The relationships between IJMA and Ia value are examined by means of using alarge number of strong motion records. Results show that Ia value estimates IJMA with reasonableaccuracy in wide intensity ranges. For a small computing system like a strong-motion seismograph,it is easier to process Ir than processing IJMA. Therefore, Ir is suitable for using in an EEW system basedon the concept of JMA seismic intensity.

Key words : Seismic intensity, Real-time processing, Earthquake early warning, Real-time seismicintensity, Approximate seismic intensity

� 1. � � � �'�()*+,-./�012 3�45�� 672 89:;<=�'��>?@AB0CD)2 E�F)GHIJ45�KLMN,OPQ�>��ABRS,T UBV�OPQ�)*SR72 WXYZC4[RS,\��]�7^_`a�6b,cd>eST fg2 GHIJ45M�hi�:;72 �j>k,ClmnB,opqrst-.u)v9w,��>b,012 �xG�)yz�b,ph4�j>{|RS4S)r}}~V�2 GHIJ45>�~B,��i� ���qi����{>�+VB4ST U��2 ��� ��� 5\M?@�001)GHIJM�[0� CShph)2 #t�

� �305�0006 �t����� 3�1

�F)��AB0'��]�6b,��MrC)�0��>4ABB�2 ��i�)Y�R���>�VB�wS6b�hT U�ph4��}V2 ��MWXYZC�0i��J�OPQ����>�nBRS,CU�6b,>2 U�01)72 �@��M����6�,UC>��C4,T �}�4>V2 �@��7'��>���0�)oM�kw,UCM  C�R9¡ABRS,012 ����6oM�,UC>6D4ST U�012 ����¢M!£RS,�¤M¥����2�"=¦�4§�6�@��M����6�kw,¨� ������� ��� >��C4,T�@����k#�7$© 8%ªZ«¬­� 4®691VBR*q ¯ªZ« (1996)°2 ±��k)72²³�´&µM"SR2 89(¶·¸�0'�¹'Mº(»)

Page 2: AReal-Time Processing of Seismic Intensity

����������� ���� ���������������������� !�"#$%����&�'� �#()�*� +,-.#/0���1� ��02���33415� !�6��72$%#8)9:;<� =�>?�@A (2006)B� 29:CD�2�EFGHI#8) ��<�*� �762J)�KLMN���OP�Q'�� RS T�>?0.1UV�W �"#X�CY�'� 2�*� Z[.�\]�6$��2�&^D_`7�a2b�0cd31efg#'�6��7#h$�ij29:=�>?�kl (2003)��mnl (2003)� @A (2006)B�op���'� �3�� �1Cq�26��7r$#s7�\ t��9:�<�*� u26$v7wxyz�C{5�|}�<�~>1��2J)�� �72F�����r$����C� 6$v7��`�#����9:��'2�K��<�q��C� 2��#����*� [.��2������#'�� �2b�0cd#��5�� 6��7r$#��F�����t�9: =��m�(2006)B ��'����� �'6$v7��`�#���>�F������7r$:#op��

� 2. ���������2.1 � �������6��72$%9:C�� 8������  4¡

�J¢£¤2J)��*1��' =��� (1996) 2¥ 1.2.2QJ¦ 2.2.(2)B� §5� _`7���� �EFGHI� ¨©ª���2������� «�EFGHI#¬�� 3�­2����©®#X�¯� �12 3�­

Fig. 2. Acceleration seismogram in EW component recorded at NIG019 for the 2004 Chuetsuearthquake (top trace), and corresponding filtered seismograms with the JMA filter (middle) and theproposed filter (bottom).

Fig. 1. The filter responses in frequency forthe original filter (solid line A), defined byJapan Meteorological Agency (JMA) andthe proposed filter (dotted line B), describedin the Appendix of this paper.

�� °m±² ³mkl�´mµ¶·8m¸¹º»244

Page 3: AReal-Time Processing of Seismic Intensity

����������� ��������� ������������������� 0.3 !"���#�$%&��#���'()�*+,����-.�&�'()�*+�/& 0�1�234�5��6�47�� �8�/9(���:;��<=,��!�6��"�>%& ?@!';A8�9(B��C D��E�#�*+,��!�4F"G� ��-.�& �'()H*�IGD/& 0�1�2�����5��JK��LM5���NDG�� � & O%D�'()*+�PQ�RS,!& �������JK��LM4���!AT4F8U& V8WX�,YD�PQZ�[,��!"\JK��LM4].�!�4F��!�^_\��������`��4���/���24����H*�].�!�6��"��& ^abcd4;%�8DG�0�1�2�����/& ��ef�0�1�g1h1ijk1�l�mn>%& JK��LM5��o4F����2�����Sp�q4F"GZ�47�� >�rD& JK��LM4�5��6�"s��/& tuE"ef�Zv����4H*�]wx��T"G�& ��tu�����yz"{)4|}4F�"�U& V8�G>�'()H*/`E"Z�!"�� V�4& Appendix�d >PQ�-~���24;�A8>tu������� & �'()H*��o��f����]r>�

Fig. 1 /& �� >tu�������ef�& ^a

bcd4;%�8DG���������ef!7w�Dd >Z�47�� "I& tu�������� D/��ef���tu & ��ef�tu�h D/�� DG"G� �8/�������& �� ��>,���2����4/`����"���ef�Zv>%47�� Fig. 2 ! Fig. 3 �/&��4�� >tu����!& �'()H*�������`���(B��o >��d >� Fig. 2 �/ 1 �)���E�0��z���,��(���! D 2004���9( �M 6.8, �A 13 km� � K-NET�� ¡'¢(NIG019) �£¤��& ¥>& Fig. 3 /& 0.3 �)�-~¦0��z���,��(���! D 2003�§¨©ª9( �M 7.0, �A 71 km) � K-NET«¬¡'¢(MYG011) �­���dA8DG�� �8�����/!Z�& ®¯�°±)²B�& �¯� FFT�GD�������0�1�24o >��& ³¯�tu��������24o >��47~� G´8���IGDZ������/µ¶E�/:· DI~& tu�����GD�'()H*�].���& `E"{)�Zv�!��¸4F��

2.2 ���������� �¹º�IGD& ���24;�A8>�����G��!4& �'()H*�o .����������8��!�dA8>�4& ��& ���������� D�'()H*�JK��LM»���,��

Fig. 3. Acceleration seismogram in NS component recorded at MYG011 for the 2003 Miyagiken-okiearthquake (top trace), and corresponding filtered seismograms with the JMA filter (middle) and theproposed filter (bottom).

()�JK��LMH*� 245

Page 4: AReal-Time Processing of Seismic Intensity

���������� 3� ���������������������� !"� #������$%&'�(���) 0.3*+,-��.�/0 123� &'�(4567+89:� #�.$%������;��8-< =>������� 60*(�������) %?-@+A&'�(4567�>9�� 60*@+�.�$ -#+)B,8< CD� �(EF�����G8�HI��JK67������) %??L� MANO� 60*(�PQ+��&'�(4567�>9#+)B-< #�!0� RS��JTUV�����.� -#+)WX+,-< YZL� [U\HUV]^ 0.01*_`�ab) %??L� Nc0.01*@+A�����.� -#+)WX+,-< #?%�defg$%� hGij ,k��lmHI��JK����n+��� oQpqr)50-�������67AP�� 23� 2s�tu�!Dn�vwx-<��(EF�yz�����G8�� _`�ab�[U

\HUV@+A������ -<������) %?-@+A� NO� 60*(�PQ+��&'�(4567�>9<,{� |} ~���� (2006)� A{8�� &'�(4567�PQ� 10*(+��8!)� =>������)>��8-67n+C���-!0A� ��60*(A�0�8-< Fig. 4 A� ia�Dn� 2004

������ K-NET�����s (NIG019) ���abA�G�� %?!�����.�r�!< #�Y� _`�ab)[U\HUV]^ 0.01* %?�8-!0�. 0.01*@+����+,��8-<#����� NO 60*(�PQ+x-&'�(4567��gA��� N�.A���$%� {{�� 60*(��.)���?-+89��)�-)� #��(�,N�.)� �����$%; �?-�������(IJMA) AP¡x-l��-< 23� ���5¢A£¤¥���� (IJMA) +¦§x-!0A� ��vwx-Dnl+0!�������������`}.

Fig. 4. Acceleration seismograms in three components recorded at NIG019 for the 2004 Chuetsuearthquake (upper three traces) and the corresponding Ir (real-time seismic intensity), calculated bythis procedure (bottom trace). Horizontal dotted line in the bottom indicates 6.732 as JMA seismicintensity. Vertical lines with letters P and S indicate arrival times of P and S waves, respectively.Filled circles in the bottom indicate remarkable points of Ir.

�� ¨�©ª «��¬­®�¯°±>�²³´µ246

Page 5: AReal-Time Processing of Seismic Intensity

(Ir: real-time seismic intensity)� ��������������������� (Ia: approximate seis-

mic intensity) � ������ ��������������������� Fig. 4 � !� ������ Ia )!� 6.696 "������!#$�%& 1

'( )����*��*� + !,��-����#$�%& 3'( )./���� 0�� ���12345���� (IJMA) ! 6.732 "���67� ������ (Ia) !� 8�9:��;�<=�>?�� .6.� ������*7� �� 1�@ !,���AB�� C�<� !��� ����� D�2/8E2F�GH��$�I�F����;��-JKL�

� 3. ������������ !� 8E�I�F���/� ���1234C��.����� (IJMA) �� �M �N.��� ��.������� (Ia) �O���� � �����;�-JKL ��P� �� ���;��!� ��Q��12RHS���T�B�;� (preci-

sion) !�5� U.V�W������X� (ac-

curacy) 2 ���<� "��� -J2���I�F�!� !YZQ[\]^_�K-NET �1996" 6`a2007" 7`�� 116367#b� � KiK-net �1997" 10

`a2007" 7`�� 93280#b�� cd$����e�f%g&��h�' �1996" 10`a 2005"��2007"%()*i&�� 2007"+ji&��� 9504

#b� ,7H�� � 219151#� 3k�l��F� "�� Table 1 2!���I�F����mPRnh�'o��-.$).�� 0/2I�0p1�������qr�s2!� tuvwx�y��C�&�2R�I�F��@���z{*��� �H!2���F��5|U#&��}���~� � �s2P������F�� 3���@*&*���4���� "�� .6.� �� KL;�-J !� #�5�&�2R�F�<|U��/�}��3d�.�� �H!tuvwx�y��C�&��@67����2RW�-J2���&�0�8j��2�W*�����4���� "�� 92� Fig. 1 2"�RL2������� �������:,�*�#$2R�/�L��� ;���#$k�|U}��3d�./-JKL��!�< "��

Fig. 5 !� =0�I�F�23./��.�� ������ (Ia) � ������ (IJMA) ��O).�<� "�� >}���2���/0?!R5� ��*@�67�� 7( ������23./�A "�

��*)GH/��� Fig. 6 � Fig. 7 2!� Ia� IJMA

�� �%&� DI�IJMA�Ia���� �A��B).�����2!� ���� (IJMA) ��22R� DI��Bb��C�*�H/��*� �H7!PPU� �b./PW� �����;��B�*������22R�/�C5C�.����)./��� �P� >}��3d�.� DI��#�! �0.267, ���!0.247, D��! �0.021, 1���! 0.037 "�� �H7��!�� 4%9 (IJMA�3.5) �}�� �5130���@3d2���� DI��#�*�0.175� ���*0.200� D��*�0.021� 1���* 0.042��W� ����2P�/<��=�� )��

DI�D� 2¡�� �RMS¢�� r!�>E����;��p1�./��7H�*� D�� a�1���s�� PPU� r2�a2£s2�¤¥2"�� ���� r�s

���RL2¦�7H� Ia2!D�� al?�F§KL�*GH "VL� .6.�H!� A��B�9 �B¨I2DK©0Gª���2 ���� .�*�/� D���F§����!� >E����;� 9Gª�0� � Ia�«#J¬ �.�*�/­®I���� ��{�¯�Gª���2��� °��K�±2!²>I���RL2� Ia³�((����L*R��´?7H���� + !,7H� Ia!D��F§K�µ2������.�� Fig. 6 � Fig. 7 67L76 "�*� DI��B! 0+¶�.�§��B

Fig. 5. Relationship between JMA seismicintensity (IJMA) and the proposedapproximate seismic intensity (Ia) bycomparison of 219151 strong-motionrecords. Circles denote data. Solid linerepresents the relation IJMA�Ia.

���·¸��¹º»�� 247

Page 6: AReal-Time Processing of Seismic Intensity

�������� �� ������������������ ��� DI������ !"#�$%&'�(��)*�+!,-�./0�1 (Table 2) )230 �45�67����)890�� ��1��� :�*�+!;�� DI� ;<( 7=�$%&>0.05� 9=�$%&> 0.10� 99? �$%&>0.15� @ABC��$%&> 0.20� !"#D������E��� FG .H*� (IJMA) � 0.1IJ��>KE����)LM�� ��./��� N�OPQ�R��LM���� �; DI� 99? �S�>T0.15� !"#���) 0)UV�B�WXQY!Z���� (��� �� 0.058[�!\ZB��]^_`� ]^`� SI� �a�b*c����def)���.H*�!g/B�45�./���$%&�a�hi�jk� ;;lm 0.13n0.9��� �>o��pqr���� s�Mt Uu (2003) �

�vwu (2003) xy (2006)z �> ����45�{C�R�45�./���|��

� 4. � �4.1 �������}~���89!<� �45�./��� def)���]^_`��a�b*c����.H*�)��B�45 ��� def5�B�� �R�<�R|�����r��� ����def5��������� N����)}��0��b*����)���0�.H*��def s�Mt �v�� (1996) ��v� (1999)�� (2000) ��v�� (2005)z ������)R��LM���� ��!����45>� ./��)O��!� *c�¡¢£¤!,-�¥W�¦���� *�§/!���¨©ª&� £�') f�B�� (1/f )1/2 �«¬­�)R® ��¨©ª&��)r

Table 1. The break-down record numbers by each strong-motion seismograph network, and classifiedby JMA seismic intensity scale.K-NET: Kyoshin network operated by National Research Institute for Earth Science and DisasterPrevention (NIED).KiK-net: Kiban-Kyoshin network operated by NIED.JMA: Seismic intensity meter network operated by Japan Meteorological Agency.ALL: Total of three networks.5L, 5U, 6L, 6U denote 5 lower, 5 upper, 6 lower, 6 upper, respectively.

NetworkJMA seismic intensity scale

0 1 2 3 4 5L 5U 6L 6U 7 Total

K-NET 14549 53348 34787 10826 2390 301 123 33 99 1 116367

KiK-net 39942 34146 14069 4059 884 106 54 18 1 1 93280

JMA 21 1199 3411 3664 993 129 65 18 4 0 9504

ALL 54512 88693 52267 18549 4267 536 242 69 14 2 219151

Table 2. The break-down data in ranges defined by IJMA and D I ( IJMA¯Ia).Upper value in each cell is number of data. Lower value is percentage to number of all range,shown in the most right column, which is defined by IJMA. °DI° denotes the absolute value of DI.

Range of IJMA

Range of DI

°DI°±0.05 °DI°±0.10 °DI°±0.15 °DI°±0.20 All range

IJMA²5.559

69.41?79

92.94?85

100.00?85

100.00? 85

IJMA²4.5625

72.42?838

97.10?859

99.54?863

100.00? 863

IJMA²3.53675

71.64?4982

97.12?5112

99.65?5130

100.00? 5130

All range16924377.23?

21549598.33?

21863699.77?

21910599.98? 219151

�� ¡v´µ ¶vUu·v�¸:¹vº�»¼248

Page 7: AReal-Time Processing of Seismic Intensity

��������� ������� ����������� ���������������������� �!��"�����#$%&'(��) $��� �����*�����+��,���-�� �������������#�$�� ����������./01�2345�6�*45789:�;<��=�$%>(�*#� ?@A (2006)B) $C.��D���*����� + ?�E (2003)B � SI, (Spectrum Intensi-

ty [Housner (1975)]) FG�./HI:��� ?��JKE (2003)B �L�%� #M��NI"�� �OP�����Q� LR� �S�T 0.13U0.9Q�%����NI"� L�V=/��) $������NI"� W�S�T 0.058Q�7XYZ [R\#) $����]T�^���*� @A(2006) �� _`F��ab�cd�ef�*#�) Ng1�hI�i L�� (1/f )1/2j�� ���klmn� �� Ng1�hI>op./q�(�� �����+Ng1�Xr�(�s%ef(�*t� ?�� (1989)B) Ng1�uvNI��7�� Ng1�hIklmncd7r�*V %!� L�$��/. LR� wx7"�y#���� �z/.� $cd�{R"�*#�) �.���|���i L�_`F��ab�cd�}~�7b�7{R"�����#) ��7�#*>��F�#�klmn��#����� Ng1�hIklmn

_`F��ab�$�cd�V t���7�����[R�y#"��%�V=/��)���������%/� �&a�7�#Ng1�hI��|���� Y��%/"��y#V=/��%� k����HhI'����1N b�� 1(�Q�%�� LR� F���)����$%*�#) ��� Fig. 4 Ng1��+, (Ir) �� P�,�./� 0.35( 1� 17� 0.47( 1� 37� 2.08

( 1� 5�7� 5.78( 1� 77� �(|�7,%�t-���*#�) $��1����/=���=�%� $[|����-�:�7� 0.1(Q�F���)%!� ¡��) $�7r�*�� �� ¢£��F�#�klmn��#��� �� k����H��#���7�¤¥o7¦�#hI'� ��y ���§.¨©ª�©«�¬­ F���)����$%®) L�) klmnhINI'���¯/,NI7!���NI'� ?�=°� �± (1994)

11. 9B �0 LR� $���S�� SI,NI7!���NI'�[R�¦�- WOP� �!�¯/,NI�!�:�Z� �1N b��!�®) L�)

4.2 ���������� �$�­ 7²��[|7� ¢£�� 6�/��Ng1��+, (Ir) �� 01�,�³7F��7����%/� ´��, L�Ng1�µI, (Ia) 7�:� ���¶*#�) $Ng1�µI, (Ia) �� w��!�

Fig. 7. Comparison of histograms betweenIJMA and Ia WDI·IJMA¸Ia). The bin width is0.01. The histograms in black, dark gray,and light gray, were respectively plottedfrom all of data, the data whose IJMA is 3.5,4.5, and 5.5 or above.

Fig. 6. Comparison of histograms betweenIJMA and Ia WDI·IJMA¸Ia). The bin width is0.01. The histograms in black, dark gray,and light gray, were respectively plottedfrom all of data, the data whose IJMA is 2.5,and 3.5 or above.

1��ºmn»¼hI� 249

Page 8: AReal-Time Processing of Seismic Intensity

����������� (IJMA) ������� ����� (Ir) ���� �� �� ���������� ����� ���� ����������� �� ����������� !"#��$%&����'�( �)��*������� �+���� ,��- �!"�./01 �����%2�3���4�+3����%#5�6���7�8��9$:%#%�;�' ��� <�==���+��&'�>?(��9 �����%2�3���4��6�����' �@� �����+3����%������49 A)��*�+ B��C����6 ,-�D. E3/0FGHI1J�KLMH�/,-��D.N ��� 2����4@7��� 0.323���' �O� ,��- �!"(0PFGHI!"9QH!4RST�UV WX��./6;��Y ��7�59 �+���6�7�MZ[\]F���89^_�`:3��aC6��;b�'�)��*�����9 ;�c�d< e�����f ������� (IJMA) �+=�� >?ghHIS#i���������� (Ir) �+��8�'��:@(8� ����� (Ir) 9 ghHIS#i3���� ��jkghHIS#���lm�6086��n��'

� 5. ����)�9 �-Ao�pBFGHI 88� ;�c�+d< e35 ����q+ >?ghHIS#i����r8�sC� t8�+���6�7 uvD��ghHIS#��q+�� �*��'�*���9 E�F��D.��� ����� (Ir: real-time seismic intensity) %G7��' ����� (Ir) 9�-F/H��%7 <����;�����w+ (Ia: approximate seismic intensity)

I��JK 6r' ������w+ (Ia) 9 602-�*�xL ������������ (IJMA) �^��6��;�'Myz{|N}~O (K-NET, KiK-net) ���P�2�Q�xL3��� 2191511�c�xL 88� ����w+ (Ia) ��������f���� (IJMA)

R�����b 99��S�c�xL� Ia� IJMA%�0.15�T���������%�U3��' ��9<VW��� 0.058X�YZ� �������@7>?( 88����� [�����016t8���;�'����� (Ir) 88�� ����-F�/

H \���%�C �� ����������� !"#��$%&����'=��*��q+�9F[g�]� E�F����Ra�� q+^�%_�8�Yc���0����T�������6`0&��;�'�)��*��q+��9 ;�c�d< e�����f ������� (IJMA) �+=� >?ghHIS#i������� (Ir) �+��8�' ��:@(8� ����� (Ir) 9 ghHIS#���lP��6��;�'

� ��}~�9 c�xL��� Myz{|N}~O�

K-NET� KiK-net���xL��@ ��P�����a���*�� E��Pc�2�� 2004�2005

b DVD-ROMcL0 �d��PWEB�SM���0N�xL �8�=��'=�e��/9 GMT

[Wessel and Smith (1995)] 88=��' ��P�f�g�h�6��i��jkh (0PlmnZ��o��h��:���dp9�) �q������8r)k=��' x���s8��=�'

� �

t  u�¡¢vw 1996, *�+c3d<�x�8��P�����^£¤ y¥}~ 48, 547�550.z��w�{|�} 2005, pb�c�xL��f*�+c3d<0�����[�� *o¦~{§�vm 7, 214�246.�� � 1989, �����ir8� ¨�� 52,

43�68.Housner, G. W., 1975, Measures of severity of earth-

quake ground shaking, Proc. U.S. Conf. EarthquakeEngineering, 25�33.f�g� 2006, ghHIS#��+=��Y��D.©� ¨�� 69, 155�169.�ª�� 1981, ����(0P���0�c�*+���2� «)Myz{|N¬­I[}~� 44,1�61.��P 1996, �� �� E��P���N ®¯�°8 238 pp.�� � 2000, K-NETc�xL��f��P���������±H²g���£¤ *� 2, 53, 89�93.�� ���³ �����´�zµ¶��¦I��

2006, ��-��!"�������YZ�w+�� ��*�{§·q�)m D020.{|�}�z��w���¸¹ 1999, �����º��P��(0P*�+c3�d<��£¤ *o¦~{§�vm 1, 51�56.�� � 2003, �"F�*�+c�d<�sC ��{§*�»{�vm 27, 1�4.

�� ���³ �����´�zµ¶���|��250

Page 9: AReal-Time Processing of Seismic Intensity

����� 1994, ������� ������ ������ 299 pp.������ �� 2003, ����������� JR EAST Technical Review, 3, 53�60.

Wessel, P. and W. H. F. Smith, 1995, New version ofthe generic mapping tools (GMT) version 3.0 relea-sed, EOS Trans. Am. Geophys. Union, 76, 33, 329.

Appendix�������� ���� !�"�#�$%&'()*+,�-./01 23�4(5 �� Fig. 1 067!890� /:�� �+,�-;��<�=>� ?�@0.5 Hz ABC#�>?�@DBD(0EF2 1G�HI7 J1GKLM�<N� ?�@ 0.5O10 HzC#�>?�@DPD(0EF2 0.5G�HI7 J0.5GHI�<N� ?�@ 10 HzAPC#�>?�@DPD(0EF27Q 0HI�D�RST(UV�W( JXYM�<N5)*+,�->�U'Z�=[\]�D^T _`abc-�+,�- (IIR) [�@d� 2ef4(5

IIRV72gh�R( 1GHI[i1KLM+,�-V72>� j (1)klk�m��&'(+,�-DW(5

1/(w0sn1o1) (1)

!Q7� w0p2pf0

UU�� f0>+,�-qr s+?�@[�$4(MktY-�W(5u$v"� 0.5GHI[iwxyv"��zT�<[i1+,�-V72>� j (2)klk�m��&'(+,�-DW(5

[(w1sn1o1)(4w1sn1o1)(0.25w1sn1o1)]/[(w1sn1o2)

(w1sn1o8)(w1sn1o0.5)] (2)

!Q7� w1p2pf1 .

UU�� f1> 0.5G�HI4(?�@�#{|[�$4(MktY-�W(5 T}� j (2)��&'(+,�->�

(w1sn1o1)/(w1sn1o2) (3)

(4w1sn1o1)/(w1sn1o8) (4)

(0.25w1sn1o1)/(w1sn1o0.5) (5)

V�&'(~1+,�-[�G��&�(UV0�7 5

10 HzAP?�@C#0}�(��\]+,�-�<>�?�h�[��4(!�0��Ti�W(5�����:�> 30 HzT 7 40 Hz8�� ?�@>���@��d����&'2 (!�� U �)*��>���T\]�����D^T 5U!�U �> 2G�HI4(iV72)*4

(5 U�<[ef4(XYM+,�-V72>� j(6)klk�m��&'(+,�-DW(5

w22sn2/(1o2hw2sn1ow2

2sn2) (6)

!Q7� w2p2pf2 .

UU�� f2>+,�-qr s+?�@[� h>�����[�$4(MktY-�W(5 U'Z� j (1), (3),

(4), (5), (6)��&'(+,�-V���T�![ g"4(�L���[�#0� ¡¢�'£)*+,�-[gh�R(5 UVR� +,�-�<[¤� XY�4(MktY-> ( f0, f1, f2, h, g) 5¥VT(5 U'Z�[� �;��<Vu¦�¡ §� ���T/]��[¨©072ª$7!VU«� )*�¡ $ MktY-� ¡¢�V72� ( f0p0.45[Hz], f1p7.0[Hz], f2p11.0[Hz], hp0.9, gp1.409) [%!5 UMktY-[� !VR¬¡�T)*+,�-;��<D Fig. 1 06&'2 (5+,�-klk�m�6D&­Z''£� z�m[� 2bc-�+,�-[gh4(UVD�R(5 UU�>� �B (1981) 0TZF2� bc-�+,�-[gh4(5 klk�m®j� F (s)p (awasn1o1) /

(wasn1ob), wap2pfa , V�&'( 1G+,�- z�mF(z) >� DT[¯�l°��"±� z[²³\]´V72� sn1p(DT/2)(1ozn1)/(1nzn1) ['�4'£�

F(z)p(b0ozn1b1)/(a0ozn1a1) (7)

a0pwao2b/(DT)

a1pwan2b/(DT)

b0pwaao2/(DT)

b1pwaan2/(DT)

�W(5 �!�µ# x(k) 0U+,�-[��&�!�!�µ# y(k) [%(0>�

y(k)p[na1y(kn1)ob0x(k)ob1x(kn1)]/a0 (8)

T(\][¶­£8 5 UU�� k>·rl@V4(5¸!� klk�m®j� G(s)pwb

2sn2/(1o2hbwbsn1

owb2sn2), wbp2pfb , V�&'( 2G+,�- z�m

G(z) >� sn1p(DT/2)(1ozn1)/(1nzn1) }8¹� sn2p(DT/121/2)2(1o10zn1ozn2)/(1nzn1)2['�4'£�

G(z)p(b0ozn1b1ozn2b2)/(a0ozn1a1ozn2a2) (9)

a0p12/(DT)2o12hbwb/(DT)owb2

a1p10wb2n24/(DT)2

a2p12/(DT)2n12hbwb/(DT)owb2

b0pwb2

b1p10wb2

b2pwb2

�W(5 �!�µ# x(k) 0U+,�-[��&�!�!�µ# y(k) [%(0>�

y(k)p[na1y(kn1)na2y(kn2)ob0x(k)ob1x(kn1)

��°»�-L¼\]� 251

Page 10: AReal-Time Processing of Seismic Intensity

�b2x(k�2)]/a0 (10)

�������� ������������� gc ���������� x(k), ������ y(k) � !�

y(k)"gcx(k) (11)

�������� �#$!� �%&'()*+,-./0� !�� 1234567 !� 84(9:(;<.-+,-.���=�6���

1 a"0.0, b"1.0, fa"f0 � !� > (7), (8)(��2 a"1.0, b"2.0, fa"f1 � !� > (7), (8)(��3 a"4.0, b"8.0, fa"f1 � !� > (7), (8)(��4 a"0.25, b"0.5, fa"f1 � !� > (7), (8)(��5 hb"h, fb"f2 � !� > (9), (10)(��6 gc"g � !� > (11)(��

?�@(+,-.A�� +,-.BC�DE !�FC(G�H:(+,-.� !IJE��?�KLM� HN6;<.-+,-.(OPCQR��ST6U��0VW�QR6XY!� GOPC&'LZ[ ?(�\�+,-.(]^_`.(ab��cdW6T�e��Tfg3h�i (Ia) (T�j3Kkl �#@�mno#p� > (9)(;<.-+,-.(JE6�� wb"2 tan(pfbDT)/DT� �qrst`u�vw xL� s�1(DT/)(1�z�1)/(1�z�1), s�2"[(DT/2)(1�z�1)/(1�z�1)]2�)*��yz qHNW�{HF|}w Kp�#� cdW�T�j3�X~ ��?�� �8 (1981) (yz�U���m#��������\� ��L�?�@��U �

�� ���� ����������������252