Low-frequency seismic wave attenuation in porous media due to microscale yielding
|Location||International Geological Congress,oslo 2008|
|Author||Yarushina, Viktoriya; Podladchikov, Yuri|
|Holding Date||08 October 2008|
We revisit the idea of microscale yielding being responsible for attenuation of small amplitude waves in a wide frequency range. Quality factor (Q) measurements indicate that hydrocarbon-saturated zones often show anomalously high values of attenuation. While Q is considered to be frequency dependent over a wide frequency band it is unclear whether the frequency dependence of Q can be observed in seismic data. In fairly dry rock over limited frequency ranges Q is essentially independent of frequency. It is also well established that microcracks in rock can significantly influence attenuation. The combined observations of frequency independent Q and the role of microcracks in attenuation have been interpreted by many authors in terms of frictional sliding at grain boundaries or across crack faces. However, for typical strain amplitudes of seismic waves and for reasonable microcrack dimensions the computed slip across crack faces was negligible. In addition, it has been shown that frictional attenuation results in nonlinear wave propagation while early available data showed that at low strains typical to seismic waves (<10-6) the behavior of rocks was linear. So, it was concluded that such a nonlinear mechanism as friction cannot be relevant for seismic waves.
The series of recent observations show the presence of nonlinear effects in rocks at strains as small as 10-9 and the lower limit of nonlinearity was not yet observed. Over broad ranges of stress, strain and frequency rocks exhibit nonlinear stress-strain relations, dependence of wave velocity and attenuation on strain amplitude and even the presence of permanent deformation. Indirect evidence for the latter comes from small strain laboratory experiments frequently reporting cusped stress-strain hysteresis loops. The permanent and, importantly, time independent (plastic) deformation in rocks at typical seismic strains was explicitly observed in experiments. Plastic yielding is not expected if a stress-free rock sample is loaded by small seismic strains. However, sediments may be already in a yield state or close to it as a result of complex burial and tectonic loading history. Moreover, rocks are very heterogeneous and heterogeneities may act as local stress concentrators, so that the actual microscopic stresses around cavities and inclusions may be much higher than the macroscopic stress level.
We study attenuation of seismic P- and S-waves due to local plastic yielding around cavities in porous media. Following the effective media approach, we consider low porosity material containing non-interacting isolated spherical or cylindrical pores under cyclic loading by both isotropic and shear stress field imitating passage of a wave, and evaluate resulting dissipation in terms of quality factor Q. Assuming initial local microscopic stress state around the cavity at the yield, we show that even for small seismic strains attenuation can be high and independent of both frequency and strain amplitude.