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Extreme Environmental Events pp 364–383Cite as

Earthquake Scaling Laws

  • Reference work entry

Article Outline

Glossary

Definition of the Subject

Introduction

Earthquakes and Seismic Radiation

Earthquake Fault Models: The Scaling of Geometry and Stress

Earthquake Dynamics and the Scaling of Energy

Kinematics and Statistical Models for Fault Slip

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Seismic moment:

The most fundamental measure of the size of an earthquake. In the simplest situation it represents the moment of on of the couples of forces that make up a dipolar source. In more general cases it is a 3 by 3 symmetric tensor of elementary force couples.

Seismic radiation:

The seismic waves emitted by a seismic source. For point sources these are spherical P and S waves emitted by the point tensor source.

Seismic spectrum:

The absolute value of the Fourier transform of the displacement field radiated by an earthquake in the far field. For almost all earthquakes it has a common shape: flat at low frequencies and decays like the inverse squared power at high very high values of frequency.

Corner frequency:

The low and high frequency asymptotes of the earthquake spectrum intersect at a characteristic frequency, called the corner frequency. The corner frequency scales with the size of the earthquake measured by the seismic moment.

Radiated or seismic energy:

Total energy of the seismic waves radiated by a seismic source. It can be computed from the energy flow relatively far from the source of the earthquake.

Apparent stress:

Originally defined as the product of seismic efficiency times the average stress during earthquake slip. In practice, it is computed from the ratio of radiated energy to moment release of the earthquake multiplied by the shear modulus.

Energy release rate:

Amount of energy per unit surface used to make a rupture advance by a unit distance.

Static stress drop:

The static change in shear traction between the sides of the fault occurs during an earthquake. In principle, it could be determined by measuring stress before and after the earthquake. In practice stress drop is computed using very specific source models, like a circular crack.

Dynamic stress drop:

The stress change in shear traction as a function of time while the rupture is still growing. It can only be estimated from seismic records obtained in the near field by elaborate inversion schemes. The relation between static and dynamic stress drop can only be estimated once the friction law between the sides of the fault has been defined.

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Acknowledgments

This research was partially funded by the SEISMULATORS contract with ANR under program Catastrophes Telluriques et Tsunamis, and by the Research training network SPICE of the 7th PCRD of the European Union. I am deeply indebted to Luis Rivera, Martin Mai and Art McGarr for their careful and patient review of an initial version of this paper.

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  1. Ecole Normale Superieure, Laboratoire de Géologie, Paris, France

    Raul Madariaga

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Madariaga, R. (2011). Earthquake Scaling Laws. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_22

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