General Anisotropy Research Articles

Symmetries and symmetry-generated averages of elastic constants up to the sixth order of nonlinearity for all crystal classes, isotropy and transverse isotropy.

Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.

The sensitivity of lowermost mantle anisotropy to past mantle convection

It is widely believed that seismic anisotropy in the lowermost mantle is caused by the flow-induced alignment of anisotropic crystals such as post-perovskite. What is unclear, however, is whether the anisotropy observations in the lowermost mantle hold information about past mantle flow, or if they only inform us about the present-day flow field. To investigate this, we compare the general and seismic anisotropy calculated using Earth-like mantle convection models where one has a time-varying flow, and another where the present-day flow is constant throughout time. To do this, we track a post-perovskite polycrystal through the flow fields and calculate texture development using the sampled strain rate and the visco-plastic self-consistent approach. We assume dominant slip on (001) and test the effect of the relative importance of this glide plane over others by using three different plasticity models with different efficiencies at developing texture. We compare the radial anisotropy parameters and the anisotropic components of the elastic tensors produced by the flow field test cases at the same location. We find, under all ease-of-texturing cases, the radial anisotropy is very similar (difference <2%) in the majority of locations and in some regions, the difference can be very large (>10%). The same is true when comparing the elastic tensors directly. Varying the ease-of-texture development in the crystal aggregate suggests that easier-to-texture material may hold a stronger signal from past flow than harder-to-texture material. Our results imply that broad-scale observations of seismic anisotropy such as those from seismic tomography, 1-D estimates and normal mode observations, will be mainly sensitive to present-day flow. Shear-wave splitting measurements, however, could hold information about past mantle flow. In general, mantle memory expressed in anisotropy may be dependent on path length in the post-perovskite stability field. Our work implies that, as knowledge of the exact causative mechanism of lowermost mantle anisotropy develops, we may be able to constrain both present-day and past mantle convection.

Diffusion spectrum imaging in patients with idiopathic normal pressure hydrocephalus: correlation with ventricular enlargement

BackgroundTo investigate the association between white matter changes and ventricular expansion in idiopathic normal pressure hydrocephalus (iNPH) based on diffusion spectrum imaging (DSI).MethodsWe included 32 patients with iNPH who underwent DSI using a 3T MRI scanner. The lateral ventricles were manually segmented, and ventricular volumes were measured. Two methods were utilised in the study: manual region-of-interest (ROI) delineation and tract diffusion profile analysis. General fractional anisotropy (GFA) and fractional anisotropy (FA) were extracted in different white matter regions, including the bilateral internal capsule (anterior and posterior limbs) and corpus callosum (body, genu, and splenium) with manual ROI delineation. The 18 main tracts in the brain of each patient were extracted; the diffusion metrics of 100 equidistant nodes on each fibre were calculated, and Spearman’s correlation coefficient was used to determine the correlation between diffusion measures and ventricular volume of iNPH patients.ResultsThe GFA and FA of all ROI showed no significant correlation with lateral ventricular volume. However, in the tract diffusion profile analysis, lateral ventricular volume was positively correlated with part of the cingulum bundle, left corticospinal tract, and bilateral thalamic radiation posterior, whereas it was negatively correlated with the bilateral cingulum parahippocampal (all p < 0.05).ConclusionsThe effect of ventricular enlargement in iNPH on some white matter fibre tracts around the ventricles was limited and polarizing, and most white matter fibre tract integrity changes were not associated with ventricular enlargement; this reflects that multiple pathological mechanisms may have been combined to cause white matter alterations in iNPH.

Propagation of elastic waves in fibrous composite with general anisotropy from two families of obliquely inclined fibers

AbstractAn isotropic elastic solid reinforced with two families of aligned fibres behaves anisotropic to any deformation. For arbitrary orientation of fibres in either family, one set of fibres may be inclined obliquely to the aligned fibres in other family. A plane that contains the two families of aligned fibres becomes the plane of symmetry for composite material to exhibit monoclinic anisotropy. For this fibrous anisotropy, a fourth‐order elastic tensor is derived to define the constitutive relations between stress tensor and strain tensor. Components of this elastic tensor involve two Lame's moduli, eight fibroelastic coefficients and the angular deviation between two obliquely inclined fibre‐families. The velocities of bulk waves are calculated for propagation along general direction in this anisotropic composite. Propagation of surface wave is considered along the stress‐free plane boundary of anisotropic elastic half‐space. In a coordinate system with coordinate planes deviating from the plane boundary of the medium and/or plane of anisotropic symmetry, the fibrous composite is treated as triclinic for mathematical convenience. Mathematical model is derived to calculate the phase velocity of the surface wave, which varies with direction on the plane boundary. Horizontal energy flux at the boundary is calculated to determine the group velocity and ray direction of the surface wave. Effects of fibre‐orientations are analysed, numerically, on the wave velocities and ray direction of surface wave.

Life-course neighbourhood deprivation and brain structure in older adults: the Lothian Birth Cohort 1936.

Neighbourhood disadvantage may be associated with brain health but the importance of exposure at different stages of the life course is poorly understood. Utilising the Lothian Birth Cohort 1936, we explored the relationship between residential neighbourhood deprivation from birth to late adulthood, and global and local neuroimaging measures at age 73. A total of 689 participants had at least one valid brain measures (53% male); to maximise the sample size structural equation models with fullinformation maximum likelihood were conducted. Residing in disadvantaged neighbourhoods in mid- to late adulthood was associated with smaller total brain (β = -0.06; SE = 0.02; sample size[N] = 658; number of pairwise complete observations[n]=390), grey matter (β = -0.11; SE = 0.03; N = 658; n = 390), and normal-appearing white matter volumes (β = -0.07; SE = 0.03; N = 658; n = 390), thinner cortex (β = -0.14; SE = 0.06; N = 636; n = 379), and lower general white matter fractional anisotropy (β = -0.19; SE = 0.06; N = 665; n = 388). We also found some evidence on the accumulating impact of neighbourhood deprivation from birth to late adulthood on age 73 total brain (β = -0.06; SE = 0.02; N = 658; n = 276) and grey matter volumes (β = -0.10; SE = 0.04; N = 658; n = 276). Local analysis identified affected focal cortical areas and specific white matter tracts. Among individuals belonging to lower social classes, the brain-neighbourhood associations were particularly strong, with the impact of neighbourhood deprivation on total brain and grey matter volumes, and general white matter fractional anisotropy accumulating across the life course. Our findings suggest that living in deprived neighbourhoods across the life course, but especially in mid- to late adulthood, is associated with adverse brain morphologies, with lower social class amplifying the vulnerability.

Surface acoustic waves in laterally periodic superlattices

The existence of surface acoustic waves (SAWs) is studied in laterally periodic superlattices, modelled as an anisotropic elastic half-space with an arbitrary periodic variation of its material properties along the stratification direction (call it X) parallel to the surface. Unlike a homogeneous half-space, such a structure allows for more than one (dispersive) SAW. Specifically, it is shown that any superlattice with a generic shape of periodicity profile admits at most three SAW dispersion branches ω(Kx), i.e., at most three different SAW frequencies at any fixed Bloch wavenumber Kx. Moreover, the total number of SAWs at fixed Kx in a pair of superlattices with periodicity profiles obtained from one another by the inversion of the axis X cannot exceed three either. At least one SAW branch must exist in one of these two superlattices unless the bulk-wave threshold is the so-called exceptional (i.e., admits surface skimming wave). The SAW branch is unique in the particular case of a superlattice invariant to the inversion X→−X. The above general results are illustrated by the perturbation theory derivations for the weakly modulated superlattices. Explicit leading-order formulas are obtained for the quasi-Rayleigh wave branch evolving from the Rayleigh wave in each of the mutually ”inverse” superlattices and for the quasibulk wave branch evolving from the exceptional bulk-wave threshold in one of the superlattices.

An anisotropic hyperelastic strain energy function based on 21 icosahedron fiber distributions

The microscopic Cauchy strain energy for linear elasticity based on the sum of quadratic strain energies due to pair potentials has only 15 material rari-constants. It is shown that the six vectors connecting opposing vertices of a regular icosahedron can be used to develop a strain energy function for general linear elastic anisotropic response with 21 material constants. Specifically, the six strains of material fibers characterized by these vectors are enhanced by 15 fiber distribution strains due to all combinations of distinct pairs of these vectors. These two-vector fiber distributions introduce coupling that is essential to obtaining general anisotropy. The model is generalized for large deformations by replacing the strains with stretches and by using a Fung-type exponential strain energy which couples the responses of the 21 stretches. The resulting nonlinear hyperelastic strain energy function can be used to model the anisotropic hyperelastic response of fibrous tissues.

A new Stroh formalism for gradient electro-mechanics with applications to Lamb waves in piezoelectric and flexoelectric coupled plates

In this paper, a new Stroh formalism for gradient electro-mechanics is derived for the first time, which is both mathematically concise and numerically powerful, applicable to generally coupled anisotropic material systems. Based on this new formalism, the complicated Lamb wave in flexoelectric and piezoelectric plates is investigated. The dispersion equation is obtained by solving the eigenvalue problem along with the unconditionally stable dual-variable and position method. From the obtained dispersion equation, the dispersion curves and mode shapes of the Lamb wave are calculated by the 1D form of the multidimensional moduli ratio convergence method. Two important and interesting features are observed from our analysis: One is the difference in the mode shape symmetry between the piezoelectric and flexoelectric cases, and the other is the size-dependent property of the flexoelectric effect as observed by nondimensionalization. These features are further illustrated by comparing the dispersion curves and wave-mode shapes among the three different material models (purely piezoelectric, purely flexoelectric, and flexoelectric and piezoelectric coupled). The newly derived Stroh formalism offers a robust, concise, and unified approach for dealing with strain gradient electro-mechanic materials with crystal systems of general anisotropy. The present work also explains the physical mechanism of symmetry breaking observed, as induced by flexoelectric coupling in piezoelectric materials.

Fast 3D simulation of magnetotelluric data in anisotropic media using a rational Krylov method

This study introduces a computational method aimed at accelerating multifrequency 3D magnetotelluric (MT) forward modeling in 3D conductivity structures with general anisotropy. The approach combines an edge-based finite-element (FE) method with a rational Krylov subspace method. In this method, the MT source term is expressed as a planar current source, and the frequency-dependent electric field response is the product of a transfer function and a constant vector of the current source. Consequently, the rapid approximate electric field for multifrequency calculations can be obtained by constructing the orthogonal basis of the rational Krylov subspace. By applying this technique, the large sparse matrix resulting from FE discretization can be projected onto a much lower-order matrix, significantly reducing its size to tens or hundreds. Incorporating the direct solver PARDISO to construct the orthogonal basis enables a considerably faster solution compared with the previous FE method. Moreover, the algorithm is implemented using Julia, a high-level programming language known for its readability, maintainability, and extensibility. The validity of the algorithm is demonstrated through a 1D anisotropic model, and two additional 3D models are designed to further evaluate the applicability and effectiveness of our algorithm. Numerical experiments illustrate a notable increase in modeling speed compared with the traditional edge-based FE method.

Inertial self-propelled particles in anisotropic environments

Self-propelled particles in anisotropic environments can exhibit a motility that depends on their orientation. This dependence is relevant for a plethora of living organisms but difficult to study in controlled environments. Here, we present a macroscopic system of self-propelled vibrated granular particles on a striated substrate that displays orientation-dependent motility. An extension of the active Brownian motion model involving orientation-dependent motility and inertial effects reproduces and explains our experimental observations. The model can be applied to general n-fold symmetric anisotropy and can be helpful for predictive optimization of the dynamics of active matter in complex environments.

Mechanical model of strut-based metamaterials based on direct stiffness method

The mechanical properties of micro-struts manufactured through laser powder bed fusion (LPBF) are influenced by a multitude of factors including forming angle, thickness, process parameters, and equipment. This results in the failure of mechanical models for strut-based metamaterials that are based on bulk material properties. By incorporating mechanical property data from micro-struts produced using LPBF into a direct stiffness method, we developed a mechanical model capable of predicting the elastic tensor and strength surface of strut-based metamaterials. The robustness of this methodology was evaluated through quasi-static compression experiments on 3D double-arrowhead (DAH) auxetic metamaterials produced using LPBF and finite element analysis (FEA). Results indicate that the deviations of Young's modulus, Poisson's ratio, and strength between the theoretical model's predictions and experimental results are within 30 %, 50 %, and 25 %, decreasing to within 15 %, 30 %, and 15 % as relative density increases, respectively. Deviations from FEA results under the assumption of uniform strut performance remain within 15 %, 25 %, and 20 %, correspondingly. Furthermore, the theoretical model can predict the elasticity and strength of metamaterials under any loading direction and identify the most vulnerable strut in the metamaterial unit. The theoretical model effectively represented the general anisotropy of metamaterials resulting from LPBF manufacturing factors. This study presents a transplantable method for developing mechanical models of strut-based metamaterials, improving the accuracy of performance prediction and promoting their application in LPBF-manufactured parts.

Analysis of near-interface cracks in three-dimensional anisotropic multi-materials by efficient BIEM

This paper presents the full analysis of near-interface cracks in three-dimensional linear elastic multimaterial bodies by a weakly singular boundary integral equation method (BIEM). The proposed technique was implemented in a general framework that allowed the treatment of finite cracked bodies with general configurations, material anisotropy, and mode-mixity. A system of integral equations governing unknown data on the boundary, crack surface, and material interface was established using a pair of weakly singular weak-form displacement and traction integral equations together with continuity along the material interface. A symmetric Galerkin boundary element method along with the finite element technique were implemented to solve the governing integral equations. In addition, the special near-front interpolation was employed to enhance the approximation of the relative crack-face displacement in the neighborhood of the crack front. The solved crack-face data were used directly to post-process the stress intensity factors and T-stresses along the crack front. An extensive numerical study was carried out not only to demonstrate the accuracy, convergence, and capability of the proposed technique, but also to explore the influence of material stiffness and distance to the material interface on fracture data along the crack front.

Basal Ganglia Compensatory White Matter Changes on DTI in Alzheimer's Disease.

The volume reduction of the gray matter structures in patients with Alzheimer's disease is often accompanied by an asymmetric increase in the number of white matter fibers located close to these structures. The present study aims to investigate the white matter structure changes in the motor basal ganglia in Alzheimer's disease patients compared to healthy controls using diffusion tensor imaging. The amounts of tracts, tract length, tract volume, quantitative anisotropy, and general fractional anisotropy were measured in ten patients with Alzheimer's disease and ten healthy controls. A significant decrease in the number of tracts and general fractional anisotropy was found in patients with Alzheimer's disease compared to controls in the right caudate nucleus, while an increase was found in the left and the right putamen. Further, a significant decrease in the structural volume of the left and the right putamen was observed. An increase in the white matter diffusion tensor imaging parameters in patients with Alzheimer's disease was observed only in the putamen bilaterally. The right caudate showed a decrease in both the diffusion tensor imaging parameters and the volume in Alzheimer's disease patients. The right pallidum showed an increase in the diffusion tensor imaging parameters but a decrease in volume in Alzheimer's disease patients.

Comparison study of different forward modeling approaches by using the finite-element method for 3D magnetotelluric data in anisotropic media

We have examined three approaches for analyzing 3D magnetotelluric (MT) data with general anisotropy. These included the direct electromagnetic (EM) approach, which solved the electric field Helmholtz equation directly, and the Coulomb-gauged and Ungauged approaches. The three approaches are discretized using finite-element (FE) methods. First, the correctness of the three approaches is validated using a typical isotropic 3D model and a 2D anisotropic model. The FE solutions of each approach obtained by the direct solver MUMPS are compared with the analytical solutions to demonstrate that all approaches generated accurate results. Subsequently, an anisotropic 3D model is designed to investigate the forward characteristics of the different approaches. The FE solutions are obtained using the quasi-minimum residual (QMR) solver with a symmetric successive overrelaxation (SSOR) preconditioner in this model. The forward modeling results of each approach were compared in terms of stiffness matrices, the convergence of the iterative solver, and apparent resistivity and phase. We find that the FE solution of the Coulomb-gauged and Ungauged approaches produces larger stiffness matrices, but the proportion of non-zero elements in the Coulomb-gauged approach is the least. The Ungauged approach can yield faster solutions over a wide range of frequencies. Finally, a complex numerical example is provided to demonstrate the good convergence behavior of the Ungauged approach.

ON THE EQUILIBRIUM EQUATIONS OF LINEAR 6-PARAMETER ELASTIC SHELLS

We consider the linearized theory of 6-parameter elastic shells with general anisotropy. We derive the equilibrium equations from the virtual power statement and formulate the corresponding variational problem in the suitable functional framework. Then, using a Korn-type inequality for the linearized strain measures we prove the existence and uniqueness of weak solutions. Finally, we show that our general theo­rem can be applied to obtain existence results in the case of isotropic elastic shells. We illustrate this procedure by investigating three differ­ent linear shell models established previously in the literature, namely the simplified isotropic 6-parameter shell, the Cosserat isotropic model, and the higher-order 6-parameter Cosserat model.

Brain white matter correlates of learning ankle tracking using a wearable device: importance of the superior longitudinal fasciculus II

BackgroundWearable devices have been found effective in training ankle control in patients with neurological diseases. However, the neural mechanisms associated with using wearable devices for ankle training remain largely unexplored. This study aimed to investigate the ankle tracking performance and brain white matter changes associated with ankle tracking learning using a wearable-device system and the behavior–brain structure relationships in middle-aged and older adults.MethodsTwenty-six middle-aged and older adults (48–75 years) participated in this study. Participants underwent 5-day ankle tracking learning with their non-dominant foot using a custom-built ankle tracking system equipped with a wearable sensor and a sensor-computer interface for real-time visual feedback and data acquisition. Repeated and random sequences of target tracking trajectories were both used for learning and testing. Ankle tracking performance, calculated as the root-mean-squared-error (RMSE) between the target and actual ankle trajectories, and brain diffusion spectrum MR images were acquired at baseline and retention tests. The general fractional anisotropy (GFA) values of eight brain white matter tracts of interest were calculated to indicate their integrity. Two-way (Sex × Time) mixed repeated measures ANOVA procedures were used to investigate Sex and Time effects on RMSE and GFA. Correlations between changes in RMSE and those in GFA were analyzed, controlling for age and sex.ResultsAfter learning, both male and female participants reduced the RMSE of tracking repeated and random sequences (both p < 0.001). Among the eight fiber tracts, the right superior longitudinal fasciculus II (R SLF II) was the only one which showed both increased GFA (p = 0.039) after learning and predictive power of reductions in RMSE for random sequence tracking with its changes in GFA [β = 0.514, R2 change = 0.259, p = 0.008].ConclusionsOur findings implied that interactive tracking movement learning using wearable sensors may place high demands on the attention, sensory feedback integration, and sensorimotor transformation functions of the brain. Therefore, the SLF II, which is known to perform these brain functions, showed corresponding neural plasticity after such learning, and its plasticity also predicted the behavioral gains. The SLF II appears to be a very important anatomical neural correlate involved in such learning paradigms.

Anisotropy with respect to the applied magnetic field of spin qubit decoherence times

Electron spin qubits are a promising platform for quantum computation. Environmental noise impedes coherent operations by limiting the qubit relaxation (T1) and dephasing (Tϕ) times. There are multiple sources of such noise, which makes it important to devise experimental techniques that can detect the spatial locations of these sources and determine the type of source. In this paper, we propose that anisotropy in T1 and Tϕ with respect to the direction of the applied magnetic field can reveal much about these aspects of the noise. We investigate the anisotropy patterns of charge noise, evanescent-wave Johnson noise, and hyperfine noise in hypothetical devices. It is necessary to have a rather well-characterized sample to get the maximum benefit from this technique. The general anisotropy patterns are elucidated. We calculate the expected anisotropy for a particular model of a Si/SiGe quantum dot device.

Seismic and thermo-compositional insights into the uppermost mantle beneath the Northern Andes magmatic arc

The mantle wedge beneath the Northern Andes magmatic arc is expected to be latitudinally heterogeneous as suggested by the highly variable composition of recovered xenoliths, a discontinuous pattern of low seismic velocity zones, and unusually high Vp/Vs ratios below volcanic centers. Such heterogeneity might be controlling the development of the modern arc which currently shows a narrow northern volcanic segment between ∼4° and 6°N (<75 km wide), a volcanic gap of hundreds of km in its central portion (∼2°-4°N), and a wider southern volcanic expression between ∼2°S and 2°N (>120 km wide). Through an analysis of Pn and Sn inter-station wave speed estimates, the seismic structure dissimilarity and latitudinal thermo-compositional insights were constrained within the uppermost mantle beneath the arc. Results, integrating wave speed estimates, anisotropy, and thermo-compositional inferences obtained by wave velocity comparison using physical properties of minerals and phase equilibria modeling, suggest a seismically slower structure, higher anisotropy, and warmer conditions beneath the northern region (>4°N), whereas a faster, less anisotropic, and colder mantle towards the south (<2°N). We interpret the warmer and higher degree of anisotropy in the northern uppermost mantle as influenced by the Caldas tear, prompting hot mantle influx. Beneath the gap region, seismic speeds are similar to those in the north, yet a colder thermal state is suggested. We interpret the colder temperatures and the abrupt reduction in surface volcanism as reflecting an absence, or a reduced amount of magma pounding within the Moho vicinity. The southern upper mantle is seismically faster and colder compared to the northern portions of the arc. We interpret the fast velocities, and a wider volcanic expression on the surface, as influenced by the Carnegie ridge interaction prompting a shallower subduction with respect to the north. Our wave speed estimate and thermo-compositional inferences draw an increase in temperature and seismic anisotropy in the uppermost mantle from south to north along the Northern Andes magmatic arc. The main controlling factor of the general anisotropy below the entire arc seems to be the preferred orientation of olivine and pyroxene rather than an aligned melt fabric.

Quantification of changes in white matter tract fibers in idiopathic normal pressure hydrocephalus based on diffusion spectrum imaging

PurposePatients with idiopathic normal pressure hydrocephalus (iNPH) present white-matter abnormalities. The analytical methods described to date only measure mean diffusion parameter alterations of iNPH-specific brain regions or in a certain fasciculus. This study quantitatively analyzed whether iNPH-tract abnormalities are confined to specific sections or involve entire fibers based on diffusion spectrum imaging (DSI). MethodTwenty-two patients with iNPH and 20 normally aging subjects were included. The 18 main tracts in the brain of each subject were extracted, and the diffusion parameters of 100 equidistant nodes on each fiber were calculated to quantitatively evaluate integrity changes in different regions along these tracts. Two diffusion metrics were measured, i.e., general fractional anisotropy (GFA) and fractional anisotropy (FA). ResultsCompared to normally aging (P < 0.05), in iNPH, the GFA and FA of the left uncinate fasciculus and FA of the bilateral superior longitudinal fasciculus 1 were reduced in areas where the entire fiber was involved (%nodes with significant differences > 90%). Most other fasciculi detected presented GFA or FA alterations limited to specific regions. Increased and decreased GFA or FA co-occurred in different sections of the same fibers, including the corticospinal tract and left thalamic radiation posterior in iNPH. ConclusionsFew iNPH fibers presented diffusion abnormalities involving nearly all tracts. Most fiber abnormalities in iNPH were confined to specific areas, and different parts of the same fasciculus showed diverse diffusion alterations in few cases. This DSI-based tract analysis provided detailed information on iNPH white-matter changes.

A goal-oriented adaptive finite-element approach for 3-D marine controlled-source electromagnetic problems with general electrical anisotropy

SUMMARY We present a goal-oriented adaptive finite-element algorithm for accurately modelling marine controlled-source electromagnetic responses in 3-D media with general electrical anisotropy. We formulate the primal boundary value problem in terms of the total electric field for general applications. Following the goal-oriented adaptivity concept, the dual problem is derived from a functional designed to measure the data errors of interest in light of the data quality. We approximate the solutions to the primal and dual formulations using the edge finite-element method on tetrahedral grids for a flexible treatment of complex geological settings and survey geometries. To control the mesh adaptation, we develop a reliable residual-type a posteriori error estimation that takes account of the volumetric residual and the numerical discontinuity of the normal component of the electrical current density and that of the tangential component of the magnetic field with respect to non-smooth and anisotropic coefficients. We demonstrate the proposed modelling solver on 1-D MCSEM scenarios with varying degrees of electrical anisotropy. The comparison with goal-oriented adaptivity results obtained from other three commonly used error indicators shows that our approach is robust in dealing with both moderate and strong electrical anisotropy. After that, we constructed a 3-D hydrocarbon-bearing reservoir model with slope seafloor topography and tilted transverse isotropy in the background to examine our algorithm for the case of multiple sources. Finally, we implement a sensitivity analysis procedure to evaluate the resolution of the electrical anisotropy. The quantitative results indicate limitations and preferences of conventional MCSEM data in resolving anisotropic models, providing fundamental insights for inversion based data interpretation.