大地震破裂方向性研究
研 究 生：張若磐
指導教授：王乾盈 博士
摘 要
大地震的破裂方向性研究提供了對地震基本斷層參數的了解， 這
些參數間的關係(稱為震源尺度律)可描述大地震破裂的一些基本物理特
性。本研究利用表面波走時差的方法來決定大地震的破裂方向性，即利用主震
及其附近參考地震的表面波走時差來評估各測站的震源歷時，並進行破裂方向性
分析，但是，若大地震附近並無合適的參考地震時，此法並不適用，因此，本研
究進一步提出一個新方法來解決參考地震的問題，就是利用全球表面波相速分
布圖來取代參考地震，在相速圖上計算從地震至測站的走時可視為參考地震的表
面波走時，也就是合成格林函數的觀念。藉此可以快速及有效的決定大地震的破
裂方向性，克服無真實參考地震的缺點。
本研究共分析由1999 至2008 年震矩規模大於7.6 的地震，共計8 個，包括
6 個逆斷層及2 個走向平移斷層，採用震央距離30°-90°的表面波資料，逆斷層型
態的地震利用雷利波分析，而走向平移斷層型態的地震則利用洛夫波分析。除
2004 年蘇門達臘地震採用週期150 秒雷利波分析外，其餘皆利用週期100 秒的雷
利波或洛夫波。結果顯示本研究所提的分析方法確實可行，對一些無合適參考地
震的大地震(如2001 年崑崙地震、2008 年四川地震)都能得到合理的破裂方向性
分析。其次，整體而言，震源歷時及破裂長度隨地震矩(震矩規模)增加而增加，
其中以2004 年蘇門達臘地震(Mw 9.0-9.3)具有最長的震源歷時及破裂長度；以同
規模地震而言，走向平移斷層較逆斷層有較長的破裂長度及震源歷時。再則，破
裂方位分析能有效判斷走向平移斷層型態地震的斷層面，然對逆斷層型態的地震
則無法全部判讀。因整個震源歷時包括破裂時間和震源上揚時間，故由整個震源
歷時易低估破裂速度，透過表面波頻譜節點週期的分析可評估震源上揚時間，因
此可得到較合理的破裂速度。本研究所提方法的優點在於不需要主震附近的參考
地震，因此，當大地震發生後，可快速有效的決定其破裂方向性和斷層參數，而
且也適合用來重新評估一些歷史地震的斷層參數，如早期的1960 年智利地震和
1964 年阿拉斯加地震等。

Rupture Directivity Analysis for Large Earthquakes
Postgraduate：Jo-Pan Chang
Adviser：Dr. Chien-Ying Wang
Abstract
Rupture directivity analysis for large earthquakes can provide some basic fault
parameters. Relationships between these fault parameters, the so-called scaling law,
lead to understand the physical properties of earthquakes. Many methods and seismic
data can investigate the rupture directivity of an earthquake. In this study, we use the
differences of surface-wave travel time between the mainshock and reference
earthquake to determine the fault parameters for large earthquakes. Above mentioned,
constraint on such work is that there must be reference earthquakes in the vicinity of
the mainshock. Here, we propose a new method to analyze the rupture directivity of an
earthquake without using reference earthquakes. That is, we calculate the surface-wave
travel time using the global surface-wave phase-velocity maps to be the travel times
from reference earthquakes. The concept is similar to the Green’s function.
In this study, 8 large earthquakes occurring from 1999 to 2008 with Mw
7.6-9.0(9.3) are analyzed using surface waves with epicentral distances between 30°
and 90°. We use the Rayleigh waves to perform the rupture directivity analysis for
trust-type earthquakes; on the contrary, using the Love waves to analyze the rupture
directivity for strike-slip-type earthquakes. Results show that the proposed method is
valid for the rupture directivity analysis of a large earthquake. On the whole, the
source duration and rupture length increase with seismic moment (or Mw). Among
these analyzed earthquakes, the 2004 Sumatra-Andaman earthquake (Mw 9.0-9.3) has
the longest source duration and rupture length. Besides, earthquakes with
strike-slip-type mechanism have relatively larger source duration and rupture length
than those with thrust-type mechanism. The optimal rupture azimuth can efficiently
provide the judgment on which is the fault plane from the beach ball for the strike-slip
earthquakes. However, it is ambiguous to judge the fault plane for the trust-type
earthquakes. The rupture velocity is easily underestimated from the whole source
duration (including the rupture time and rise time). By investigating the period of
spectral node, we can determine the rise time, and then derive the reasonable rupture
velocity. The advantage of our proposed method is that it is not in want of the
reference earthquakes and can quickly and efficiently determine the fault parameters of
large earthquakes from rupture directivity analysis. Also, the proposed method is
appropriate to re-examine some historical earthquakes, such as the 1960 Chile
earthquake and 1964 Alaska earthquake.

參考文獻
Aki, K., Scaling law of seismic spectrum, J. Geophys. Res., 72, 1217-1231, 1967.
Aki, K., and P. G. Richards, Quantitative Seismology: Theory and Methods, W. H.
Freeman, San Francisco., 932 pp., 1980.
Ammon, C. J., A. A. Velasco, and T. Lay, Rapid estimation of rupture directivity:
Application to the 1992 Landers (Ms=7.4) and Cape Mendocino (Ms=7.2),
Califorina earthquake, Geophys. Res. Lett., 20, 97-100, 1993.
Ammon, C. J., A. A. Velasco, and T. Lay, Rapid estimation of first-order rupture
characteristics for large earthquakes using surface waves: 2004
Sumatra-Andaman earthquake, Geophys. Res. Lett., 33, L14314,
doi:10.1029/2006GL026303, 2006.
Ammon, C. J., C. Ji, H.-K. Thio, D. Robinson, S. Ni, V. Hjorleifsdottir, H. Kanamori,
T. Lay, S. Das, D. Helmberger, G. Ichinose, J. Polet, and D. Wald, Rupture
Process of the 2004 Sumatra-Andaman Earthquake, Science, 308, 1133-1139,
2005.
Båth, M., Spectral Analysis in Geophysics, Developments in Solid Earth Geophysics
Series, Vol. 7, Elsevier Sci., Amsterdam, 563 pp., 1974.
Ben-Menahem, A., Radiation of seismic surface-waves from finite moving sources,
Bull. Seism. Soc. Am., 51, 401-435, 1961.
Ben-Menahem, A. and D. G. Harkrider, Radiation patterns of seismic surface waves
from buried dipolar point sources in a flat stratified Earth, J. Geophys. Res., 69,
2605-2620, 1964.
Ben-Menahem, A., M. Rosenman, and M. Israel, Source mechanism of the Alaskan
earthquake from amplitude of free oscillations and surface waves, Phys. Earth
Planet. Inter., 5, 1-29, 1972.
Bollinger, G. A., Determination of earthquake fault parameters from long-period P
waves, J. Geophys. Res., 73, 785-807, 1968.
Bollinger, G. A., Fault length and fracture velocity for the Kyushu, Japan, earthquake
of October 3, 1963, J. Geophys. Res., 75, 955-964, 1970.
Brune, N., J. E. Naff, and J. E. Oliver, A simplified method for the analysis and76
synthesis of dispersed wave trains, J. Geophys. Res., 65, 287-303, 1960.
Bufe, C. G., Comparing the November 2002 Denali and November 2001 Kunlun
earthquakes, Bull. Seism. Soc. Am., 94, 1159-1165, 2004.
Cipar, J., Source processes of the Haicheng, China earthquake from observations of P
and S waves, Bull. Seism. Soc. Am., 69, 1903-1916, 1979.
Chang, J.-P., R.-D. Hwang, C.-Y. Wang, G.-K. Yu, W.-Y. Chang, and T.-W. Lin.,
Analysis of rupture directivity for the 2004 Sumatra earthquake from the
Rayleigh-wave phase velocity, Terr. Atmos. Ocean. Sci., 2009. (accepted)
Choy, G. L., and J. Boatwright, Radiated energy and the rupture process of the Denali
fault earthquake sequence of 2002 from broadband teleseismic body waves, Bull.
Seism. Soc. Am., 94, S269-S277, 2004.
Chung, W.-Y., and H. Kanamori, Variation of seismic source parameters and stress
drops within a descending slab and its implications in plate mechanics, Phys.
Earth Planet. Inter., 23, 134-159, 1980.
de Groot-Hedlin, C. D., Estimation of the rupture length and velocity of the Great
Sumatra earthquake of Dec 26, 2004 using hydroacoustic signals, Geophys. Res.
Lett., 32, L11303, doi:10.1029/2005GL022695, 2005.
Dunham, E. M., and R. J. Archuleta, Evidence for a supershear transient during the
2002 Denali Fault earthquake, Bull. Seism. Soc. Am., 94, S256-S268, 2004.
Dziewonski, A. M., and D. L. Anderson, Preliminary reference Earth model. Phys.
Earth planet. Inter., 25, 297-356, 1981.
Eberhart-Phillips, D., P. J. Haeussler, J. T. Freymueller, A. D. Frankel, C. M. Rubin, P.
Craw, N. A. Ratchkovski, G. Anderson, G. A. Carver, A. J. Crone, T. E. Dawson,
H. Fletcher, R. Hansen, E. L. Harp, R. A. Harris, D. P. Hill, S. Hreinsdóttir, R. W.
Jibson, L. M. Jones, R. Kayen, D. K. Keefer, C. F. Larsen, S. C. Moran, S. F.
Personius, G. Plafker, B. Sherrod, K. Sieh, N. Sitar, and W. K. Wallace, The
2002 Denali fault earthquake, Alaska: A large magnitude, slip-partitioned event,
Science, 300, 1113-1118, 2003.
Ekström, G. , J. Tromp, and E. W. F. Larson, Measurements and global models of
surface wave propagation. J. Geophys. Res., 102, 8137-8157, 1997.Filson, J., and T. V. McEvilly, Love spectra and the mechanism of the 1966 Parkfield
sequence, Bull. Seism. Soc. Am., 57, 1245-1257, 1976.
Furumoto, M., Initial phase analysis of R waves from great earthquakes, J. Geophys.
Res., 84, 6867-6874, 1979.
Furumoto, M., and I. Nakanishi, Source times and scaling relations of large
earthquakes, J. Geophys. Res., 88, 2191-2198, 1983.
Geller, R. J., Scaling relations for earthquake source parameters and magnitudes, Bull.
Seism. Soc. Am., 66, 1501-1523, 1976.
Guilbert, J., J. Vergoz, E. Schisselé, A. Roueff, and Y. Cansi, Use of hydroacoustic
and seismic arrays to observe rupture propagation and source extent of the Mw =
9.0 Sumatra earthquake, Geophys. Res. Lett., 32, L15310,
doi:10.1029/2005GL022966, 2005.
Hanks, T. C., and M. Wyss, The use of body-wave spectra in the determination od
seismic-source parameters, Bull. Seism. Soc. Am., 62, 561-589, 1972.
Hwang, R.-D., G.-K. Yu, and J.-H. Wang, Rupture directivity and source-process time
of the September 20, 1999 Chi-Chi, Taiwan, earthquake estimated from
Rayleigh-wave phase velocity, Earth Planets Space, 53, 1171-1176, 2001.
Ishii, M., P. M. Shearer, H. Houston, and J. E. Vidale, Extent, duration and speed of
the 2004 Sumatra–Andaman earthquake imaged by the Hi-Net array, Nature,
435, 933-936, doi:10.1038/nature03675, 2005.
Kanamori, H., and D. L. Anderson, Theoretical basis of some empirical relations in
seismology, Bull. Seism. Soc. Am., 65, 1073-1095, 1975.
Kanamori, H., and J. W. Given, Use of long-period surface waves for rapid
determination of earthquake-source parameters, Phys. Earth Planet. Inter., 27,
8-31, 1981.
Khattri, K. N., Determination of earthquake fault plane, fault area and rupture velocity
from the spectra of long period P waves and the amplitude of SH waves, Bull.
Seism. Soc. Am., 59, 615-630, 1969.
Krüger, F., and M. Ohrnberger, Tracking the rupture of the Mw = 9.3 Sumatra
earthquake over 1,150 km at teleseismic distance, Nature, 435, 937-939,
doi:10.1038/nature03696, 2005.
Lay, T., H. Kanamori, C. J. Ammon, M. Nettles, S. N. Ward, R. C. Aster, S. L. Beck,
S. L. Bilek, M. R. Brudzinski, R. Butler, H. R. DeShon, G. Ekström, K. Satake,
and S. Sipkin, The Great Sumatra-Andaman Earthquake of 26 December 2004.
Science, 308, 1127-1133, doi:10.1126/science.1112250, 2005.
Liao, B.-Y., and H.-C. Huang, Rupture process of the 2002 Mw 7.9 Denali earthquake,
Alaska, using a newly devised hybrid blind deconvolution method, Bull. Seism.
Soc. Am., 98, 162-179, 2008.
Lin, A., M. Kikuchi, and B. Fu, Rupture segmentation and process of the 2001 Mw 7.8
central Kunlun, China, earthquake, Bull. Seism. Soc. Am., 93, 2477-2492, 2003.
Lin, T.-W., R.-D. Hwang, K.-F. Ma, and Y.-B. Tsai, Simultaneous determination of
source parameters using far-field P waves: Focal mechanism, seismic moment,
rupture length and rupture velocity, Terr. Atmos. Ocean. Sci., 17, 463-487, 2006.
Lomax, A., Rapid estimation of rupture extent for large earthquakes: Application to
the 2004, M9 Sumatra-Andaman mega-thrust, Geophys. Res. Lett., 32, L10314,
doi:10.1029/2005GL022437, 2005.
Mai, P. M., and G. C. Beroza, Source scaling properties from finite-fault-rupture
models, Bull. Seism. Soc. Am., 90, 604-615, 2000.
Ni, S., H. Kanamori, and D. Helmberger, Energy radiation from the Sumatra
earthquake, Nature, 434, 582, doi:10.1038/434582a, 2005.
Ozacar, A. A., and S. L. Beck, The 2002 Denali fault and 2001 Kunlun fault
earthquakes: Complex rupture processes of two large strike-slip events, Bull.
Seism. Soc. Am., 94, S278-S292, 2004.
Pegler, G., and S. Das, Analysis of the relationship between seismic moment and fault
length for large crustal strike-slip earthquakes between 1977-92, Geohpys. Res.
Lett., 23, 905-908, 1996.
Press, F., A. Ben-Menahem, and M. N. Toksöz, Experimental determination of
earthquake fault length and rupture velocity, J. Geophys. Res., 66, 3471-3485,1961.
Rhie, J., D. Dreger, R. Bürgmann, and B. Romanowicz, Slip of the 2004
Sumatra-Andaman earthquake from joint inversion of long-period global seismic
waveforms and GPS static offsets, Bull. Seism. Soc. Am., 97, S115-S127, 2007.
Romanowicz, B., Strike-slip earthquakes on quasi-vertical transcurrent faults:
inferences for general scaling relations, Geophys. Res. Lett., 19, 481-484, 1992.
Romanowicz, B., and J. B. Rundle, On scaling relations for large earthquakes, Bull.
Seism. Soc. Am., 83, 1294-1297, 65-70, 1993.
Ruff, L., and H. Kanamori, The rupture process and asperity distribution of three great
earthquakes from long-period diffracted P-wave, Phys. Earth Planet. Inter., 31,
202-230, 1983.
Scholz, C. H., Scaling laws for large earthquakes: consequences for physical models,
Bull. Seism. Soc. Am., 72, 1-14, 1982.
Scholz, C. H., A reappraisal of large earthquake scaling, Bull. Seism. Soc. Am., 84,
215-218, 1994.
Scholz, C. H., Size distributions for large and small earthquakes, Bull. Seism. Soc. Am.,
87, 1074-1077, 1997.
Scholz, C. H., C. Aviles and S. Wesnousky, Scaling differences between large
intraplate and interplate earthquakes, Bull. Seism. Soc. Am., 76, 65-70, 1986.
Simon, R. B., Earthquake Interpretations, Colorado School of Mines, Golden,
Colorado, 99 pp., 1972.
Singh, S. K., J. Pacheco, M. Ordaz, and V. Kostoglodov, Source time function and
duration of Mexican earthquakes, Bull. Seism. Soc. Am., 90, 468-482, 2000.
Stacey, F. D., Physics of the Earth, 3rd edn., Brookfield Press, Brisbane, Australia, 513
pp., 1992.
Stein, S., and E. A. Okal, Speed and size of the Sumatra earthquake, Nature, 434,
581-582, doi:10.1038/434581a, 2005.
Stein, S., and M. Wysession, An Introduction to Seismology, Earthquake, and Earth
Structure, Blackwell Publishing, UK, 498 pp., 2003.
Stoffa, P. L., P. Buhl, and G. M. Bryan, The application of homomorphicdeconvolution to shallow-water marine seismology—Part I: models, Geophysics,
39, 401-416, 1974.
Trampert, J., and J. H. Woodhouse, Assessment of global phase velocity models,
Geophys. J. Int., 144, 165-174, 2001.
Tsai, V. C., M. Nettles, G. Ekström, and A. M. Dziewonski, Multiple CMT source
analysis of the 2004 Sumatra earthquake, Geophys. Res. Lett., 32, L17304,
doi:10.1029/2005GL023813, 2005.
Vassiliou, M. S., and H. Kanamori. The energy release in earthquakes, Bull. Seism.
Soc. Am., 72, 371-387, 1982.
Velasco, A. A., C. J. Ammon, J. Farrell, and K. Rupture directivity of the 3 November
2002 Denali fault earthquake determined from surface waves, Bull. Seism. Soc.
Am., 94, S293-S299, 2004.
Velasco, A. A., C. J. Ammon, and T. Lay, Empirical green function deconvolution of
broadband surface waves: Rupture directivity of the 1992 Landers, California
(Mw=7.3), earthquake, Bull. Seism. Soc. Am., 84, 735-750, 1994.
Vigny, C., W. J. F. Simons, S. Abu, R. Bamphenyu, C. Satirapod, N. Choosakul, C.
Subarya, A. Socquet, K. Omar, H. Z. Abidin, and B. A. C. Ambrosius, Insight
into the 2004 Sumatra–Andaman earthquake from GPS measurements in
southeast Asia, Nature, 436, 201-206, doi:10.1038/nature03937, 2005.
Walker, K. T., and P. M. Shearer, Illuminating the near-sonic rupture velocity of the
intracontinental Kokoxili Mw 7.8 and Denali fault Mw 7.9 strike-slip
earthquakes with global P wave back projection imaging, J. Geophys. Res., 114,
B02304, doi:10.1029/2008JB005738, 2009.
Wang, C.-Y., Wave theory for seismogram synthesis. Ph.D. Dissertation, Saint Louis
University, Saint Louis, 235 pp., 1981.
Wang, J.-H., and S.-S. Ou, On scaling of earthquake faults, Bull. Seism. Soc. Am., 88,
758-766, 1998.
Warren, L. M., and P. M. Shearer, Systematic determination of earthquake rupture
directivity and fault planes from analysis of long-period P-wave spectra.
Geophys. J. Int., 164, 46-62, doi:10.1111/j.1365-246X.2005.02769.x, 2006.Wells, D. L., and K. J. Coppersmith, New empirical relationships among magnitude,
rupture length, rupture width, rupture area, and surface displacement, Bull. Seism.
Soc. Am., 84, 974-1002, 1994.
Wen, Y.-Y., K.-F. Ma T.-R. Alex Song, and W. D. Mooney, Validation of the rupture
properties of the 2001 Kunlun, China (Ms=8.1), earthquake from seismological
nd geological observations, Geopgys. J. Int., 177, 555-570,
doi:10.1111/j.1365-246X.2008.04063.x, 2009.
Yagi, Y., Preliminary Results of Rupture Process for 2004 off coast of Northern
Sumatra giant earthquake, posted on http://iisee.kenken.go.jp/staff/yagi/eq/
Sumatra2004/Sumatra2004.html, 2005.
Yamanaka, Y., EIC Seismological Note No. 161+ : Off the West Coast of Northern
Sumatra Earthquake (M9.0), posted on http://www.eri.u-tokyo.ac.jp/sanchu/
Seismo_Note/2004/EIC161ea.html, 2005.
Yu, G. K. and B. J. Mitchell, Regionalized shear velocity models of the Pacific upper
mantle from observed Love and Rayleigh wave dispersion, Geophys. J. R. astr.
Soc., 57, 311-341, 1979.
Zhang, J., and H. Kanamori, Source finiteness of large earthquakes measured from
long-period Rayleigh waves, Phys. Earth. Planet. Inter., 52, 56-84, 1988.
黃瑞德，由表面波頻散推延中國大陸之上部地函構造，國立中央大學地球物理研
究所博士論文，台灣，中壢，127 頁，1999。