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1

Złożoność trzęsień ziemi i ich prognozowanie

Senatorski P.

Przegląd Geofizyczny

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2004

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Z. 3-4

131-146

EN

According to the time predictable model of seismic cycles, based on Reid's elastic rebound concept, consecutive earthquakes are represented by two parameters: occurrence time, and size, characterized by seismic moment or the mean coseismic slip. Recently, it has been shown that even in the simplest case of the Parkfield section of the San Andreas fault, the model fails. The next large earthquake, expected about 30-15 years ago, has not struck the fault till now. This work is an attempt to show that the deviation from the predictability of earthquakes expected by the tested model is related with the source heterogeneity, and with locality of fault stability conditions. These features are not taken into account in Reid's concept, which can be treated as a uniform approximation of seismic sources. Conclusions presented in this work are illustrated by computer simulations based on the more realistic model of the heterogeneous seismic source. Using simulated seismicity for predictive purposes seems to be unrealistic in the nearest future, because of a lack of any satisfactory earthquake theory. The present work suggests more modest objective, namely, searching for statistical relations between earthquake parameters. The scaling relationship for the seismic energy as a function of the seismic moment and other macroscopic parameters of seismic events, can be significant in estimations of future earthquake danger in a given region.

2

Scaling and statistical trends of the apparent stress for heterogeneous seismic sources

Senatorski P.

Acta Geophysica Polonica

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2003

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Vol. 51, nr 2

125-134

EN

The apparent stress can be understood as the correlation integral of the slip velocity field over an earthquake rupture area (Senatorski, 2003). This means that the apparent stress is a macroscopic function, which can be expressed as an average of microscopic quantities describing details of the rupture process. Here it is shown, using this statistical mechanics approach and a view of the slip velocity pulse-like rupture propagation, that the apparent stress can be formulated as a function of three other macroscopic parameters - the seismic moment, the rupture area and the slip acceleration 0 treated as independent variables. Moreover, the scaling relationship for these quantities is derived. This relationship is used to explain statistical trends of the apparent stress and other macroscopic earthquake parameters observed in earthquake populations.

3

Random fluctuations of the apparent stress among heterogeneous seismic sources

Senatorski P.

Acta Geophysica Polonica

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2003

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Vol. 51, nr 1

23-36

EN

The apparent stress, (tau)a, defined as the ration of seismic energy, Es, and seismic moment, M0, has been formulated as the average stress associated with radiation resistance of a sliding fault during as earthquake. The over damped dynamics approximation of a seismic source implies that the seismic energy rate at a given time is proportional to the square of the slip velocity integrates over the rupture area. This result allows us to interpret the apparent stress as a correlation integral of the slip velocity field over space and time. Consequently, other macroscopic parameters, such as momentary and local apparent stress, (tau)m and (tau)l, are proposed to characterize spatial and temporal heterogeneity of complex seismic sources. This approach is used to understand fluctuations of the apparent stress, and other macroscopic parameters in earthquake populations, in terms of their microscopic representation.

4

Slip weakening and energy-moment scaling relationship

Senatorski P.

Acta Geophysica Polonica

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2001

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Vol. 49, nr 1

75-93

EN

The ratio of radiated seismic energy and seismic moment estimated for global sets of earthquakes does not exhibit any systematic changes with seismic moment. In contrast, for regional sets of earthquakes the ratio decreases with decreasing moment. This paper proposes a statistical relationship among radiated energy, seismic moment, and source dimension: Ea M0(1.5) / r which is consistent with both kinds of data. The relation is explained by a fault zone model based on the slip-dependent constitutive law and the overdamped dynamics approximation. Since potential damages caused by an earthquake are related to the radiated seismic energy, the derived relation can help to estimate them if the expected earthquake source dimension and moment release are known.

5

Model of earthquake cycles with a slip-dependent constitutive law. Part II - Simulations

Senatorski P.

Acta Geophysica Polonica

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2000

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Vol. 48, nr 4

423-453

EN

Long-term seismic activity is simulated using a 3D model of interacting faults presented in Part I of this paper. It is show that the system can generate complex behavior, with earthquakes of all sizes, characteristic earthquake cycles with features changing from one cycle to another, and interrelations between local quantities in qualitative agreement with laboratory data. By comparison of a single, two distant and two close fault behavior the role of fault interactions is studied. Interactions with a secondary fault, despite its low activity, change patterns of seismicity generated by the system.

6

Model of earthquake cycles with a slip-dependent constitutive law. Part I - Theory

Senatorski P.

Acta Geophysica Polonica

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2000

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Vol. 48, nr 3

299-316

EN

3D model of interacting faults is presented The use of the slip-weakening friction law, tectonic loading from the sides of a fault zone, and continuous time formulation of governing equations are its major ingredients. The model can be used for simulations of seismic activity both in time scales of single earthquakes, earthquake cycles, and a long-term system evolution. It allows to study time variations of energy release and tectonic stresses, as well as patterns of slips, slip rates and internal stresses measured at individual locations. Results of such an analysis are presented in Part II of this paper.

7

Slip movements along interacting faults. Part II: 3-D model

Senatorski P.

Acta Geophysica Polonica

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1998

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Vol. 46, nr 2

127-134

EN

Long-term slip movements along a zone of two parallel faults are simulated, using a 3-D deterministic model. Two different cases of close and distant faults are considered; fault interactions caused by internal stresses are weaker in the second case, which results in an exponential distribution of seismic energy release obtained for a zone of distant faults. Patterns of energy release are different for the case of close (i.e., interacting) faults, for which we obtain a power-law distribution. It is known that a power-law statistics privileges bigger events; fault interactions are responsible for this effect.

8

Slip movements along interacting faults. Part 1: 2-D model

Senatorski P.

Acta Geophysica Polonica

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1998

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Vol. 46, nr 1

1-12

EN

Long-term slip movements along a zone of four parallel faults are simulated using a 2-D deterministic model. Both antiplane and inplane cases are considered for two different situations of close and distant faults. Fault interactions caused by internal stresses are weaker in the case of distant faults; therefore, we can determine their role played during the system evolution. Slip movements patterns obtained for the antiplane case show that driving tectonic forces lead the system towards a periodic, regular regime, whereas the interactions due to internal stresses play a role of random fluctuactions and destabilize the system behavior. More detailed studies of energy release patterns obtained for the inplane case show, both for regular and irregular regime, calm periods of the same length in which stresses are being built up.