Wave speeds and attenuation of elastic waves in material containing cracks

Summary. Expressions now exist from which may be calculated the propagation constants of elastic waves travelling through material containing a distribution of cracks. The cracks are randomly distributed in position and may be randomly orientated. The wavelengths involved are assumed to be large compared with the size of the cracks and with their separation distances so that the formulae, based on the mean taken over a statistical ensemble, may reasonably be used to predict the properties of a single sample. The results are valid only for small concentrations of cracks.
Explicit expressions, correct to lowest order in the ratio of the crack size to a wavelength, are derived here for the overall elastic parameters and the overall wave speeds and attenuation of elastic waves in cracked materials where the mean crack is circular, and the cracks are either aligned or randomly orientated. The cracks may be empty or filled with solid or fluid material. These results are achieved on the basis of simply the static solution for an ellipsoidal inclusion under stress.
The extension to different distributions of orientation or to mixtures of different types of crack is quite straightforward.     

Seismic body waves in anisotropic media: propagation through a layer

Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform.     

Effective anisotropic elastic constants for wave propagation through cracked solids

Summary. Theoretical developments of Hudson demonstrate how to calculate the variations of velocity and attenuation of seismic waves propagating through solids containing aligned cracks. The analysis can handle a wide variety of crack configurations and crack geometries. Hudson associates the velocity variations with effective elastic constants. In this paper we associate the variation of attenuation with the imaginary parts of complex effective elastic constants. These complex elastic constants permit the simulation of wave propagation through two-phase materials by the calculation of wave propagation through homogeneous anisotropic solids.     

Seismic anisotropy beneath Dronning Maud Land, Antarctica, revealed by shear wave splitting

Shear wave splitting analyses have been carried out using teleseismic data from broad-band seismograph stations deployed at temporary and permanent locations in Dronning Maud Land (DML), Antarctica. In most cases, the observed anisotropy can be related to major tectonic events that formed the present-day Antarctic continent. We rule out an anisotropic contribution from recent asthenospheric flow. At the Russian base Novolazarevskaya near the coast in central DML, waveform inversion suggests a two-layer model where the fast direction of the upper layer is oriented parallel to Archean fabrics in the lithosphere, whereas the anisotropy of the lower layer is interpreted to have been created during the Jurassic Gondwana break-up. Recordings at the South African base Sanae IV, however, show enigmatic results. For narrow backazimuthal segments, splitting parameters show strong variations together with a multitude of isotropic measurements, indicative of complex scattering that cannot be explained by simple one- or two-layer anisotropic models. In the interior of the continent, the data are consistent with single-layer anisotropy, but show significant spatial variations in splitting parameters. A set of temporary stations across the Heimefront shear zone in western DML yield splitting directions that we interpret as frozen anisotropy from Proterozoic assembly of the craton. An abrupt change in fast axis direction appears to mark a suture between the Grunehogna craton, a fragment of the Kalahari–Kaapvaal craton in southern Africa and the Mesoproterozoic Maudheim Province.     

Seismic coda due to non-linear elasticity

Non-linear elastic response of rocks has been widely observed in laboratory, but very few seismic studies are reported in the literature, even though it is the most natural environment where this feature could be observed. Analytic solutions to the non-linear wave propagation phenomena are not readily available, and there is a need to use approximated techniques. It is clear that when a seismic wave propagates through a homogeneous non-linear elastic media, it will be perturbed by the non-linearity. This perturbation can be treated as a source of scattering, spreading the energy of the primary wave in space and time, contributing to the seismic coda. This is in some sense similar to the effect of heterogeneities. The properties of the coda due to the non-linearity depend on the amount of non-linearity and the seismic moment. Using a perturbation approach we calculate the amplitude of the scattered waves, and show that it can describe reasonably well the main features of real seismic codas.