Two-dimensional anisotropic magnetotelluric inversion using a limited-memory quasi-Newton method

We have developed a two-dimensional (2D) anisotropic magnetotelluric (MT) inversion algorithm that uses a limited-memory quasi-Newton (QN) method for bounds-constrained optimization. This algorithm solves the inverse problem, which is non-linear, by iterative minimization of linearized approximations of the classical Tikhonov regularized objective function. The QN approximation for the Hessian matrix is only implemented for the data-misfit term of the objective function; the part of the Hessian matrix for the regularization is explicitly computed. This adjustment results in a better approximation for the data-misfit term in particular. The inversion algorithm considers arbitrary anisotropy, and is extended for special cases including azimuthal and vertical anisotropy. The algorithm is shown to be stable and converges rapidly for several simple anisotropic models. These synthetic tests also confirm that the anisotropic inversion produces a correct anomaly with different but equivalent anisotropic parameters. We also consider a complex 2D anisotropic model; the successful results for this model further confirm that the inversion algorithm presented here, which uses the novel modified limited-memory QN approach, is capable of solving the 2D anisotropic magnetotelluric inverse problem. Finally, we present a practical application on MT data collected in northern Tibet to demonstrate the effectiveness and stability of our algorithm.

Analysis of S waves singularity points in porous rock with two orthogonal sets of mesoscale fractures

SUMMARY The shear waves phase velocity surfaces in orthorhombic (ORT) and lower symmetry anisotropic models touch each other in one or more points resulting in so called singularity points or acoustic axes. These singularity points result in dramatic changes of velocities, amplitudes and polarizations creating problems in seismic data processing and analysis. Considering the frequency-dependent anisotropy due to mesoscale fractures in Chapman's model, we describe the singularity points in porous rock with two orthogonal sets of mesoscale fractures. First, we give the equations for frequency-dependent phase velocities of P, S1 and S2 waves in this anelastic ORT media. Then, we derive the expressions for frequency-dependent singularity points within the symmetry planes and discuss the conditions to detect the existence of singularity point. Finally, the influences of frequency, porosity, fracture density, fracture scale and saturating fluid style on the positions of singularity points within the symmetry plane are investigated.

Influence of Anisotropic White Matter on Electroosmotic Flow Induced by Direct Current

Treatment of cerebral edema remains a major challenge in clinical practice and new innovative therapies are needed. This study presents a novel approach for mitigating cerebral edema by inducing bulk fluid transport utilizing the brain’s electroosmotic property using an anatomically detailed finite element head model incorporating anisotropy in the white matter (WM). Three representative anisotropic conductivity algorithms are employed for the WM and compared with isotropic WM. The key results are (1) the electroosmotic flow (EOF) is driven from the edema region to the subarachnoid space under an applied electric field with its magnitude linearly correlated to the electric field and direction following current flow pathways; (2) the extent of EOF distribution variation correlates highly with the degree of the anisotropic ratio of the WM regions; (3) the directions of the induced EOF in the anisotropic models deviate from its isotropically defined pathways and tend to move along the principal fiber direction. The results suggest WM anisotropy should be incorporated in head models for more reliable EOF evaluations for cerebral edema mitigation and demonstrate the promise of the electroosmosis based approach to be developed as a new therapy for edema treatment as evaluated with enhanced head models incorporating WM anisotropy.

Gravitationally decoupled non-static anisotropic spherical solutions

This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.

Geostatistical analysis of spatial variability of the liquefaction potential – Case study of a site located in Algiers (Algeria)

The city of Algiers (Algeria) is a highly seismic area, and therefore, soil liquefaction poses a major concern for structures resting on sandy soil. A campaign of 62 static penetration tests or cone penetrometer tests (CPT) was carried out on a site located in the commune of Dar El Beïda in Algiers. The soil Liquefaction Potential Index (LPI) values were assessed, for each borehole, based on the simplified procedure of Seed and Idriss. On the other hand, the geographic information system and geostatistical analysis were used to quantify the risk of soil liquefaction at the studied site. It is worth mentioning that the (LPI) was taken as a regionalized variable. In addition, the experimental variogram was modeled on the basis of a spherical model. Also, the interpolation of the LPI values in the unsampled locations was performed by the Kriging technique using both isotropic and anisotropic models. Kriging standard deviation maps were produced for both cases. The cross-validation showed that the anisotropic model exhibited a better fit for the interpolation of the values of the soil liquefaction potential. The results obtained indicated that a significant part of the soil is liable to liquefy, in particular in the northwestern region of the study area. The findings suggest that there is a proportional relationship between the risk of liquefaction and the increase or decrease in seismic acceleration.

PERTURBATION OF PHASE VELOCITIES IN ELASTIC ORTHORHOMBIC MEDIA

The parameterization of anisotropic models is very important when focusing on specific signatures of seismic waves and reducing the parameters crosstalk involved in inverting seismic data. The parameterization is strongly dependent on the problem at hand. We propose a new parameterization for an elastic orthorhombic model with on-axes P- and S-wave velocities and new symmetric anelliptic parameters. The perturbation approach is well defined for P waves in acoustic orthorhombic media. In the elastic orthorhombic media, the P-wave perturbation coefficients are very similar to their acoustic counterparts. However, the S-waves perturbation coefficients are still unknown. The perturbation coefficients can be interpreted as sensitivity coefficients, and they are important in many applications. We apply the second-order perturbation in anelliptic parameters for P, S1 and S2 wave phase velocities in elastic orthorhombic model. We show that using the conventional method some perturbation coefficients for S waves are not defined in the vicinity of the singularity point in an elliptical background model. Thus, we propose an alternative perturbation approach that overcomes this problem. We compute the first- and second-order perturbation coefficients for P and S waves. The perturbation-based approximations are very accurate for P and S waves compared with exact solutions, based on a numerical example. The reductions to transversely isotropic and acoustic orthorhombic models are also considered for analysis. We also show how perturbations in anelliptic parameters affect S-wave triplications in an elastic orthorhombic model.

Estimation of the Hourly Global Solar Irradiation on the Tilted and Oriented Plane of Photovoltaic Solar Panels Applied to Greenhouse Production

Agrometeorological stations have horizontal solar irradiation data available, but the design and simulation of photovoltaic (PV) systems require data about the solar panel (inclined and/or oriented). Greenhouses for agricultural production, outside the large protected production areas, are usually off-grid; thus, the solar irradiation variable on the panel plane is critical for an optimal PV design. Modeling of solar radiation components (beam, diffuse, and ground-reflected) is carried out by calculating the extraterrestrial solar radiation, solar height, angle of incidence, and diffuse solar radiation. In this study, the modeling was done using Simulink-MATLAB blocks to facilitate its application, using the day of the year, the time of day, and the hourly horizontal global solar irradiation as input variables. The rest of the parameters (i.e., inclination, orientation, solar constant, albedo, latitude, and longitude) were fixed in each block. The results obtained using anisotropic models of diffuse solar irradiation of the sky in the region of Castile and León (Spain) showed improvements over the results obtained with isotropic models. This work enables the precise estimation of solar irradiation on a solar panel flexibly, for particular places, and with the best models for each of the components of solar radiation.

Radial Anisotropy and it's Relation to Fast and Slow Moving Tectonic Plates

<p>We present a new radially anisotropic (<strong>ξ)</strong> tomographic model for the upper mantle to transition zone depths derived from a large Rayleigh (~4.5 x 10<sup>6 </sup>paths) and Love (~0.7 x 10<sup>6</sup> paths) wave path average dispersion curves with periods of 50-250 s and up to the fifth overtone. We first extract the path average dispersion characteristics from the waveforms. Dispersion characteristics for common paths (~0.3 x 10<sup>6</sup> paths) are taken from the Love and Rayleigh datasets and jointly inverted for isotropic V<sub>s </sub>and <strong>ξ</strong>. CRUST1.0 is used for crustal corrections and a model similar to PREM is used as a starting model. V<sub>s</sub> and <strong>ξ</strong> are regionalised for a 3D model. The effects of azimuthal anisotropy are accounted for during the regionalisation. Our model confirms large-scale upper mantle features seen in previously published models, but a number of these features are better resolved because of the increased data density of the fundamental and higher modes coverage from which our <strong>ξ</strong>(z) was derived. Synthetic tests show structures with radii of 400 km can be distinguished easily. Crustal perturbations of +/-10% to V<sub>p</sub>, V<sub>s</sub> and density, or perturbations to Moho depth of +/-10 km over regions of 400 km do not significantly change the model. The global average decreases from <strong>ξ~</strong>1.06 below the Moho to <strong>ξ</strong>~1 at ~275 km depth. At shallow depths beneath the oceans <strong>ξ</strong>>1 as is seen in previously published global mantle radially anisotropic models. The thickness of this layer increases slightly with the increasing age of the oceanic lithosphere. At ~200 km and deeper depths below the fast-spreading East Pacific Rise and starting at somewhat greater depths beneath the slower spreading ridges, <strong>ξ</strong><1. At depths ≥200 km and deeper depths below most of the backarc basins of the western Pacific <strong>ξ</strong><1. The signature of mid-ocean ridges vanishes at about 150 km depth in V<sub>s</sub> while it extends much deeper in the <strong>ξ</strong> model suggesting that upwelling beneath mid-ocean ridges could be more deeply rooted than previously believed. The pattern of radially anisotropy we observe, when compared with the pattern of azimuthal anisotropy determined from Rayleigh waves, suggests that the shearing at the bottom of the plates is only sufficiently strong to cause large-scale preferential alignment of the crystals when the plate motion exceeds some critical value which Debayle and Ricard (2013) suggest is about 4 cm/yr.</p>