Seismic anisotropy as measured under high-pressure, high-temperature conditions

Summary. Four types of crustal and upper-mantle rocks have been used for the investigation of seismic P -wave velocities in three mutually perpendicular directions. Hydrostatic pressure, up to 6 kbar and temperatures up to 500°C were applied to the samples. Measurements of the ultrasonic P -wave travel times and velocities were carried out along two geotherms. All rock types show an anisotropic behaviour which is caused by the orientation of certain minerals. The anisotropy is not dependent on temperature and pressure. Gneiss and peridotite have 5–6 per cent anisotropy whereas granite and a metagabbro show values of only 2–3 per cent. The smallest velocity is always in the z direction, perpendicular to a schistocity or foliation. It is shown that the data agree with those of field observation. We conclude that anisotropy caused by preferred orientation of minerals must be expected in the whole lithosphere. Additional effects of layering, of cracks, and of nonhydrostatic stresses are estimated.     

The Oblique Seismic Experiment on DSDP Leg 52

Summary. The Oblique Seismic Experiment (OSE) has been proposed to increase the usefulness of the IPOD crustal borehole as a means of investigating layer 2 of oceanic crust. Specific objectives are: to determine the lateral extent of the structure intersected by the borehole, to analyse the role of cracks in the velocity structure of layer 2, to look for anisotropy which may be caused by large cracks with a preferred orientation and, finally, to measure attenuation in oceanic crust.
The first successful Oblique Seismic Experiment in oceanic crust was carried out in 1977 March in a hole 400 miles north of Puerto Rico. An adequate study of lateral velocity variations was impossible because the hole was not deep enough, the hole was inadequately logged, and the small scale basement topography was not known. In general both P - and S -wave velocity profiles suggest that the crack density decreases with depth in layer 2. Velocities at the bottom of layer 2 are the same as matrix velocities for basalt, implying that crack density may be negligible at this depth. No convincing evidence for anisotropy in either layer 2 or 3 is found from travel time analysis. The hole was not deep enough to measure attenuation from normal incidence shots and amplitudes were not consistent enough to obtain a measure of attenuation from long range shots.     

Characterization of crack distribution: fabric analysis versus ultrasonic inversion

We analyse the relation between rock fabric, expressed by the preferred orientation of rock-forming minerals and microcracks, and elastic anisotropy of crystalline rock from the KTB pilot well. Detailed analyses of mineralogical composition, textures and microcrack fabrics were performed. In addition, ultrasonic velocity measurements of spherical samples in several directions were carried out at various confining pressures, and inverted in terms of the complete set of 21 elastic constants. By comparing the elastic tensors of the rocks at the final confining pressure (at which most of the microcracks are closed) with those at a lower pressure level, it is possible to separate the anisotropy induced by microcracks from that caused by mineral alignment. In contrast to previous work, no a priori knowledge of the type of anisotropy (triclinic, monoclinic, orthotropic etc.), or of the spatial orientation of the symmetry elements (planes, axes) of the cracked rock or of the intact rock is assumed. Furthermore, no restrictive assumptions on the orientation distribution function and the shape of the cracks are needed.
The results show that the elastic anisotropy characteristics, whether they are related to the microcracks or to the rock-forming minerals, are clearly correlated with the directly observed rock fabrics. We show that the symmetry directions of the mineral fabric and of microcrack fabric agree. A further result is that the microcrack-induced anisotropy dominates the other causes of anisotropy at confining pressures smaller than a few tens of megapascals, the situation being reversed at higher pressures. The laboratory data are quantitatively compared with sonic log data from the KTB well, showing the influence of pore fluids, effective pressure and crack density reduction on the anisotropy in situ .     

Seismic anisotropy of the subcrustal lithosphere as evidence for dynamical processes in the upper mantle

Summary. Anisotropy of seismic waves in the uppermost mantle has not only been observed in the oceanic but recently also in the continental lithosphere. Laboratory experiments on the formation of preferred orientation of olivine crystals suggest plastic flow às the most likely mechanism for the genesis of anisotropy in the upper mantle. Since the direction of maximum velocity correlates in the ocean and on the continent with a number of tectonic features, a causal connection between anisotropy and dynamical processes related to plate motions must be suspected.     

On the origin of the seismic anisotropy of the lithosphere

Summary. It is known that flow in the mantle can produce preferred orientation in olivine crystals with seismic anisotropy as a consequence. Flow in the subcrustal lithosphere is unlikely because of the high viscosity. Lenses of high temperature and low-viscosity ( anomalous mantle ) are located under the crust in many tectonically active regions, and viscous flow can easily arise in such material resulting in seismic anisotropy. After cooling, such anomalous mantle acquires high viscosity and becomes incorporated into the lithospheric layer preserving the anisotropy produced by the flows which existed previously. The interaction of the stresses with cracks in the upper crust can be one of the causes of anisotropy in this layer.     

P-wave velocity anisotropy in crystalline rocks

Summary. Compressional wave velocities and anisotropy coefficients determined at high hydrostatic pressures are compiled from the data published for the main types of crystalline rocks. The crack-free elastic anisotropy of igneous crustal rocks is generally very low, between 1 and 3 per cent on average. The anisotropy of metamorphic rocks is higher (up to 22 per cent), but very variable. The average anisotropy coefficients in schists and amphibolites are about 10 per cent, in gneisses between 3 and 7 per cent, and in granulites less than 3 per cent. The average anisotropy of olivine ultramafites is between 7 and 12 per cent, whereas in pyroxenites and eclogites it is usually less than 4 per cent. A comparison of ranges of average velocities and average anisotropies for the individual rock groups suggests that, whereas in the crust the lateral velocity variations are mainly due to compositional changes, in the olivine of the uppermost mantle the velocity variations due to anisotropic structures could be of the same magnitude as the variations due to inhomogeneities.     

The magnitude, symmetry and origin of upper mantle anisotropy based on fabric analyses of ultramafic tectonites

Summary. Seismic anisotropy within the upper mantle originates from the preferred orientation of highly anisotropic single crystals. The symmetry and magnitude of anisotropy depend upon: (1) the volume percentages of the minerals constituting the upper mantle, (2) the degree and symmetry of preferred orientation of each mineral and (3) the alignment of the minerals' crystallographic axes relative to one another. The nature of upper mantle anisotropy can be examined by studying mineral orientations within ultramafic rocks which were once part of the mantle. Petrofabric data for olivine and pyroxene have been used to obtain velocity anisotropy patterns over large regions of ultramafic rocks from the Samail ophiolite, Oman, the Troodos ophiolite, Cyprus, the Bay of Islands ophiolife, Newfoundland, the Twin Sisters ultramafic, Washington, USA, the Dun Mountain ophiolite, New Zealand, the Red Hills ophiolite, New Zealand and the Red Mountain ophiolite, New Zealand. The compressional wave anisotropy calculated for these massifs ranges from 3 to 8 per cent, in excellent agreement with observed seismic anisotropy in the upper continental and oceanic mantle. The symmetry varies from orthorhombic to axial, with the axial symmetry axis corresponding to the olivine a-axes maxima and subparallel to spreading directions in oceanic upper mantle. Pyroxene a -, b - and c -axes maxima generally parallel olivine b -, c - and a -axes, respectively, and anisotropy decreases with increasing pyroxene content. Shear-wave splitting is predicted for all propagation directions within the upper mantle. Symmetry is also orthorhombic or axial, with the minimum difference in velocity between the two shear-waves parallel to the maximum compressional wave velocity.     

Three-dimensional image of the anisotropic bodies beneath central Honshu, Japan

Shear-wave splitting from local deep earthquakes is investigated to clarify the volume and the location of two anisotropic bodies in the mantle wedge beneath central Honshu, Japan. We observe a spatial variation in splitting parameters depending on the combination of sources and receivers, nearly N–S fast in the northern region, nearly E–W fast in the southern region and small time delays in the eastern region. Using forward modelling, two models with 30 and 10 per cent anisotropy are tested by means of a global search for the locations of anisotropic bodies with various volumes. The optimum model is obtained for 30 per cent anisotropy, which means a 5 per cent velocity difference between fast and slow polarized waves. The northern anisotropic body has a volume of 1.00° (longitude) × 0.5° (latitude) × 75 km (depth), with the orientation of the symmetry axis being N20°E. The southern anisotropic body has a volume of 1.25° × 1.25° × 100 km with the symmetry axis along N95°E. Our results show that the anisotropic bodies are located in low-velocity and low- Q regions of the mantle. This, together with petrological data and the location of volcanoes in the arc, suggests that the possible cause of the anisotropy is the preferred alignment of cracks filled with melt.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

Surface wave tomography for azimuthal anisotropy in a strongly reduced parameter space

Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.     

Shear-wave polarization anisotropy in the Pacific Basin

Summary. Inversion of 295. Love- and Rayleigh-wave phase travel times across the Pacific Basin has yielded a structure which has a channel that is anisotropic with respect to the polarization of shear waves. The velocity of SH waves is approximately 4.24 km/s, and the velocity of SV waves is approximately 4.10 km/s in the low-velocity channel. The lid to the channel is isotropic with respect to the polarization of S waves and the velocity is approximately 4.60 km/s. The lid to the low-velocity channel increases in thickness with lithospheric age at the expense of the channel, and its thickness is apparently still increasing at a sea-floor age of 150 Myr.
These results can be explained in terms of a model with both randomly-and preferentially-oriented, liquid-filled cracks in the channel. In the model, it is assumed that the liquid-filled cracks are due to partial melting in the channel, and that any preferred orientation is caused by a shear-flow gradient resulting from differential motion between the lid and the deeper parts of the mantle.     

An anisotropic model of the Earth's crust in the Baikal rift zone

Summary. An attempt is made to explain the existence of intracrustal low-velocity layers in rift zones by using an anisotropic model. It is supposed that the anisotropy is due to the preferred orientation of micas and amphiboles in metamorphic rocks forming the upper crust. Analysing the velocity distribution along different directions in anisotropic media the authors conclude that the low-velocity layer must be isotropic (randomly oriented) with an anisotropic lid.     

Seismic P-wave anisotropy in the subcrustal lithosphere of north-west Australia

Summary. Reduced P_n travel times from the Archaean Pilbara Craton of north-west Australia show a strong correlation with azimuth, which could be used as evidence of anisotropy. However, the azimuthal correlation could also be explained by a southerly dip of between 1 and 2° on the crust–mantle boundary, although the models from several reversed seismic profiles across the craton suggest a smaller dip.
A time-term analysis of the P_n date yielded several models. The preferred solution, in which the dip on the crust–mantle boundary is similar to that in the models from the reversed profiles, has approximately 2 per cent anisotropy in the uppermost mantle, with the direction of maximum velocity 30° east of north. One possible cause of the anisotropy is that olivine crystals were aligned by syntectonic recrystallization and/or power law creep in the tensional environment caused at the base of the lithosphere by flexure during loading of the lithosphere by the strata of the Hamersley Basin which overlies the Pilbara Craton.
A seismic discontinuity occurs about 15 km below the crust–mantle boundary under the craton. A qualitative analysis of all available seismic data suggests that the velocity below the boundary is probably also anisotropic, with the direction of maximum velocity between north and 40° west of north. The direction of minimum velocity below the sub-Moho boundary correlates loosely with the direction of basement lineaments in the Proterozoic Capricorn Orogenic Belt to the south of the craton, suggesting that the anisotropy under the boundary may be younger than that immediately under the crust/mantle boundary. This is consistent with the notion that the Archaean lithosphere was thinner than the present lithosphere.     

Finite-frequency vectorial tomography: a new method for high-resolution imaging of upper mantle anisotropy

Amplitude measurements of the transverse component of SKS waves, the so-called splitting intensity, can be used to formulate a non-linear inverse problem to image the 3-D variations of upper mantle anisotropy. Assuming transverse isotropy (or hexagonal symmetry), one can parametrize anisotropy by two anisotropic parameters and two angles describing the orientation of the symmetry axis. These can also be written as two collinear pseudo-vectors. The tomographic process consists of retrieving the spatial distribution of these pseudo-vectors, and thus resembles surface wave vectorial tomography. Spatial resolution results from the sensitivity of low-frequency SKS waves to seismic anisotropy off the ray path. The expressions for the 3-D sensitivity kernels for splitting intensity are derived, including the near-field contributions, and validated by comparison with a full wave equation solution based upon the finite element method. These sensitivity kernels are valid for any orientation of the symmetry axis, and thus generalize previous results that were only valid for a horizontal symmetry axis. It is shown that both lateral and vertical subwavelength variations of anisotropy can be retrieved with a dense array of broad-band stations, even in the case of vertically propagating SKS waves.     

Crack propagation by differential insolation on desert surface clasts

In the southwest U.S., cracks in alluvial fan surface clasts have a preferred orientation independent of rock fabric and shape. In this paper, we show that differential insolation of incipient cracks of random orientations predicts a distribution of crack orientations consistent with field observations. In this model, crack growth by hydration and/or thermal weathering is primarily a function of local water content at the crack tip. Crack tips that experience minimal solar insolation maintain a greater average moisture and, hence, weather more rapidly than cracks that experience greater solar insolation. To show this, we used a numerical radiative transfer code to quantify the solar insolation of rectangular cracks at 35° N. latitude with a range of depths and orientations. The amount of solar energy reaching the bottom of each crack was calculated at 5-min intervals over the day for several days of the year to determine hourly, daily, seasonal, and annual energy deposition as a function of crack depth and orientation. By assuming that only crack orientations that effectively shield their interiors and minimize their water loss are able to grow, the pattern of cracks produced by the model is consistent with field observations. The annual average insolation, which controls water retention, is associated with the two primary modes of crack orientation. The effect of daily recharge by summer rains of the North American monsoon system is consistent with the observed deviations from these primary modes. Model results suggest that both the annual average insolation and the daily pattern of rainfall is recorded in the preferred crack orientations of surface clasts in the southwest U.S.     

Ray tracing and inhomogeneous dynamic ray tracing for anisotropy specified in curvilinear coordinates

Ray tracing has recently been expressed for anisotropy specified in a local Cartesian coordinate system, which may vary continuously in a model specified by elastic parameters. It takes advantage of the fact that anisotropy is often of a simpler nature locally (and is thus specified by a smaller number of elastic parameters) and that the orientation of its symmetry elements may vary. Here we extend this approach by replacing the local Cartesian coordinate system with a curvilinear coordinate system of global extent and by applying the new approach to ray tracing and inhomogeneous dynamic ray tracing. The curvilinear coordinate system is orthogonal and is constructed so that the coordinate axes are consistent with the considered anisotropy of the medium. Our formulation allows for computation of ray attributes (e.g. ray velocity vector and paraxial ray attributes) in the curvilinear coordinate system, while rays are computed in global Cartesian coordinates. Compared to the classic formulation in terms of 21 elastic moduli in global Cartesian coordinates, the main advantages are improved efficiency, lower computer-memory requirements, and conservation of anisotropic symmetry throughout the model.     

Anisotropy in the oceanic lithosphere of the North-western Pacific Basin

Summary. A series of long-range explosion seismological experiments has been conducted by the use of specially designed ocean bottom seismographs (OBSs) in the Western Pacific. OBS studies of apparent velocity measurements by the use of natural earthquakes have also been made. The experiments have made clear that large-scale P -wave anisotropy exists in the entire thickness of the oceanic lithosphere. The existence of the large-scale anisotropy in the oceanic lithosphere has been demonstrated for the first time by seismic body-wave studies. Previously, anisotropy had been found only in the uppermost oceanic mantle in the Eastern Pacific.
The azimuth of the maximum velocity, 8.6 km s^-1, is about 155° clock-wise from north. The direction is perpendicular to the magnetic lineation of the region, however, the direction differs from the direction of the present plate motion by about 30°. So it appears that the anisotropy has been 'frozen' at least since the change of the plate motion that occurred 40 Myr ago. The frozen anisotropy should set important constraints on the mechanical properties of the lithosphere such as the viscosity and temperature of the lower lithosphere.     

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.     

Earthquake prediction: a new physical basis

Summary. Subcritical crack growth in the laboratory occurs slowly but progressively in solids subjected to low stresses at low strain rates. The cracks tend to grow parallel to the maximum compressive stress so that, when this stress is aligned over a large enough region, the cracks will also be aligned and possess effective seismic anisotropy. It is suggested that such subcritical crack growth produces extensive-dilatancy anisotropy (EDA) throughout earth-quake preparation zones. This process is a possible driving mechanism for earthquake precursors observed at substantial distances from impending focal zones, and provides, in the shear-wave splitting which has been observed in several seismic regions, a possible technique for monitoring the build-up of stress before earthquakes.     

Magnetic anisotropy produced by magma flow: theoretical model and experimental data from Ferrar dolerite sills (Antarctica)

Volcanic rocks forming sills, dykes or lava flows may display a magnetic anisotropy derived from the viscous flow during their emplacement. We model a sill as a steady-state flow of a Bingham fluid, driven by a pressure gradient in a horizontal conduit. The magma velocity as a function of depth is calculated from the motion and constitutive equations. Vorticity and strain rate are determined for a reference system moving with the fluid. The angular velocity and the orientation of an ellipsoidal magnetic grain immersed in the fluid are calculated as functions of time or strain. Magnetic susceptibility is then calculated for a large number of grains with a uniform distribution of initial orientations. It is shown that the magnetic lineation oscillates in the vertical plane through the magma flow direction, and that the magnetic foliation plane changes periodically from horizontal to vertical. The results are compared with the magnetic fabric of Ferrar dolerite sills (Victoria Land, East Antarctica) derived from low-field susceptibility measurements.