A transverse harmonic seismic wave, which propagates through the upper fractured layer of the Earth towards the Earth's surface, is considered. It is shown that the attenuation of a seismic wave in the Earth's upper crust is due to internal friction, i.e., friction between the sides of micro-fractures. Such a damping mechanism does not work in the deeper layers of the Earth where high lithostatic pressure prevents the movement along fractures. The governing equation for a brittle fractured medium is nonlinear. In the study of wave propagation, an approximate method of harmonic linearization is used. It is shown that internal friction in the upper crust leads to the transformation of a transverse harmonic wave into a shock wave.
Citation: Boris I. Birger. Internal friction in the Earth' crust and transverse seismic waves[J]. AIMS Geosciences, 2022, 8(1): 84-97. doi: 10.3934/geosci.2022006
A transverse harmonic seismic wave, which propagates through the upper fractured layer of the Earth towards the Earth's surface, is considered. It is shown that the attenuation of a seismic wave in the Earth's upper crust is due to internal friction, i.e., friction between the sides of micro-fractures. Such a damping mechanism does not work in the deeper layers of the Earth where high lithostatic pressure prevents the movement along fractures. The governing equation for a brittle fractured medium is nonlinear. In the study of wave propagation, an approximate method of harmonic linearization is used. It is shown that internal friction in the upper crust leads to the transformation of a transverse harmonic wave into a shock wave.
| [1] |
Murrell SAF (1976) Rheology of the lithosphere—experimental indications. Tectonophysics 36: 5-24. 10.1016/0040-1951(76)90003-2 doi: 10.1016/0040-1951(76)90003-2
|
| [2] |
Berckhemer H, Auer F, Drisler J (1979) High-temperature anelasticity and elasticity of mantle peridotite. Phys Earth planet Inter 20: 48-59. https://doi.org/10.1016/0031-9201(79)90107-9 doi: 10.1016/0031-9201(79)90107-9
|
| [3] |
Birger BI (2007) Attenuation of seismic waves and universal rheological model of the Earth's mantle. Izv Phys Solid Earth 43: 635-641. 10.1134/S1069351307080034 doi: 10.1134/S1069351307080034
|
| [4] | Birger BI (2016) Dynamics of the Earth's lithosphere. Moscow: Lenand. |
| [5] | Karato S (2008) Deformation of Earth Materials. An Introduction to the Rheology of Solid Earth. New York: Cambridge University Press. https://doi.org/10.1017/S0016756809006323 |
| [6] | Bogolyubov NN, Mitropolsky YA (1958) Asymptotic methods in the theory of nonlinear oscillations. Moscow: GIFFL. |
| [7] | Palmov VA (1976) Oscillations of elastic-plastic bodies. Moscow: GIFFL. |
| [8] |
Byerlee JD (1968) Brittle-ductile transition in rocks. J Geophys Res 73: 4741-4750. https://doi.org/10.1029/JB073i014p04741 doi: 10.1029/JB073i014p04741
|
| [9] |
Byerlee JD (1978) Friction in rocks. Pure Appl Geophys 116: 615-626. https://doi.org/10.1007/BF00876528 doi: 10.1007/BF00876528
|
| [10] |
Kirby SH (1980) Tectonic stresses in the lithosphere: constraints provided by the experimental deformation of rocks. J Geophys Res 85: 6353-6363. https://doi.org/10.1029/JB085iB11p06353 doi: 10.1029/JB085iB11p06353
|
| [11] | Pavlenko OV (2019) The shock wave as a possible mechanism for generating abnormally high accelerations during the Tohoku earthquake on March 11, 2011 (M = 9.0). Reports of the Academy of Sciences, 484: 98-103. https://doi.org/10.31857/S0869-5652484198-103 |
| [12] | Whitham GB (1974) Linear and Nonlinear Waves. New York: John Wiley & Sons. 10.1002/9781118032954 |
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Boris I. Birger. Internal friction in the Earth' crust and transverse seismic waves[J]. AIMS Geosciences, 2022, 8(1): 84-97. doi: 10.3934/geosci.2022006
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