Multifractal Measures of Time Series of Earthquakes.

Lee, Chung-Wein

doi:10.4294/jpe1952.45.331

Cited by 12 publications

(10 citation statements)

References 22 publications

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“…The different scaling relationships could be attributed to the difference in rupture dynamics. The more heterogeneous the slip distributions for moderate earthquakes might be related to the variations in breaking strength over the fault plane as suggested by Wang and Lee (1997); while the more homogenous slip distribution for larger earthquakes (M w > 7.0) might suggest more significant influence from dynamic rupture process, e.g., thermal pressurization or melting (Kanamori and Brodsky 2004;Ma et al 2006). Discrepancies in source scaling for earthquakes have been observed and discussed previously (Shimazaki 1986;Wang 1997;Wang and Ou 1998;Hanks andBakun 2002, 2008;Manighetti et al 2007;Shaw and Wesnousky 2008).…”

Section: Discussionmentioning

confidence: 99%

“…A fractal distribution of fault surface roughness has been shown in the field observations (Aviles et al 1987;Okubo and Aki 1987) and laboratory experiments (Brown and Scholz 1985;Power et al 1987). Wang and Lee (1997) suggested that the fractal geometry of a fault might have a strong relationship with the fractal heterogeneous distribution of the breaking strengths over the fault. Our study shows different scaling exponents (n) between larger earthquakes of M w > 7.0 (n ≈ 0.7) and moderate earthquakes of M w = 4.5 -7.0 (n < 0.7), suggesting the slip distribution for larger magnitude earthquakes tend to be more homogenous.…”

Section: Discussionmentioning

confidence: 99%

“…Mandelbrot (1983) proposed another concept, fractal geometry, and stated that a fractal dimension can describe the scale invariance of natural phenomena. This concept has been widely applied to describe the spatial distribution and time series of earthquakes (Turcotte 1989(Turcotte , 1997Ogata and Abe 1991;Hirabayashi et al 1992; Papadopoulos and Dedousis 1992; Koyama et al 1995;Wang 1996;Wang and Lee 1997;Wang et al 2014) and fault activities (cf. Okubo and Aki 1987;Lee and Schwarcz 1995).…”

Section: Introductionmentioning

confidence: 99%

“…In several studies the scale invariance property in earthquakes has been used for simulating the rupture process. For instance, Wang and Lee (1997) applied a fractal distribution of the breaking strengths in a spring-block model to simulate earthquakes to study the scaling relation between the earthquake frequencies and rupture length. Ide and Aochi (2005) and Ide (2009, 2011) proposed a model of the wide-scale growth of dynamic rupture during an earthquake.…”

Section: Introductionmentioning

confidence: 99%

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Heterogeneous Slip Distribution Self-Similarity on a Fault Surface

Lee

Fong²,

Yen

2016

Terr. Atmos. Ocean. Sci.

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The earthquake slip distribution self-similarity is investigated in this study. We complied finite fault slip models for earthquakes in the Taiwan orogenic belt and global earthquakes to determine the slip distribution self-similarity. Forty-one earthquakes (19 Taiwan earthquakes and 22 global earthquakes) in the M w = 4.6 -8.9 magnitude range were examined. The fault slip exhibited self-similar scaling between the rupture slip and area. The average area ratio (R s ) and slip ratio (R d ) follows a scaling of R 10 ( ) s a n Rd = -. Slip self-similarity implies that a fault rupture exhibits fractal behavior. The scaling exponent can be considered as a measure for the roughness degree of the slip distribution on the fault surface. This study suggests that the slip distribution for large earthquakes (M w > 7.0) tends to have a more homogeneous slip. Scaling exponents can provide insight into earthquake rupture mechanics and the scaling of heterogeneous slips on the fault surface provides a basis for ground motion simulation for a finite fault for an earthquake scenario, particularly for near-fault motion.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Heterogeneous Slip Distribution Self-Similarity on a Fault Surface

Lee

Fong²,

Yen

2016

Terr. Atmos. Ocean. Sci.

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“…Mandelbrot (1983) proposed the fractal geometry with fractal dimension to describe the scale-invariant natural phenomena. This concept has been applied to seismology (Turcotte 1989;Korvin 1992), including the fault properties (Aviles et al 1987;Okubo and Aki 1987;Lee and Schwarcz 1995;Candela et al 2012), the spatial distribution of earthquakes (Hirabayashi et al 1992;Turcotte 1997;Wang and Shen 1999), the temporal variation in earthquakes (Smalley et al 1987;Hirata 1989;Kagan and Jackson 1991;Ogata and Abe 1991;Papadopoulos and Dedousis 1992;Koyama et al 1995;Lee 1995, 1997;Wang 1996a;Kagan 2007;Michas et al 2014), and earthquake ruptures (Wang 1995(Wang , 1996bAochi and Ide 2004;Aochi 2005, 2014;Manighetti et al 2005;Lee et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China

Chen¹,

Chang²

2017

Terr. Atmos. Ocean. Sci.

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The M ≥ 6 earthquakes occurred in the South-North Seismic Belt, Mainland China (longitudes from 98 -107°E and latitudes from 21 -41°N) during 1900 -2016 are taken to measure the multifractal dimensionsspatial distribution and time sequence of events and the dominant periods. The multifractal dimensions, D q , are measured from the log-log plots of C q (r) versus r and C q (t) versus t, where C q (r) and C q (t) are the generalized correlation integrals for the epicentral distribution and time sequence of events, respectively. r and t are the epicentral distance and inter-event time, respectively, at positive q. The log-log plot of C q (r) versus r shows a linear portion when log(r l ) ≤ log(r) ≤ log(r u ). The r l and r u values are, respectively, 120 and 560 km for M ≥ 6 events, 100 and 560 km for M ≥ 6.5 events, and 63 and 560 km for M ≥ 7 events. The r l value decreases with the lower-bound magnitude. D q monotonically decreases with increasing q. The D q values are between 1.618 and 1.426 for M ≥ 6 events, between 1.562 and 1.108 for M ≥ 6.5 events, and between 1.365 and 0.841 for M ≥ 7 events. The log-log plot of C q (t) versus t show a linear distribution when log(t l ) ≤ log(t) ≤ log(t u ), where t l and t u are, respectively, 5 and 50.1 years for M ≥ 6 events, 5 and 50.1 years for M ≥ 6.5 events, and 16 and 63.1 years for M ≥ 7 event, thus suggesting that the time sequences of earthquake in the study region are multifractal. The D q values are between 0.830 and 0.703 for M ≥ 6 events, between 0.835 and 0.820 for M ≥ 6.5 events, and between 0.786 and 0.685 for M ≥ 7 events. The Morlet wavelet technique is applied to analyze the dominant periods of temporal variations in numbers of yearly earthquakes for the three magnitude ranges, i.e., M ≥ 6, M ≥ 6.5, and M ≥ 7. The resultant dominant period is 2.94 years for M ≥ 6 events and cannot be evaluated for M ≥ 6.5 and M ≥ 7 events.

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Argument on the magnitude-frequency relation

et al. 2002

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The complexity of seismicity and the relation of magnitude and frequency are discussed in this paper on the basis of nonlinear dynamics and multifractal theory. We argue that seismic active systems normally have multifractal characteristics, either for the spatial-temporal distribution or the intensity distribution of events. In the view of multifractal theory the nonlinear characteristics of the magnitude-frequency relation are discussed and the formullion is revised.Also, one example of the variance of bq estimated based on the recent New Zealand catalogue is enumerated. Key words: the relation of magnitude and frequency; multifraetal analysis; nonlinear characteristics + CLC number: P315.3 2 Document code: A * ACTA SEISMOLOGICA SINICA Vol. 15cause this deviation from G-R law, especially for events with larger magnitude, could seriously affect the seismic hazard risk estimation that evaluated with seismicity based on (1), the seismological community have tried to reform this magnitude-frequency relation; many rewrote formulas, for example, more than 10 of which are collected in IASPEI (Healy, et al, 1997), and modification methods such as fitting the data with polynomials taking place of the linear form like (1) (JIANG, DAI, 1993), have been proposed. Based on the statistical tests, WANG, et al (1994) argued that the distribution of magnitude could probably be better described by a Weibull distribution than by the power-law indicated by (1). In this situation, the G-R law is the case of the parameter ,o=0 in the Weibull functions. Also, based on statistical physics and information theory, the magnitude frequency has been rewritten as n(m) = n o exp(-alm -flMo) or n(Mo) = noMo~e -a~° (2)

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Multifractal Measures of Time Series of Earthquakes.

Cited by 12 publications

References 22 publications

Heterogeneous Slip Distribution Self-Similarity on a Fault Surface

Heterogeneous Slip Distribution Self-Similarity on a Fault Surface

Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China

Argument on the magnitude-frequency relation

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