Fast Axis Orientation Research Articles

Feasibility of Deep Learning in Shear Wave Splitting analysis using Synthetic-Data Training and Waveform Deconvolution

Teleseismic shear-wave splitting analyses are often performed by reversing the splitting process through the application of frequency- or time-domain operations aimed at minimizing the transverse-component energy of waveforms. These operations yield two splitting parameters, ɸ (fast-axis orientation) and δt (delay time). In this study, we investigate the applicability of a baseline recurrent neural network, SWSNet, for determining the splitting parameters from pre-selected waveform windows. Due to the scarcity of sufficiently labelled real waveform data, we generate our own synthetic dataset to train the model. The model is capable of determining ɸ and δt with a root mean squared error (RMSE) of 9.7° and 0.14 s on a noisy synthetic test data. The application to real data involves a deconvolution step to homogenize the waveforms. When applied to data from the USArray dataset, the results exhibit similar patterns to those found in previous studies with mean absolute differences of 9.6° and 0.16 s in the calculation of ɸ and δt respectively.

Optimized configuration for liquid crystal Stokes polarimeters in the presence of fast-axis orientation errors.

We present an optimal configuration for Stokes polarimeters based on liquid crystal variable retarders, with the minimum number of measurements. Due to the inherent variations of the director orientation of the liquid crystal molecules, we propose a configuration that minimizes the sensibility of the polarimeter to fast-axis variations. For the optimization we consider a scheme that maximizes the volume of a tetrahedron inscribed in the Poincare sphere, to address additive and Poisson noise, with one of the vertices invariant to changes in the axis positions. We provide numerical simulations, considering misalignment errors, to analyze the robustness of the configuration. The results show that the proposed configuration helps to maintain the volume enclosed by the tetrahedron with high tolerance to fast-axis orientation errors. The condition number will remain below 3.07 for common misalignment errors and below 1.88 for more controlled liquid crystals. This optimization will improve the performance of liquid crystals polarimeters, with a more robust configuration that also considers misalignment errors, beyond additive and Poisson noise.

Anisotropic gradients in Iran: Quasi-Love waves illuminate the deep structure and deformation style of the Zagros, Alborz, and Kopet Dagh

We investigate the presence of the quasi-Love wave (qL) at 51 seismic stations of a temporary seismic network across the western Arabia-Eurasia collision zone. We quantify the intensity of the qL observations from the April 12, 2014 Solomon Islands earthquake by calculating the peak-to-peak amplitude ratios of the qL and Love waves, and compare them with predicted qL intensities from previous shear-wave splitting results. We determine the polarity, timing, and period-dependence of the qL observations within the period range of 50–100 s. Our analysis reveals that the qL observations at stations in the Zagros and Alborz mountain belts exhibit opposite characteristics. In contrast to the Alborz stations, the intensity of qL observations at the Zagros stations exhibits relatively negligible dependence on the period, while their receiver-scatterer distances are considerably period-dependent. We approximately locate the anisotropic gradients that generate the qL waves. Our results suggest that a lithospheric gap is responsible for the shallow and abrupt variation in the belt-parallel trend of fast-axis orientations in the westernmost part of the Zagros. Additionally, the period/depth dependence of the anisotropic gradients along the boundary between the central Zagros and central Iran provides insight into the variation in the downward dip of the Arabian lithosphere. The anisotropic gradient located to the north of the Doruneh fault in eastern Iran indicates its role as a major shear zone and lithospheric boundary. Finally, we observe that the spatial distribution of the anisotropic gradient in northeastern Iran matches the higher strain-rate areas in the Kopet Dagh Mountains, suggesting coupling between the lithospheric mantle and crust in that region.

Total retardance measurements based on the complex Fourier coefficients for the rotating polarizer analyzer system

We propose a demodulation algorithm based on the calculus of the complex Fourier coefficients; we used a dual rotating polarizer-analyzer polarimeter to show the feasibility of our proposal. Our demodulation algorithm considers the frequency response obtained by the system, and its possible to calculate the total retardation, fast axis orientation and ellipticity of a sample. Our proposal does not require recovering the full Mueller matrix from getting those parameters. In addition, as the proposal does not use retarders for the measurement, the system presents potential applications for multi-wavelength measurements on phase retardation samples. We show experimental results showing the capabilities of our proposal in characterizing a polarization retardance sample.

Determination of birefringence of biological tissues using modified PS-OCT based on the quaternion approach

Introduction: Polarization-sensitive optical coherence tomography (PS-OCT) is a functional extension of standard OCT. PS-OCT systems can be generally categorized into two categories based on the number of input polarization states on the sample: multi-input polarization state (multi-IPS) and single IPS. In addition, each category includes two configurations: fiber-based system and bulk optics-based system. However, there are complex and time-consuming steps to calibrate the polarization states of light among the reference, the sample, and detection arms for fiber-based system. And it is not compact and robust enough for bulk optics-based system.Methods: In the modified SD PS-OCT system with structural symmetry in both arms of the reference and sample, there are no bulk polarization optical elements in both arms of the reference and the sample. A circularly polarized light was used to incident on sample, and Stokes vector of backscattered light was employed to characterize the birefringence of biological tissues based on the quaternion approach, which directly establishes the relationship between Stokes vectors of backscattered light and Jones matrix of the sample.Results and discussion: The new algorithm provides the analytic solution of retardance and fast-axis orientation. To evaluate the performance of the developed system, an eighth-wave plate is used. Then, the polarization properties of the myocardial tissue in vivo are quantitatively reconstructed based on the quaternion approach. The results demonstrated that the proposed method has an advantage over Jones formalism based on a single input state and two polarization input states. In the future, the modified SD PS-OCT could be improved as a common path SD PS-OCT for clinical applications.

Jones tomographic diffractive microscopy with a polarized array sensor.

Tomographic diffractive microscopy (TDM) based on scalar light-field approximation is widely implemented. Samples exhibiting anisotropic structures, however, necessitate accounting for the vectorial nature of light, leading to 3-D quantitative polarimetric imaging. In this work, we have developed a high-numerical aperture (at both illumination and detection) Jones TDM system, with detection multiplexing via a polarized array sensor (PAS), for imaging optically birefringent samples at high resolution. The method is first studied through image simulations. To validate our setup, an experiment using a sample containing both birefringent and non-birefringent objects is performed. Araneus diadematus spider silk fiber and Pinna nobilis oyster shell crystals are finally studied, allowing us to assess both birefringence and fast-axis orientation maps.

Three-dimensional seismic anisotropy in the Pacific upper mantle from inversion of a surface-wave dispersion data set

SUMMARYWe present a new, 3-D model of seismic velocity and anisotropy in the Pacific upper mantle, PAC13E. We invert a data set of single-station surface-wave phase-anomaly measurements sensitive only to Pacific structure for the full set of 13 anisotropic parameters that describe surface-wave anisotropy. Realistic scaling relationships for surface-wave azimuthal anisotropy are calculated from petrological information about the oceanic upper mantle and are used to help constrain the model. The strong age dependence in the oceanic velocities associated with plate cooling is also used as a priori information to constrain the model. We find strong radial anisotropy with vSH > vSV in the upper mantle; the signal peaks at depths of 100–160 km. We observe an age dependence in the depth of peak anisotropy and the thickness of the anisotropic layer, which both increase with seafloor age, but see little age dependence in the depth to the top of the radially anisotropic layer. We also find strong azimuthal anisotropy, which typically peaks in the asthenosphere. The azimuthal anisotropy at asthenospheric depths aligns better with absolute-plate-motion directions while the anisotropy within the lithosphere aligns better with palaeospreading directions. The relative strengths of radial and azimuthal anisotropy are consistent with A-type olivine fabric. Our findings are generally consistent with an explanation in which corner flow at the ridge leads to the development and freezing-in of anisotropy in the lithosphere, and shear between the lithosphere and underlying asthenosphere leads to anisotropy beneath the plate. We also observe large regions within the Pacific basin where the orientation of anisotropy and the absolute-plate-motion direction differ; this disagreement suggests the presence of shear in the asthenosphere that is not aligned with absolute-plate-motion directions. Azimuthal-anisotropy orientation rotates with depth; the depth of the maximum vertical gradient in the fast-axis orientation tends to be age dependent and agrees well with a thermally controlled lithosphere–asthenosphere boundary. We observe that azimuthal-anisotropy strength at shallow depths depends on half-spreading rate, with higher spreading rates associated with stronger anisotropy. Our model implies that corner flow is more efficient at aligning olivine to form lattice-preferred orientation anisotropy fabrics in the asthenosphere when the spreading rate at the ridge is higher.

Panoptic View of Mantle Flow Beneath Trans‐Continental Northeast Asia: Distinct Variation Detected From ∼2,000 km Shear Wave Splitting Profile

AbstractWe obtained a panoptic view of the pattern of mantle flow in the “Big Mantle Wedge” associated with the stagnation of the subducting Pacific slab. We applied a simultaneous inversion of multiple waveforms method to measure SKS‐wave splitting parameters for a dense seismic array in trans‐continental Northeast Asia. We identify distinct patterns separated by the North‐South Gravity Lineament (NSGL): to the west, the ENE fast axis orientation with small δt reflects limited frozen anisotropy in the stable lithosphere; while to the east, local variation of anisotropy is superimposed on the NNW‐dominated fast direction, suggesting contribution of other mechanisms rather than the only asthenospheric flow. Within a distance of 200 km crossing the NSGL, we reveal a gradual clockwise rotation in the fast direction, and the keel‐deflected flow caused by the 60–80 km reduction in the lithosphere thickness across the NSGL might contribute to the variation of anisotropy.

Patterned achromatic elliptical polarizer for short-wave infrared imaging polarimetry

Short-wave infrared (SWIR) imaging polarimetry has widespread applications in telecommunication, medical imaging, surveillance, remote-sensing, and industrial metrology. In this work, we design, fabricate, and test an achromatic SWIR elliptical polarizer, which is a key component of SWIR imaging polarimetry. The elliptical polarizer is made of a patterned linear polarizer and a patterned optical elliptical retarder. The linear polarizer is a wire grid polarizer. The elliptical retarder is constructed with three layers of nematic phase A-plate liquid crystal polymer (LCP) films with different fast axis orientations and physical film thicknesses. For each LCP layer, four arrays of hexagonal patterns with individual fast-axis orientations are realized utilizing selective linearly polarized ultraviolet (UV) irradiation on a photo-alignment polymer film. The Mueller matrices of the optical filters were measured in the wavelength range 1000 nm to 1600 nm and compared with theory. Our results demonstrate the functionality and quality of the patterned retarders with normalized analyzer vector parameter deviation below 7% over this wavelength range. To the best of our knowledge, this work represents the first polymer-based patterned elliptical polarizer for SWIR polarimetry imaging applications.

Comparative Study of Modified Mueller Matrix Transformation and Polar Decomposition Parameters for Transmission and Backscattering Tissue Polarimetries

Mueller matrix polarimetry is widely used in biomedical studies and applications, for it can provide abundant microstructural information about tissues. Recently, several methods have been proposed to decompose the Mueller matrix into groups of parameters related to specific optical properties which can be used to reveal the microstructural information of tissue samples more clearly and quantitatively. In this study, we thoroughly compare the differences among the parameters derived from the Mueller matrix polar decomposition (MMPD) and Mueller matrix transformation (MMT), which are two popular methods in tissue polarimetry studies and applications, while applying them on different tissue samples for both backscattering and transmission imaging. Based on the Mueller matrix data obtained using the setups, we carry out a comparative analysis of the parameters derived from both methods representing the same polarization properties, namely depolarization, linear retardance, fast axis orientation and diattenuation. IN particular, we propose several modified MMT parameters, whose abilities are also analyzed for revealing the information about the specific type of tissue samples. The results presented in this study evaluate the applicability of the original and modified MMT parameters, then give the suggestions for appropriate parameter selection in tissue polarimetry, which can be helpful for future biomedical and clinical applications.

Evidence for asthenospheric flow rotation in northwest Canada: insights from shear wave splitting

SUMMARYThe Mackenzie Mountains (MM) of northwest Canada are an actively uplifting, seismogenic salient of the northern Canadian Cordillera that lie 750 km NE of the main Pacific–North America plate boundary. We present new shear wave splitting measurements from a linear array transecting the region to characterize upper-mantle anisotropy and the relative role of the lithosphere and asthenosphere in MM uplift. A gradual rotation in anisotropy occurs across the Canadian Cordillera, with stations nearest to the craton yielding NE fast-axis orientations that are subparallel to North America absolute plate motion (∼230°). Moving SW from the craton, across the MM and towards the plate boundary, fast-axis orientations rotate to become aligned with major lithospheric fabrics (NW–SE). Previous work has shown that the Cordilleran lithosphere is thin (≈50 km) in this region. We therefore interpret these results to primarily reflect sublithospheric flow. Three possibilities for asthenospheric flow are presented, but none of them fit the data well. Therefore, we believe that flow in the SW is due to upwelling from the slab window that opened up around 45–25 Ma, although it is possible the lithosphere is more than 50 km in thickness, in which case these splits reflect the tectonic fabric of the region.

Crustal structure and upper mantle anisotropy of the Afar triple junction

The Afar region is a tectonically distinct area useful for studying continental break-up and rifting. Various conflicting models have been suggested to explain the lateral variations of the anisotropy in this region. To address this issue, we investigated the tectonics of the Afar region using receiver function and shear-wave splitting measurements based on broadband seismic data from 227 stations in the region. Further, the receiver function results were inverted to obtain the crustal thickness and Vp/Vs ratio of the region. Our results reveal a thick African crust (thicker than 40 km) with typical Vp/Vs values for the continental crust, elongated down to 21 km along the rift system with very high Vp/Vs values near the fractured zones, suggesting crustal thinning near the fractured zones. Our shear-wave splitting measurements indicate a general fast axis orientation of N030E. However, substantial disparities in the fast anisotropy direction exist in the triple junction region, with some stations displaying a direction of N120E, which is perpendicular to the fast directions measured at the surrounding stations. In addition, many stations located close to the rifts and within the Arabian Plate provide mostly null measurements, indicating the presence of fluids or isotropic media. This study uses several methodologies to unravel the structure and evolution of the Afar region, providing valuable insight into the Afar, a tectonically distinct region, which will be useful for elucidating the mechanisms and characteristics of a continental break-up and the rifting process.

Velocity and azimuthal anisotropy structure underneath the Reelfoot Rift region from Rayleigh wave phase velocity dispersion curves

SUMMARYPhase velocity and azimuthal anisotropy maps for fundamental mode Rayleigh waves are determined for a portion of the central United States including the seismically active Reelfoot Rift (RFR) and the enigmatic Illinois Basin. Dense seismic array installations of the Northern Embayment Lithosphere Experiment, the EarthScope transportable array and the Ozarks Illinois Indiana Kentucky array allow a detailed investigation of phase velocity and anisotropy in a broad period range (20–100s).We obtain more than 12 000 well-constrained, unique two-station paths from teleseismic events. The two-station method is used to determine dispersion curves and these are inverted for isotropic phase velocity maps and azimuthal anisotropy maps for each period. The presence of fast phase velocities at lower crustal and uppermost mantle depths is found below the RFR, and Ste. Genevieve and Wabash Valley fault zones. At periods of 30s and higher, the RFR is underlain by slow phase velocities and is flanked to the NW and SE by regions of fast velocity. Fast phase velocities are present below the centre of the Illinois Basin in the period range 75–100s. Anisotropy fast axis orientations display complex patterns for each period and do not trend parallel to the direction of absolute plate motion. Anisotropy fast directions are consistently parallel to the trend of the RFR from 50s to higher periods, suggesting the presence of either frozen-in anisotropic fabric or fabric related to material transport from a recently discovered, pronounced low velocity zone below the Mississippi Embayment.

The competing effects of olivine and orthopyroxene CPO on seismic anisotropy

Orthopyroxene is the second most abundant mineral in the upper mantle and, like olivine, can form crystallographic preferred orientations (CPO) during mantle deformation that may influence mantle seismic anisotropy. Here we use a compilation of 21 peridotites in which both olivine and orthopyroxene CPOs are preserved to document the range of orthopyroxene CPO types and to explore their effects on seismic anisotropy of peridotites. In addition to four previously published orthopyroxene CPO types, this study establishes three new CPO types, two of which result in orthopyroxene fast axes aligned parallel to the lineation and the direction of mantle shear/flow. We calculate bulk elastic tensors for each sample from the measured olivine and orthopyroxene CPOs, and use those in turn to calculate Vp and Vs velocities and anisotropy percentages. In order to explore the relative influence of olivine and orthopyroxene on anisotropy, these properties were calculated for a range of possible modal percentages, from 100% olivine to 100% orthopyroxene. While the effect of orthopyroxene CPO appears to be a negligible influence on the orientation of bulk seismic fast axes, the presence of increasing orthopyroxene decreases the anisotropic signal overall. However, at very low olivine modal percentages, olivine and orthopyroxene can be mutually destructive, where the addition of olivine to a mostly orthopyroxene rock can actually decrease anisotropy.

Realization of doubly inhomogeneous waveplates for structuring of light beams

Waveplates having spatially varying fast-axis orientation and retardance provide an elegant and easy way to locally manipulate different attributes of light beams, namely, polarization, amplitude, and phase, leading to the generation of exotic structured light beams. The fabrication of such doubly inhomogeneous waveplates (d-plates) is more complex, compared with that of singly inhomogeneous waveplates (s-plates) having uniform retardance, which can be easily fabricated by different means such as photoalignment of liquid crystals, metasurfaces, etc. Here, exploiting the SU(2) formalism, we establish analytically that any d-plate can be equivalently implemented using a pair of quarter-wave s-plates and a half-wave s-plate. To underline the scope of this method, we propose novel d-plates toward complex amplitude shaping and also for imparting a polarization-dependent phase profile to a scalar light beam. For these two illustrations, the corresponding three-s-plate gadget is constructed, and its functioning is validated with extensive numerical simulations. The main result and its illustrations are generic and agnostic to the way the s-plates are fabricated, and we believe they carry the potential to push the current state of the art in interdisciplinary applications involving structured light beams.

Shear-wave splitting observations: Implications toward the variable anisotropic structure of the upper mantle below the Kachchh rift zone, Gujarat, India

The shear-wave splitting parameters (i.e. fast axis orientation (ψ) and delay time (δt)) are measured at twelve broadband stations in the Kachchh rift zone (KRZ), Gujarat, India, using SKS/SKKS core phases. The average splitting parameters (ψ, δt) vary from (49.41 ± 5.88, 1.63 ± 0.28) at Bhachau (i.e., 4 km SE of the 2001 Bhuj mainshock location) to (103.78 ± 12.82, 1.91 ± 0.35) at Mandvi near the coast. The present study reveals a mean ψ of (76.91o ± 4.57o) with a mean δt of 1.84 ± 0.30 s, for the KRZ. The observed large mean delay 1.84 ± 0.30 s for the region suggests a combined anisotropic contribution from both the lithospheric frozen anisotropy as well as the asthenospheric flow induced anisotropy. Inferred thicknesses of the anisotropic layers from the estimated δt vary from 160 km (in the central KRZ) to 269 km (in the surrounding unrifted zones (SURZ)). The measured deviation of ψ from the absolute plate motion (APM) direction of the Indian plate varies from 8.4o (in the central KRZ) to 62.8° (in the SURZ). The large δt and large deviation of ψ from the APM (>35°) are found to be associated with those stations (e.g. MND, KNM, VGH, NGR, VJP, TPM), which lie near to the geological boundaries in the SURZ. The main finding of the present modeling study depicts a thick highly anisotropic upper mantle underlying the KRZ, where mantle anisotropy parallel to the Kachchh rift axis direction is caused by both frozen lithospheric anisotropy and asthenospheric flow-induced anisotropy. The geographical and azimuthal variations of the measured splitting parameters detect three different anisotropic continental fragments, which might have preserved an ENE-WSW trending fossilized olivine fabric, which was formed before the assemblage of these continental fragments.

Upper mantle seismic anisotropy beneath the Kachchh rift zone, Gujarat, India, from shear wave splitting analysis

Unravelling the anisotropic behaviour of the upper mantle helps to shed light on its present and past deformation processes. In this study, we attempt to explore the seismic anisotropy prevailing within the upper mantle beneath the Kachchh rift zone through shear wave splitting analysis. We have measured the splitting parameters (e.g., fast axis orientation ( $$ \varPhi $$ ) and delay time ( $$ \delta t $$ )) using SKS/SKKS core refracted phases from 112 teleseismic events recorded at NGRI network in the Kachchh region, during 2006–2009 and 2013–2016. The ‘ $$ \varPhi $$ ’ and ‘ $$ \delta t $$ ’ estimates vary from N34° to N73°E and 0.80 to 1.5 s, respectively. The average vector means of ‘ $$ \varPhi $$ ’ and ‘ $$ \delta t $$ ’ for all the stations are found to be $$ {\text{N}}\left( {58 \pm 10} \right) $$ °E and (0.99 ± 0.19) s, respectively. Measurements of 59 good SKS/SKKS splitting parameters from 112 earthquakes reveal that the upper mantle is highly anisotropic beneath the Kachchh rift zone with an average fast axis orientation of $$ {\text{N}}\left( {58 \pm 10} \right) $$ °E, which is deviated nearly $$ (\sim{\text{N}}18 $$ °E) from the absolute plate motion (APM) direction (~N40°E) of the Indian plate in a no-net-rotation reference frame. This deviation of fast axis orientation from APM direction may be attributed to the effect of Kachchh rift zone as well as the presence of structural imprints of the 65 Ma Deccan mantle plume in the study region. And the average delay time of (0.99 ± 0.19) s is consistent with the global average (1 s) for continents. Furthermore, the modelled seismic layer thicknesses reveal that anisotropic sources beneath study region are associated with both the lithospheric deformation processes (e.g., 184 Ma African rifting, 88 Ma Madagascar rifting, 65 Ma Deccan mantle plume) as well as asthenospheric flows.

Azimuthal Anisotropy of the North American Upper Mantle Based on Full Waveform Inversion

AbstractA new azimuthal anisotropy model for the North American and Caribbean Plates, namely, , is constructed based on full waveform inversion and records from the USArray and other temporary/permanent networks deployed in the study region. A total of 180 earthquakes and 4,516 seismographic stations are employed in the inversion to simultaneously constrain radially and azimuthally anisotropic model parameters: , , , and , within the crust and mantle. Thirty‐two preconditioned conjugate gradient iterations have been utilized to minimize frequency‐dependent phase discrepancies between observed and predicted seismograms for three‐component short‐period (15–40 s) body waves and long‐period (25–100 s) surface waves. Model exhibits complicated variations in anisotropic fabrics underneath the western and eastern United States, especially at depths shallower than 100 km. For instance, the fast axis orientations in model suggest the presence of trench‐perpendicular mantle flows underneath the Cascadia Subduction Zone and also follow the strikes of the Snake River Plain, the Ouachita Orogenic Front, and the Grenville and Appalachian Orogenic Belts. The amplitudes of azimuthal anisotropy reduce to around 1% at depths greater than 200 km, and the orientations are subparallel to the global plate motion directions to the east of the Rocky Mountain, except for large discrepancies in central and eastern Canada. At a depth of 700 km, the fast axes change along the trajectory of the Farallon slab underneath the Great Lakes region and Gulf of Mexico, which might indicate the development of 2‐D poloidal‐mode mantle flows perpendicular to the strike of the sinking slab within the uppermost lower mantle. Comparisons between model with a western U.S. model from ambient noise tomography and SKS splitting measurements demonstrate a relatively good agreement for the fast axis orientations, considering the usage of different data sets and imaging techniques. However, the absolute magnitude of azimuthal anisotropy in model might be underestimated, especially at greater depths, given the poor agreement on the amplitudes of predicted and observed SKS splitting times. At the current stage, the agreement among different azimuthal anisotropy models at global and continental scales is still poor even for the United States with a dense station coverage.

A method of calculating compensators in polarization-sensitive optical systems

A simple method to measure and compensate polarization-sensitive optical components (retarders) is proposed, based on Stokes vector polarimetry. First, the Mueller matrix of an unknown polarization-sensitive element with arbitrary retardance and fast-axis orientation is obtained by means of a conventional measurement and calculation polarimetric procedure. Then a novel numerical technique is proposed, allowing to express the measured retarder’s Mueller matrix in terms of retardance δ and fast axis orientation θ. Further, a method for calculating polarization compensators is proposed, to balance phase differences introduced by one or more retarders. Compensation is achieved by a single compensating retarder whose parameters are derived from the original retarder’s Mueller matrix, or its equivalent (δ,θ) pair. The technique works for all possible fast-axis orientations of the original retarder. The method was validated using an electrically controllable liquid crystal retarder as a compensator. The approach described here is constrained to optical elements that behave as nearly pure retarders, i.e. their diattenuation and depolarization are negligible. Possible applications are in the design of polarization-sensitive systems (biomedical, environmental, chemical, optical communications, etc.) where recovery and/or precise control of the polarization state of light is needed, in polarization tracing models based on the Mueller matrix formalism, and others.

Crustal anisotropy from shear-wave splitting of local earthquakes in the Garhwal Lesser Himalaya

SUMMARYCrustal anisotropy of the Garhwal Lesser Himalaya has been studied using local earthquake data from the Tehri seismic network. Earthquakes with magnitude (mL) up to 3, which occurred between January 2008 to December 2010, have been used for the shear wave splitting (SWS) analysis. SWS measurements have been done for steeply incident ray paths (ic ≤ 45°) to estimate the anisotropy fast axis orientation (ϕ) and the delay time (∂t). A total of 241 waveforms have been analysed, which yielded 209 splitting measurements, and 32 null results. The analysis reveals spatial and depth variation of ϕ and ∂t, suggesting complex anisotropic structure beneath the Garhwal Lesser Himalaya. The mean ∂t is estimated to be 0.07 ± 0.065 s with a mean depth normalized ∂t of 0.005 s km–1. We present the ϕ and Vs per cent anisotropy results by segregating these as a function of depth, for earthquakes originating above and below the Main Himalayan Thrust (MHT); and spatially, for stations located in the Outer Lesser Himalaya (OLH) and the Inner Lesser Himalaya (ILH). Earthquakes above the MHT sample only the Himalayan wedge, while those below the MHT sample both the underthrust Indian crust and the Himalayan wedge. Within the Himalayan wedge, for both OLH and ILH, the mean ϕ is oriented NE–SW, in the direction of maximum horizontal compressive stress axis (SHmax). This anisotropy is possibly due to stress-aligned microcracks controlled by the local stress pattern within the Himalayan wedge. The mean of normalized ∂t for all events originating within the Himalaya is 0.006 s km–1, which yields a Vs per cent anisotropy of ∼2.28 per cent. Assuming a homogeneous distribution of stress-aligned microcracks we compute a crack density of ∼0.0228 for the Garhwal Lesser Himalaya. At stations close to the regional fault systems, the mean ϕ is subparallel to the strike of the faults, and the anisotropy, locally, appears to be structure-related. For earthquakes originating below the MHT, in OLH, the mean ϕ orientation matches those from the Himalayan wedge and the normalized ∂t decreases with depth. This suggests depth localization of the anisotropy, primarily present within the Himalayan wedge. In the ILH, we observe large variations in the mean ϕ orientation and larger values of ∂t close to the regional fault/thrust systems. This is possibly a composite effect of the structure-related shallow crustal anisotropy and the frozen anisotropy of the underthrusting Indian crust. However, these cannot be segregated in this study.