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1

Stress release during earthquake sequences

Gibowicz S.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 3

271-299

EN

The average stress drop and apparent stress released during 65 complex earthquake sequences from all over the world are estimated separately for foreshocks, main shocks and aftershocks. All of them but one occurred between 1977 and 1997. The Harvard CMT solutions are available for 60 main shocks, 38 foreshocks and 218 aftershocks. The stress drop is estimated using the values of seismic moment and source half duration and the scaling relations between various source parameters: seismic moment, source half duration, fault surface and fault length, taken from Harvard catalogues and other publications. The average stress drop is the highest during foreshocks (1.8 MPa), middle during main shocks (1.1 MPa) and the lowest during aftershocks (0.4 MPa). Similarly, the apparent stress, estimated from seismic moment and radiated energy taken from PDE-NEIC bulletins and other publications, is also the highest for foreshocks (0.6 MPa), middle for main shocks (0.4 MPa) and the lowest for aftershocks (0.2 MPa).

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

Apparent stress and stress drop from seismic events induced by mining

Gibowicz S.

Acta Geophysica Polonica

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2002

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Vol. 50, nr 1

35-49

EN

Seven sets of the values of uniformly estimated apparent stress and Brune's stress drop from 987 seismic events, with moment magnitude ranging from -3.6 to 3.8, were collected from two South African gold mines, two Polish coal and two copper mines, and from the Underground Research Laboratory (URL) in Canada. They are used to examine their relations with radiated energy, seismic moment and source dimension to provide observational evidence of differences for slip-weakening as compared to velocity-weakening friction, found from elasto-dynamic source modeling of Shaw (1998). The observations from various data sets scale differently, but their pattern is not always distinctly related to the different frictions. The distribution of the apparent stress divided by the stress drop as a function of seismic moment is the most similar to the relevant distribution obtained by modeling, and it seems that both modes of friction are possible during the generation of seismic events in various mining environments.

5

Radiated energy scaling for seismic events induced by mining

Gibowicz S.

Acta Geophysica Polonica

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2001

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Vol. 49, nr 1

95-111

EN

Seven sets of the values of radiated energy from 987 seismic events from two South African gold mines, four Polish coal and copper mines, and from the Underground Research Laboratory (URL) in Canada are used to examine their scaling with seismic moment, apparent stress and average displacement. Moment magnitude of these events ranges from -3.6 to 3.8, the seismic energy ranges from 1x10(-3) to 1x10(11) J, and the apparent stress is between 0.0025 and 5 MPa. The slope of regression straight line between the logarithm of radiated energy and that of seismic moment is very close to 1.5 in all cases, which seems to have theoretical justification. The average values of seismic energy, however, referred to the same range of seismic moment, are about 30 times higher for seismic events from South African hard-rock mines that those observed from events in Polish mines. Similarly, the slope of a linear regression between the logarithm of apparent stress and that of energy is fairly close to 1/3 for the events from South African and Polish mines. But the average apparent stress, referred to the same range of seismic energy, is about 10 times higher for the events in South Africa than for those in Poland. The relations between the average slip and the energy are on a logarithmic scale surprisingly consistent and more regular than similar relations based on seismic moment. The events from the URL follow the same trend as the events from South Africa, whereas for the events from Poland the average slip is about 5 times lower than that for the other events.