Earthquake sequences on a frictional fault model with non-uniform strengths and relaxation times

Mikumo, Takeshi; Miyatake, Takashi

doi:10.1111/j.1365-246x.1979.tb02569.x

Cited by 115 publications

(62 citation statements)

References 33 publications

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“…Many other mechanisms have been proposed for this temporal decay e.g. subcritical crack growth [35], visco-elastic relaxation [36], post-seismic creep due to stress corrosion in the regions of stress concentration after the mainshock [37], static fatigue [38], pore fluid flow [39], post-seismic slip [40] and earthquake nucleation under rate-and state-variable friction [41]. In general, it is assumed that the parameters c and τ are constants and are specific to a given aftershock sequence.…”

Section: Comparison With Observations 31 the Gutenberg Richter Lawmentioning

confidence: 99%

A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data

Bhattacharya

Chakrabarti

Kamal

2011

J. Phys.: Conf. Ser.

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Abstract. Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of one such, purely geometric, model of earthquake dynamics, namely The Two Fractal Overlap Model. The model tries to emulate the stick-slip dynamics of lithospheric plates with fractal surfaces by evaluating the time-evolution of overlap lengths of two identical Cantor sets sliding over each other. As we show later in the text, some statistical aspects of natural seismicity are naturally captured by this simple model. More importantly, however, this model also reveals a new statistical feature of aftershock sequences which we have verified to be present in nature as well. We show that, both in the model as well as in nature, the cumulative integral of aftershock magnitudes over time is a remarkable straight line with a characteristic slope. This slope is closely related to the fractal geometry of the fault surface that produces most of thee aftershocks. We also go on to discuss the implications that this feature may have in possible predictions of aftershock magnitudes or times of occurrence. IntroductionMany models of natural seismicity have been proposed over the last half-decade and more. These cover a very broad range of approaches ranging from purely physical to purely statistical. The relative successes of these very diverse models is testament to the great complexity involved in the production of natural seismicity and points to the fact that the correct model is probably neither extreme and is some elusive combination of these approaches. However, an approach that has been less pursued to some extent is the investigation of the role of the fractal surface geometry of a fracture surface topography (or self affine for most natural surfaces) in producing the known statistical properties of natural seismicity. The model we propose in this article incorporates this fractal topography of the fracture surface in a simplistic way.

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Section: Comparison With Observations 31 the Gutenberg Richter Lawmentioning

confidence: 99%

A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data

Bhattacharya

Chakrabarti

Kamal

2011

J. Phys.: Conf. Ser.

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“…In our case, however, the distance of the aftershock clusters was only several kilometers and the temperature would not differ significantly. Mikumo and Miyatake (1979) conducted numerical simulations and showed that the p value becomes smaller as the distribution of fault strength becomes more heterogeneous. Small-scale heterogeneities in geological structures would cause differences in frictional properties along aftershock faults.…”

Section: Earthquake Cycle Simulation Based On the Hierarchical Asperimentioning

confidence: 99%

The 2016 Mw 5.9 earthquake off the southeastern coast of Mie Prefecture as an indicator of preparatory processes of the next Nankai Trough megathrust earthquake

Hyodo

Nakanishi

Yamashita

et al. 2018

Prog Earth Planet Sci

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Megathrust earthquakes have occurred repeatedly at intervals of 100 to 150 years along the Nankai Trough, situated in the southwest of Japan. Given that it has been 70 years since the last event, the occurrence of the next devastating earthquake is anticipated in the near future. On April 1, 2016, a moderate earthquake (M w 5.9, M JMA 6.5) occurred off the southeastern coast of Mie Prefecture in the source region of the 1944 Tonankai earthquake (M w 8.2). In this study, we investigated the influence of the 2016 earthquake on future megathrust earthquakes. We first determined the hypocenter distributions using a precise velocity structure obtained from seismic surveys in the source region. Using data obtained from the DONET ocean-bottom observation network, we found that this earthquake occurred along the plate boundary fault, which is also believed to have slipped during past megathrust earthquakes. We then performed a preliminary numerical simulation to reproduce the occurrence of a moderate earthquake in the middle of a megathrust earthquake cycle. We used a hierarchical asperity model, in which smaller asperities causing moderate earthquakes are embedded in a hyper-asperity that serves as the source region of megathrust earthquakes. The simulation shows that moderate earthquakes, caused by ruptures of a smaller asperity, occur as a result of shrinkage of strongly coupled areas in the hyper-asperity. This result is consistent with the observation that the hypocenter of the 2016 earthquake was located at the edge of a strongly coupled region along the plate boundary. The simulation also reproduced postseismic slip (afterslip/slow slip) along the plate boundary updip of the hyper-asperity, which is consistent with the observations of slow slip events and very-low-frequency earthquakes after the 2016 earthquake. Thus, the occurrence of the moderate earthquake offshore southeastern Mie Prefecture in the middle of the megathrust earthquake cycle implies that the shrinkage of the strongly coupled area along the plate boundary is occurring as a preparatory process for the next megathrust earthquake in the region.

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“…At present, our knowledge of the nature, distribution and regional variation of asperities on the fault is too limited to fully test this model. However, if this model proves useful for interpreting seismicity patterns, more physical and dynamic models such as the one developed by Mikumo and Miyatake (1979) need to be introduced to study further details of seismicity patterns.…”

Section: Asperity Modelmentioning

confidence: 99%

The Nature of Seismicity Patterns Before Large Earthquakes

Kanamori

2013

Maurice Ewing Series

215

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Abstract. Various seismicity patterns before major earthquakes have been reported in the literature. They include foreshocks (broad sense), preseismic quiescence, precursory swarms, and doughnut patterns. Although many earthquakes are preceded by all, or some, of these patterns, their detail differ significantly from event to event. In order to examine the details of seismicity patterns on as uniform a basis as possible, we made space-time plots of seismicity for many large earthquakes by using the NOAA and JMA catalogs. Among various seismicity patterns, preseismic quiescence appears most common, the case for the 1978 Oaxaca earthquake being the most prominent.Although the nature of other patterns varies from event to event, a common physical mechanism may be responsible for these patterns; details of the pattern are probably controlled by the tectonic environment (fault geometry, strain rate) and the heterogeneity of the fault plane. Here a simple asperity model is introduced to explain these seismicity patterns. In this model, a fault plane with an asperity is divided into a number of subfaults. The subfaults within the asperity are, on the average, stronger than those in the surrounding weak zone. As the tectonic stress increases, the subfaults in the weak zone break in the form of background small earthquakes. If the frequency distribution of the strength of the subf aults has a sharp peak, a precursory swarm occurs. By this time, most of the subfaults in the weak zone are broken and the fault plane becomes seismically quiet. As the tectonic stress increases further, eventually the asperity breaks and sympathetic displacement occurs on the entire fault zone in the form of the main shock. Foreshocks do or do not occur depending upon the distribution of the strength of the subfaults within the asperity. Since the spatio-temporal change in the stress on the fault plane is most likely to dictate the change in seismicity patterns, detailed analysis of seismicity patterns would provide a most direct clue to the state of stress in the fault zone. However, because of the large variation from event to event, seismicity pattern alone is not a definitive tool for earthquake prediction; measurements of other physical parameters such as the spectra, the mechanism and the wave forms of the background events should be made concurrently.

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Earthquake sequences on a frictional fault model with non-uniform strengths and relaxation times

Cited by 115 publications

References 33 publications

A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data

A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data

The 2016 Mw 5.9 earthquake off the southeastern coast of Mie Prefecture as an indicator of preparatory processes of the next Nankai Trough megathrust earthquake

The Nature of Seismicity Patterns Before Large Earthquakes

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