Attenuation anisotropy and the relative frequency content of split shear waves

Abstract

S U M M A R YThe variation of frequency-dependent seismic wave attenuation with direction (attenuation anisotropy) contains additional information to that contained in velocity anisotropy. In particular, it has the potential to distinguish between different mechanisms that can cause velocity anisotropy. For example, aligned fracturing might be expected to cause measurable velocity and attenuation anisotropy, while preferred crystal orientation leads to significant velocity anisotropy but may cause only small amounts of attenuation. Attenuation anisotropy may also contain useful information about pore-fluid content and properties. We present a methodology for analysis of attenuation anisotropy, and apply it to a microseismic data set previously analysed for shear-wave splitting by Teanby et al. (2004). Attenuation anisotropy values obtained show a temporal variation which appears to correlate with the temporal variation in the velocity anisotropy. The comparison of the relative frequency content of fast (S1) and slow (S2) split shear waves is a convenient method for examining seismic attenuation anisotropy. Provided that S1 and S2 initially have the same spectral colouring, that no spectral distortion is introduced by the differences between receiver responses of geophone components, and that spectral distortion due to background noise can be ignored or corrected for, we can attribute any differences in their frequency content to attenuation anisotropy. Attenuation anisotropy, where present, should be detected by the different (approximately orthogonal) polarizations of S1 and S2 as they pass through the anisotropic medium. In the presence of attenuation anisotropy S1 and S2 should experience different levels of frequency-dependent attenuation. We quantify the differential attenuation of S1 and S2 using a scheme based on a spectral ratio method. We present results from a microseismic data set acquired in an abandoned oil well at Valhall, a North Sea oil field. The results are surprising in that sometimes the slower arrival, S2, is richer in high frequencies than the faster, S1. This appears to be contrary to results predicted by theoretical crack models for attenuation anisotropy (e.g. Hudson 1981). The mechanism responsible for these observations is not clear. Our differential attenuation attribute correlates with the angle between the strike of the inferred initial shear-wave source polarization and the fast shear-wave polarization, which suggests that the split shear wave with the larger amplitude is preferentially attenuated. Our attribute also correlates with the event backazimuth, and the minimum percentage anisotropy.

An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

“…The anisotropic attenuation of rocks is found from ultrasonic observation in the laboratory (Tao and King, 1990;Best et al, 2007;Zhubayev et al, 2016) and from a field seismic survey (Carter and Kendall, 2006;Clark et al, 2009;Behura et al, 2012;Shekar and Tsvankin, 2012). Because waves tend to exhibit anisotropic behavior as a result of the natural thin layering of the earth, we would expect the same waves to experience an anisotropic attenuation for the same reason.…”

Analysis of fracture induced scattering of microseismic shear-waves

“…(32) tested the (36) model on several microseismic datasets of shear-waves splitting to predict attenuation of the split shear-waves. However, (32) observed that sometimes the fast shearwave was more attenuated at higher frequencies than the slow shear-wave.…”

“…However, (32) observe that the fast shear-wave can experience larger attenuation than the slow shear-wave, and suggest that the relative peak amplitude of the split shear-waves are depend more on the initial polarization of the incident shear-wave than on the relative levels of frequencydependent attenuation. The LASR for the Normal model can be simplified based on the assumption that the shear-wave onset times will be equal (t X = t Z )…”

Frequencies of the Ricker wavelet

“…The latter is a statistical quantity that can be evaluated practically from the discrete Fourier spectrum of the seismic data. In the published literature, some works implement the evaluation of the mean frequency using the power spectrum Lee, 1989, 1990;Barnes, 1993;Loughlin and Tacer, 1997;Loughlin and Davidson, 2001;Carter and Kendall, 2006;Wang, 2014), and other works use the amplitude spectrum (Quan and Harris, 1997;Hu et al, 2013). We derive expressions analytically for both statistical cases and prove that the central frequency is close to the mean frequency evaluated from the power spectrum rather than the amplitude spectrum.…”