Anisotropic Inversion Research Articles

Sign inversion of dielectric anisotropy in nematic liquid crystal by dye doping

The present paper reports sign inversion in dielectric anisotropy of a nematic liquid crystal, i.e. 5CB, as an effect of doping dye (solvent green 3) in small amount. It is the result of strong variation of the parallel component of dielectric permittivity with temperature for a dye doped sample. This behavior is attributed to the interaction taking place between the nematic liquid crystal molecule and the dye molecule. This behavior of dielectric anisotropy has been explained on the basis of interaction between the dye (guest) and the liquid crystal molecules (host).

Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy

Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in the spherical, stationary, non-streaming Jeans equation has been handled by assuming a mass profile and fitting models to the observed kinematical data. Here, the opposite approach is considered: the equation of anisotropic kinematic projection is inverted for known arbitrary anisotropy to yield the space radial velocity dispersion profile in terms of an integral involving the radial profiles of anisotropy and isotropic dynamical pressure. Then, through the Jeans equation, the mass profile is derived in terms of double integrals of observable quantities. Single integral formulas for both deprojection and mass inversion are provided for several simple anisotropy models (isotropic, radial, circular, general constant, Osipkov-Merritt, Mamon-Lokas and Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these anisotropy models yield accurate results in the case of perfect observational data, and typically better than 70% (in 4 cases out of 5) accurate mass profiles for the sampling errors expected from current observational data on clusters of galaxies. For the NFW model with mildly increasing radial anisotropy, the mass is found to be insensitive to the adopted anisotropy profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii. This anisotropic mass inversion method is a useful complementary tool to analyze the mass and anisotropy profiles of spherical systems. It provides the practical means to lift the MAD in quasi-spherical systems such as globular clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and clusters of galaxies, when the anisotropy of the tracer is expected to be linearly related to the slope of its density.

Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media

A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters [Formula: see text] and [Formula: see text], and the tilt angle. The finite-difference discretization relies on a parsimonious mixed-grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at the source or at seismic discontinuities when [Formula: see text]. In frequency-domain modeling with absorbing boundary conditions, the unstable S-wave mode is not excited when [Formula: see text], allowing stable simulations of the P-wave mode for such anisotropic media. Some S-wave instabilities are seen in the PMLs when the symmetry axis is tilted and [Formula: see text]. These instabilities are consistent with previous theoretical analyses of PMLs in anisotropic media; they are removed if the grid interval is matched to the P-wavelength that leads to dispersive S-waves. Comparisons between seismograms computed with the frequency-domain acoustic TTI method and a finite-difference, time-domain method for the vertical transversely isotropic elastic equation show good agreement for weak to moderate anisotropy. This suggests the method can be used as a forward problem for viscoacoustic anisotropic full-waveform inversion.

Explicit expressions for the Fréchet derivatives in 3D anisotropic resistivity inversion

We have developed explicit expressions for the Fréchet derivatives or sensitivity functions in resistivity imaging of a heterogeneous and fully anisotropic earth. The formulation involves the Green’s functions and their gradients, and it is developed from a formal perturbation analysis and by means of a numerical (finite-element) method. A critical factor in the equations is the derivative of the electrical conductivity tensor with respect to the principal conductivity values and the angles defining the axes of symmetry. The Fréchet derivative expressions were derived for the 2.5D and 3D problems using constant-point and constant-block model parameterizations. Special cases such as an isotropic earth and tilted transversely isotropic (TTI) media emerge from the general solutions. Numerical examples were investigated for various sensitivities as functions of dip angle and strike of the plane of stratification in uniform TTI media.

Voltage controlled inversion of magnetic anisotropy in a ferromagnetic thin film at room temperature

The control of magnetic properties by means of an electric field is an important aspect in magnetism and magnetoelectronics. We here utilize magnetoelastic coupling in ferromagnetic/piezoelectric hybrids to realize a voltage control of magnetization orientation at room temperature. The samples consist of polycrystalline nickel thin films evaporated onto piezoelectric actuators. The magnetic properties of these multifunctional hybrids are investigated at room temperature as a function of the voltage controlled stress exerted by the actuator on the Ni film. Ferromagnetic resonance spectroscopy shows that the magnetic easy axis in the Ni film plane is rotated by 90° upon changing the polarity of the voltage Vp applied to the actuator. In other words, the in-plane uniaxial magnetic anisotropy of the Ni film can be inverted via the application of an appropriate voltage Vp. Using superconducting quantum interference device (SQUID) magnetometry, the evolution of the magnetization vector is recorded as a function of Vp and of the external magnetic field. Changing Vp allows to reversibly adjust the magnetization orientation in the Ni film plane within a range of approximately 70°. All magnetometry data can be quantitatively understood in terms of the magnetic free energy determined from the ferromagnetic resonance experiments. These results demonstrate that magnetoelastic coupling in hybrid structures is indeed a viable option to control magnetization orientation in technologically relevant ferromagnetic thin films at room temperature.

Feasibility study for an anisotropic full waveform inversion of cross‐well seismic data

ABSTRACTAnisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data.Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium.The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient.The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f−k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters.

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.

P-wave anisotropic tomography beneath Northeast Japan

We determined a 3-D P-wave anisotropic tomography beneath Northeast Japan by using first P-arrival times. The travel-time inversion is parameterized with an isotropic component and two anisotropic parameters for each grid node by assuming P-wave azimuthal anisotropy with hexagonal symmetry axis distributed horizontally. The geometries of the Conrad and Moho discontinuities and the upper boundary of the subducting Pacific plate are taken into account in the model. Our extensive synthetic tests show that the anisotropic velocity inversion method is reliable. Our results show that low-velocity zones exist below active volcanoes in the crust, in the fore-arc mantle wedge and in the central portion of the mantle wedge above the high-velocity Pacific slab, which are similar to the previous tomographic images. Anisotropic velocity variations are revealed in the crust, mantle wedge and the subducting Pacific slab. The anisotropic patterns are complex and different in the upper and lower crust. In the mantle wedge, the fast direction of P-velocity is generally trench-parallel in the fore-arc area, while it becomes trench-normal in the back-arc area, which agree well with the shear-wave splitting results. The trench-parallel fast direction is revealed beneath the volcanic front, which may suggest the existence of complex 3-D mantle flows in the mantle wedge. The fast-velocity direction in the subducting Pacific slab is mostly N–S, which is likely due to the original fossil anisotropy of the Pacific plate formed at the mid-ocean ridge. Our result also suggests that the anisotropy is weak in the upper crust and the average amplitude of the velocity anisotropy in the mantle is no larger than 4%.

Nonlinear traveltime inversion scheme for crosshole seismic tomography in tilted transversely isotropic media

Crosshole seismic tomography often is applied to image the velocity structure of an interwell medium. If the rocks are anisotropic, the tomographic technique must be adapted to the complex situation; otherwise, it leads to a false interpretation. We propose a nonlinear kinematic inversion method for crosshole seismic tomography in composite transversely isotropic media with known dipping symmetry axes. This method is based on a new version of the first-order traveltime perturbation equation. It directly uses the derivative of the phase velocity rather than the eigenvectors of the body-wave modes to overcome the singularity problem for application to the two quasi-shear waves. We applied an iterative nonlinear solver incorporating our kinematic ray-tracing scheme and directly compute the Jacobian matrix in an arbitrary reference medium. This reconstructs the five elastic moduli or Thomsen parameters from the first-arrival traveltimes of the three seismic body waves (qP, qSV, qSH) in strongly and weakly anisotropic media. We conducted three synthetic experiments that involve determining anisotropic parameters for a homogeneous rock, reconstructing a fault embedded in a strongly anisotropic background, and imaging a complicated four-layer model containing a small channel and a buried dipping interface. We compared results of our nonlinear inversion method with isotropic tomography and the traditional linear anisotropic inversion scheme, which showed the capability and superiority of the new scheme for crosshole tomographic imaging.

Anisotropic shear‐wave velocity structure of the Earth's mantle: A global model

We combine a new, large data set of surface wave phase anomalies, long‐period waveforms, and body wave travel times to construct a three‐dimensional model of the anisotropic shear wave velocity in the Earth's mantle. Our modeling approach is improved and more comprehensive compared to our earlier studies and involves the development and implementation of a new spherically symmetric reference model, simultaneous inversion for velocity and anisotropy, as well as discontinuity topographies, and implementation of nonlinear crustal corrections for waveforms. A comparison of our new three‐dimensional model, S362ANI, with two other models derived from comparable data sets but using different techniques reveals persistent features: (1) strong, ∼200‐km‐thick, high‐velocity anomalies beneath cratons, likely representing the continental lithosphere, underlain by weaker, fast anomalies extending below 250 km, which may represent continental roots, (2) weak velocity heterogeneity between 250 and 400 km depths, (3) fast anomalies extending horizontally up to 2000–3000 km in the mantle transition zone beneath subduction zones, (4) lack of strong long‐wavelength heterogeneity below 650 km suggesting inhibiting character of the upper mantle–lower mantle boundary, and (5) slow‐velocity superplumes beneath the Pacific and Africa. The shear wave radial anisotropy is strongest at 120 km depth, in particular beneath the central Pacific. Lateral anisotropic variations appreciably improve the fit to data that are predominantly sensitive to the uppermost and lowermost mantle but not to the waveforms that control the transition zone and midmantle depths. Tradeoffs between lateral variations in velocity and anisotropy are negligible in the uppermost mantle but noticeable at the bottom of the mantle.

Tomographic inversion for three-dimensional anisotropy of Earth’s inner core

Seismological studies generally suggest that the Earth’s inner core is anisotropic and the anisotropic structure changes significantly both laterally and with depth. Previous body-wave studies of the inner core have relied on ray tracing or waveform modeling using one-dimensional (1D) models. Here we present non-linear tomographic inversions of the inner core anisotropy using three-dimensional (3D) ray tracing, spline parameterization, and a large collection of PKP differential travel times. We adapt a pseudo-bending ray tracing (PBR) method in spherical coordinates for seismic rays that traverse the inner core (PKP(DF) phase). The method iteratively perturbs each discontinuity point and continuous segment of the ray through 3D earth structure so that its travel time is minimum. The 3D anisotropic structure of the inner core is approximated to the first order as 3D heterogeneous (but isotropic) structure for a given ray. The data are corrected using a scaled mantle tomographic model. The inner core anisotropy model obtained has the following major features. (1) The model has strong hemispherical and depth variation. The isotropic velocity in the topmost inner core is greater in quasi-eastern hemisphere (QEH) (40–160°E) than in quasi-western hemisphere (QWH) (other longitudes). The anisotropy is weak in QEH to the depth of 600–700 km below the inner core boundary (ICB), while in QWH, the anisotropy increases at much shallower depth (about 100–200 km below the ICB) to about 3–4%, then remains at about 2–4% throughout the rest of the inner core. (2) The anisotropy form changes abruptly (over a depth range of about 150 km) at the radius of about 600 km, slightly less than half of the inner core radius, forming a distinct inner inner core (IIC). The velocity in the IIC has maximums at equatorial and polar directions and minimum at an angle of about 40° from the equatorial plane. The velocity in the outer inner core (OIC), however, changes little for ray directions 0–40° from the equatorial plane. (3) Despite large variation of the anisotropy, the isotropic velocity (Voigt average) throughout the inner core is nearly uniform. The results suggest that the OIC is likely composed of the same type of iron crystals with uniform chemistry, but the IIC may be composed of a different type of crystal alignment, a different iron phase, or a different chemical composition. Our tests on model parameterization, mantle correction, and linear and non-linear inversion suggest the main features of our model are very robust. However, fine scale structures are likely to differ, particularly in the major transition zones, e.g., in the topmost QWH (isotropy to anisotropy), between OIC and IIC (change in the form of anisotropy), and between QEH and QWH in OIC (difference in anisotropy strength). Searches for possible waveform complications from these boundaries need to be aware of the directional dependence and geographical variation to be successful.

Asymmetry reversal of thermomagnetic avalanches in Pb films with a ratchet pinning potential

We combine transport measurements and magneto-optical imaging in order to study vortex motion in Pb samples with a square lattice of asymmetric pinning potentials formed by two antidots of different sizes. Near the boundary with the normal phase, a vortex ratchet effect is detected when an ac-current is applied. As previously observed in similar systems, inversion of vortex rectification direction occurs as the magnetic field is changed. Further inside the superconducting phase, anisotropic flux penetration patterns are formed. An inversion of anisotropy is observed as the temperature is lowered. This effect can be understood in terms of a thermomagnetic avalanche model. © 2007 The American Physical Society.

Mantle upwellings and convective instabilities revealed by seismic tomography and helium isotope geochemistry beneath eastern Africa

The relationship between intraplate volcanism and continental tectonics has been investigated for North and East Africa using a high resolution three‐dimensional anisotropic tomographic model derived from seismic data of a French experiment “Horn of Africa” and existing broadband data. The joint inversion for seismic velocity and anisotropy of the upper 400 km of the mantle, and geochemical data reveals a complex interaction between mantle upwellings, and lithosphere. Two kinds of mantle upwellings can be distinguished: The first one, the Afar “plume” originates from deeper than 400 km and is characterized by enrichment in primordial 3He and 3He/4He ratios higher than those along mid‐ocean ridges (MOR). The second one, associated with other Cenozoic volcanic provinces (Darfur, Tibesti, Hoggar, Cameroon), with 3He/4He ratios similar to, or lower than MOR, is a consequence of shallower upwelling. The presumed asthenospheric convective instabilities are oriented in an east‐west direction, resulting from interaction between south‐north asthenospheric mantle flow, main plume head and topography on the base of lithosphere.

Various pattern-forming states of nematic liquid crystal based on the sign inversion of dielectric anisotropy

The dielectric properties and various pattern-forming states of dual-frequency material in a nematic phase, as well as its mixture containing low concentrations of reactive monomers, are reported. The dielectric relaxation behaviors of nematic MLC 2048 are presented and compared to its mixture containing both mesogenic and nonmesogenic reactive monomers. The sign-inversion frequency of the dielectric anisotropy was significantly shifted on the addition of small amounts of the reactive monomers. However, all three mixtures used in this study essentially exhibited the same field-induced instabilities at different frequencies and voltage domains of the applied electric field. A broad band of modulated states were found to exist above a critical voltage and within a voltagedependent frequency band in the vicinity of the sign-inversion frequency,f I , of the dielectric anisotropy. As thef I of the mixtures shifted, so did the bands of the modulated state of the different mixtures and the temperatures, which were well matched with the measuredf I value.

Inversion of P-wave VSP data for local anisotropy: Theory and case study

We discuss, improve, and apply the slowness-polarization method for estimating local anisotropy from VSP data. Although the idea of fitting a given anisotropic model to the apparent slownesses measured along a well and polarization vectors recorded by three-component downhole geophones is hardly new, we extend the area of applicability of the technique and make the anisotropic inversion more robust by eliminating the most operationally difficult and noisy portion of the data, the shear waves. We show that the shear-wave velocity is actually unnecessary for fitting the slowness-of-polarization dependence of P-wave VSP data. For the most common geometry of a vertical borehole in a vertically transversely isotropic subsurface, such data are governed by the P-wave vertical velocity [Formula: see text] and two quantities, [Formula: see text] and [Formula: see text], that describe the influence of anisotropy. These quantities depend on conventional anisotropic coefficients [Formula: see text] and [Formula: see text] and absorb the S-wave velocity. We apply the developed theory to a 2D walkaway VSP acquired over a subsalt prospect in the Gulf of Mexico. Our data set contains geophones placed both inside the salt and beneath it, allowing us to estimate the anisotropy of different rock formations. We find the salt to be nearly isotropic in the examined [Formula: see text] [Formula: see text] depth interval. In contrast, the sediments below the salt exhibit substantial anisotropy. While the physical origins of subsalt anisotropy are still to be fully understood, we observe a clear correlation between lithology and the values of [Formula: see text] and [Formula: see text]: both anisotropic coefficients are greater in shales and smaller in the sandier portion of the well.

Anisotropic Crosshole Resistivity Tomography for Ground Safety Analysis of a High-Storied Building Over an Abandoned Mine

Crosshole resistivity tomography was performed to image the subsurface structures and mine cavities beneath a 25 story apartment building constructed at an abandoned mining site, and to provide the underground model for the safety analysis of the building. Strong electrical anisotropy was observed in the measured data, which has proven to be mainly due to geology. In order to deal with the anisotropy effect and to reconstruct the subsurface images reflecting the underground status precisely, we developed anisotropy inversion codes for resistivity tomography. The algorithm is based on finite element approximations for the forward modeling; the ACB (Active Constraint Balancing) method was adopted in the program in order to enhance the resolving power of the smoothness constraint least-squares inversion. All the acquired data were inverted by the developed inversion code so as to reconstruct the subsurface images, which match quite well with the geological mapping result. In particular, the locations of cavities were delineated more precisely owing to the anisotropic characteristics of the basement rock. Based on the subsurface model established by the resistivity tomography, rock engineering numerical analysis was further carried out. The result obtained from this analysis showed that the high-storied building is safe, even though three abandoned tunnels of the old mine are located beneath the building.

Small-angle AVO response of PS-waves in tilted transversely isotropic media

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

Magnetotelluric inversion for anisotropic conductivities in layered media

Electrical anisotropy in the Earth's crust and upper mantle has recently gained attention as a significant linking factor between electrical models and underlying structural and tectonic patterns. This interest has also motivated new methodological studies into the modelling and inversion for electrically anisotropic structures. We present an algorithm for the inversion of magnetotelluric data over layered anisotropic conductors which is a straightforward extension of the standard Occam 1-D inversion to anisotropic models. Owing to the essential limitation of magnetotellurics to resolve the complete conductivity tensor, we formulate the inversion for azimuthal anisotropy only. We treat the non-linear inverse problem as a multi-criterion minimization of the structure complexity, data misfit and anisotropy. To constrain the structure complexity, we employ the standard roughness penalty as well as non-quadratic penalties of the total variation and gradient support type that produce more focused model sections and thus conform better to the idea about sharp, non-diffuse boundaries of anisotropic structures in the Earth. Application of the anisotropy penalty is crucial for suppressing spurious anisotropy in the inverse models. We use a 2-D extension of the heuristic L-curve method to estimate the quasi-optimal penalty weights. With two non-linear iteration solvers, specifically the reweighted conjugate gradient method and the lagged diffusivity iteration, we can arrive at the minimum of the target functional, for one selected pair of regularization weights, typically after a few tens of iteration steps. To demonstrate the inverse solution, we present two simple yet not completely trivial synthetic examples, the first one based on data generated by a model with two anisotropic layers with discordant strikes, and the other showing possible misinterpretations in case a 1-D inversion with anisotropy is formally applied to data produced by simple 2-D block structures. Field data from the Variscan structures in southern Portugal bear indications, both geological and geophysical, on possible crustal anisotropy due to shearing and graphitization. We present results of a 1-D anisotropic imaging, and a preliminary 2-D modelling, for a short section of five sites over an old suture between the South Portuguese Zone and Ossa Morena Zone, aimed at explaining some essentially non-2-D effects in the data, as, e.g., systematic frequency variations of the regional strike or phases rolling out of their natural quadrants.

Spatially dependent seismic anisotropy in the Tonga subduction zone: A possible contributor to the complexity of deep earthquakes

The deep part of the Tonga subduction zone consists of two differently oriented slab segments: the northern segment within latitudes 17–19°S, and the southern segment within latitudes 19.5–27°S. The orientation of the slab is (strike/dip): 110°/57° in its northern part and 210°/46° in its southern part. Both segments are seismically active at depths from 500 to 700 km. The mechanisms of deep-focus earthquakes reported in the Harvard moment tensor catalogue contain compensated linear vector dipole (CLVD) components that behave differently in both segments. The mean value of the CLVD is 3% for the northern segment but −10% for the southern segment. The mean absolute value of the CLVD is 12% for the northern segment and 16% for the southern segment. The complex behaviour of the CLVD is explained by spatially dependent seismic anisotropy in the slab. The inversion for anisotropy from the non-double-couple components of moment tensors points to orthorhombic anisotropy in the both slab segments. The anisotropy seems to have a uniform strength of 5–7% for P-waves and 9–12% for S-waves, and is oriented according to the orientation of each segment and the stress acting in it. The spatial variation of velocities is roughly similar in both segments. The retrieved anisotropy might have several possible origins. It can be: (1) intrinsic, caused by preferentially aligned anisotropic minerals such as wadsleyite, ringwoodite, ilmenite or others, (2) effective, caused, for example, by intra-slab layering, or (3) partly apparent, produced by systematic errors in the moment tensors due to neglecting 3D slab geometry and the slab/mantle velocity contrast when calculating the Green functions in the moment tensor inversion.

Application of anisotropy borehole radar tomography in Korea

ABSTRACTAlthough the main geology of Korea consists of granite and gneiss, it is not uncommon to encounter anisotropy phenomena in cross‐hole radar tomography even when the basement is crystalline rock. To solve the anisotropy problem, we have developed an anisotropic inversion algorithm, assuming a heterogeneous elliptic anisotropy, to reconstruct three kinds of tomogram: tomograms of maximum and minimum velocities, and of the direction of the symmetry axis. We introduce some case histories of the application of anisotropic radar tomography in Korea. The first two case histories were conducted to construct social infrastructure, and their main objective was to locate cavities in limestone. The last two were performed in a granite and gneiss area. The anisotropy in the granite area was caused by fine fissures aligned in the same direction, while that in the gneiss and limestone areas was caused by the alignment of the constituent minerals. Through these case histories we aim to show that the anisotropic characteristic itself provides additional important information for understanding the internal structure of basement rock.