Normal moveout coefficients for horizontally layered triclinic media

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. WA119-WA145 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
Elastic Properties ◽  
Error Term ◽  
Single Layer ◽  
Normal Incidence ◽  
Effective Model ◽  
Pure Mode ◽  
Effective Parameters ◽  
Reflected Waves ◽  
Layered Model ◽  
The Individual

Sedimentary layers affected by vertical compaction and strong lateral tectonic stresses are often characterized by low anisotropic symmetry (e.g., tilted orthorhombic [TOR]/monoclinic or even triclinic). Considering all types of pure-mode and converted waves, we derive the normal moveout (NMO) series coefficients of near normal-incidence reflected waves in arbitrarily anisotropic horizontally layered media, for a leading error term of order six. The NMO series can be either a function of the invariant horizontal slowness (slowness domain) or the surface offset (offset domain). The NMO series coefficients, referred to also as effective parameters, are associated with the corresponding azimuthally varying NMO velocity functions. We distinguish between local (single-layer) and global (overburden multilayer) effective parameters, which are related by forward and inverse Dix-type transforms. We derive the local effective parameters for an arbitrary anisotropic (triclinic) layer, which is the main contribution of this paper. With some additional geologic constraints, the local effective parameters can then be converted into the interval elastic properties. To demonstrate the applicability of our method, we consider a synthetic layered model in which each layer is characterized with TOR symmetry. The corresponding global effective model loses the symmetries of the individual layers and is characterized by triclinic symmetry.

Fourth-order normal moveout velocity in elastic layered orthorhombic media — Part 2: Offset-azimuth domain

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. C113-C132 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
Fourth Order ◽  
Horizontal Plane ◽  
Single Layer ◽  
Normal Incidence ◽  
Azimuthal Anisotropy ◽  
Effective Parameters ◽  
Strong Anisotropy ◽  
Velocity Function ◽  
Alternative Set ◽  
Special Case

Based on the theory derived in part 1, in which we obtained the azimuthally dependent fourth-order normal-moveout (NMO) velocity functions for layered orthorhombic media in the slowness-azimuth/slowness and the slowness-azimuth/offset domains, in part 2, we extend the theory to the offset-azimuth/slowness and offset-azimuth/offset domains. We reemphasize that this paper does not suggest a new nonhyperbolic traveltime approximation; rather, it provides exact expressions of the NMO series coefficients, computed for normal-incidence rays, which can then be further used within known azimuthally dependent traveltime approximations for short to moderate offsets. The same type of models as in part 1 are considered, in which the layers share a common horizontal plane of symmetry, but the azimuths of their vertical symmetry planes are different. The same eight local (single-layer) and global (overburden multilayer) effective parameters are used. In addition, we have developed an alternative set of global effective parameters in which the “anisotropic” effective parameters are normalized, classified into two groups: two “azimuthally isotropic” parameters and six “azimuthally anisotropic” parameters. These parameters have a clearer physical interpretation and they are suitable for inversion purposes because they can be controlled and constrained. Next, we propose a special case, referred to as “weak azimuthal anisotropy,” in which only the azimuthally anisotropic effective parameters are assumed to be weak. The resulting NMO velocity functions are considerably simplified, reduced to the form of the slowness-azimuth/slowness formula. We verify the correctness of our method by applying it to a multilayer orthorhombic medium with strong anisotropy. We introduce our derived, fourth-order slowness-azimuth/offset domain NMO velocity function into the well-known nonhyperbolic asymptotic traveltime approximation, and we compare the approximate traveltimes with exact traveltimes obtained by two-point ray tracing. The comparison shows an accurate match up to moderate offsets. Although the accuracy with the weak azimuthal anisotropic formula is inferior, it can still be considered reasonable for practical use.

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

Optical properties of silicene-dielectric interfaces from IR to far UV

2021 ◽  
pp. 2150235
Author(s):  
Yujun Hou ◽  
Chun Jiang
Keyword(s):  
Optical Properties ◽  
Single Layer ◽  
Normal Incidence ◽  
Complex Surface ◽  
Optical Characterization ◽  
Potential Candidate ◽  
Dielectric Interfaces ◽  
Uv Absorbers ◽  
Uv Range

Since the growth of single layer of Si has emerged, silicene became a potential candidate material to make up the disadvantage of graphene. In this paper, the complex surface conductivity is applied to characterize the properties of silicene and we investigate the optical characterization of silicene-dielectric interfaces from IR to far UV range. The silicene-Si and silicene-Ge interfaces along both parallel and perpendicular polarization directions of electromagnetic field with normal incidence are considered in this work. The optical properties of the silicene-dielectric systems proposed in this paper lay a foundation for the performance of complex silicene-based optoelectronic devices such as sensors, detectors, filters, UV absorbers and so on.

Microstructure of SrTiO3 Thin Films as Single Layer and Incorporated in Yba2Cu3O7-x/SrTiO3 Multilayers

1995 ◽  
Vol 401 ◽  
Author(s):  
L. Ryen ◽  
E. Olssoni ◽  
L. D. Madsen ◽  
C. N. L. Johnson ◽  
X. Wang ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Thin Films ◽  
Transmission Electron Microscopy ◽  
Lattice Mismatch ◽  
Single Layer ◽  
Transmission Electron ◽  
Tilt Boundaries ◽  
Interfacial Dislocations ◽  
The Individual ◽  
Film Substrate

AbstractEpitaxial single layer (001) SrTiO3 films and an epitaxial Yba2Cu3O7-x/SrTiO3 multilayer were dc and rf sputtered on (110)rhombohedral LaAIO3 substrates. The microstructure of the films was characterised using transmission electron microscopy. The single layer SrTiO3 films exhibited different columnar morphologies. The column boundaries were due to the lattice mismatch between film and substrate. The boundaries were associated with interfacial dislocations at the film/substrate interface, where the dislocations relaxed the strain in the a, b plane. The columns consisted of individual subgrains. These subgrains were misoriented with respect to each other, with different in-plane orientations and different tilts of the (001) planes. The subgrain boundaries were antiphase or tilt boundaries.The individual layers of the Yba2Cu3O7-x/SrTiO3 multilayer were relatively uniform. A distortion of the SrTiO3 unit cell of 0.9% in the ‘001’ direction and a Sr/Ti ratio of 0.62±0.04 was observed, both in correspondence with the single layer SrTiO3 films. Areas with different tilt of the (001)-planes were also present, within each individual SrTiO3 layer.

scholarly journals Reflection moveout approximation for a P-SV wave in a moderately anisotropic homogeneous vertical transverse isotropic layer

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C75-C83 ◽  
Author(s):  
Véronique Farra ◽  
Ivan Pšenčík
Keyword(s):  
Numerical Solution ◽  
Taylor Series Expansion ◽  
Pure Mode ◽  
Isotropic Layer ◽  
Weak Anisotropy ◽  
Reflected Waves ◽  
Quartic Equation ◽  
S Waves ◽  
Conversion Point ◽  
Quartic Term

A description of the subsurface is incomplete without the use of S-waves. Use of converted waves is one way to involve S-waves. We have developed and tested an approximate formula for the reflection moveout of a wave converted at a horizontal reflector underlying a homogeneous transversely isotropic layer with the vertical axis of symmetry. For its derivation, we use the weak-anisotropy approximation; i.e., we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. Traveltimes are calculated along reference rays of converted reflected waves in a reference isotropic medium. This requires the determination of the point of reflection (the conversion point) of the reference ray, at which the conversion occurs. This can be done either by a numerical solution of a quartic equation or by using a simple approximate solution. Presented tests indicate that the accuracy of the proposed moveout formula is comparable with the accuracy of formulas derived in a weak-anisotropy approximation for pure-mode reflected waves. Specifically, the tests indicate that the maximum relative traveltime errors are well below 1% for models with P- and SV-wave anisotropy of approximately 10% and less than 2% for models with P- and SV-wave anisotropy of 25% and 12%, respectively. For isotropic media, the use of the conversion point obtained by numerical solution of the quartic equation yields exact results. The approximate moveout formula is used for the derivation of approximate expressions for the two-way zero-offset traveltime, the normal moveout velocity and the quartic term of the Taylor series expansion of the squared traveltime.

Control of cracks by interfaces in composites

1975 ◽  
Vol 341 (1627) ◽  
pp. 409-428 ◽  
Keyword(s):  
Composite Material ◽  
Elastic Properties ◽  
Adhesive Joint ◽  
Composite Structures ◽  
Crack Path ◽  
Brittle Materials ◽  
Novel Theory ◽  
The Individual ◽  
Model Crack

A novel theory is proposed to show how a crack may he accelerated or retarded when it meets an interface between two equally brittle materials of different elastic properties. Measurements of a model crack travelling through a brittle adhesive joint have substantially verified the theory. The results demonstrate that the toughness of a composite material, having a periodic stiffness change along the crack path, may be very much greater than the toughness of the individual components of the composite. The relevance of these ideas to the design of tough composite structures is discussed.

scholarly journals Electrically Tunable Broadband Terahertz Absorption with Hybrid-Patterned Graphene Metasurfaces

Nanomaterials ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 562 ◽  
Author(s):  
Longfang Ye ◽  
Xin Chen ◽  
Guoxiong Cai ◽  
Jinfeng Zhu ◽  
Na Liu ◽  
...  
Keyword(s):  
Incident Angle ◽  
Single Layer ◽  
Normal Incidence ◽  
Transverse Magnetic ◽  
Single Layer Graphene ◽  
Terahertz Waves ◽  
Broadband Absorption ◽  
Terahertz Sensing ◽  
Axisymmetric Configuration ◽  
Broadband Terahertz

We numerically demonstrate a broadband terahertz (THz) absorber that is based on a hybrid-patterned graphene metasurface with excellent properties of polarization insensitivity, wide-angle, and active tunability. Our design is made up of a single-layer graphene with periodically arranged hybrid square/disk/loop patterns on a multilayer structure. We find that broadband absorption with 90% terahertz absorbance and the fractional bandwidth of 84.5% from 1.38 THz to 3.4 THz can be achieved. Because of the axisymmetric configuration, the absorber demonstrates absolute polarization independence for both transverse electric (TE) and transverse magnetic (TM) polarized terahertz waves under normal incidence. We also show that a bandwidth of 60% absorbance still remains 2.7 THz, ranging from 1.3 THz to 4 THz, for a wide incident angle ranging from 0° to 60°. Finally, we find that by changing the graphene Fermi energy from 0.7 eV to 0 eV, the absorbance of the absorbers can be easily tuned from more than 90% to lower than 20%. The proposed absorber may have promising applications in terahertz sensing, detecting, imaging, and cloaking.

Reflective properties of iridophores and fluorescent ‘eyespots’ in the loliginid squidAlloteuthis subulataandLoligo vulgaris

2001 ◽  
Vol 204 (12) ◽  
pp. 2103-2118 ◽  
Author(s):  
L. M. Mäthger ◽  
E. J. Denton
Keyword(s):  
Large Fraction ◽  
Incident Light ◽  
Normal Incidence ◽  
Mantle Cavity ◽  
Near Ultraviolet ◽  
Quarter Wavelength ◽  
The Individual ◽  
Green Fluorescent ◽  
Reflecting Surfaces ◽  
Theoretical Analyses

SUMMARYObservations were made of the reflective properties of the iridophore stripes of the squid Alloteuthis subulata and Loligo vulgaris, and the likely functions of these stripes are considered in terms of concealment and signalling.In both species, the mantle muscle is almost transparent. Stripes of iridophores run along the length of each side of the mantle, some of which, when viewed at normal incidence in white light, reflect red, others green or blue. When viewed obliquely, the wavebands best reflected move towards the blue/ultraviolet end of the spectrum and their reflections are almost 100% polarised. These are properties of quarter-wavelength stacks of chitin and cytoplasm, predicted in theoretical analyses made by Sir A. F. Huxley and Professor M. F. Land. The reflecting surfaces of the individual iridophores are almost flat and, in a given stripe, these surfaces are within a few degrees of being parallel. Both species of squid have conspicuous, brightly coloured reflectors above their eyes. These ‘eyespots’ have iridescent layers similar to those found on the mantle but are overlaid by a green fluorescent layer that does not change colour or become polarised as it is viewed more obliquely. In the sea, all reflections from the iridophore stripes will be largely confined to the blue-green parts of the spectrum and all reflections in other wavebands, such as those in the red and near ultraviolet, will be weak. The functions of the iridophores reflecting red at normal incidence must be sought in their reflections of blue-green at oblique angles of incidence. These squid rely for their camouflage mainly on their transparency, and the ventral iridophores and the red, green and blue reflective stripes must be used mainly for signalling. The reflectivities of some of these stripes are relatively low, allowing a large fraction of the incident light to be transmitted into the mantle cavity. Despite their low reflectivities, the stripes are very conspicuous when viewed from some limited directions because they reflect light from directions for which the radiances are much higher than those of the backgrounds against which they are viewed. The reflective patterns seen, for example, by neighbouring squid when schooling depend on the orientation of the squid in the external light field and the position of the squid relative to these neighbours.

scholarly journals Predicting the bulk modulus of single-layer covalent organic frameworks with square-lattice topology from molecular building-block properties

Nanoscale ◽  
2021 ◽  
Author(s):  
Antonios Raptakis ◽  
Arezoo Dianat ◽  
Alexander Croy ◽  
Gianaurelio Cuniberti
Keyword(s):  
Bulk Modulus ◽  
Elastic Properties ◽  
Building Block ◽  
Rational Design ◽  
Computational Study ◽  
Single Layer ◽  
Building Blocks ◽  
Square Lattice ◽  
New Materials ◽  
Molecular Building Block

This computational study establishes a correlation between the elastic properties of COFs and their building-blocks towards the rational design of new materials with tailored properties.

A homogenization approach for modeling a propagating hydraulic fracture in a layered material

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. MR153-MR162 ◽  
Author(s):  
Egor V. Dontsov
Keyword(s):  
Elastic Properties ◽  
Hydraulic Fracture ◽  
Local Stress ◽  
Transversely Isotropic ◽  
Horizontal Stress ◽  
Layered Material ◽  
Elastic Response ◽  
Effective Parameters ◽  
Fine Mesh ◽  
Minimum Horizontal Stress

Shales are known to have a finely layered structure, which greatly influences the overall material’s response. Incorporating the effect of all these layers explicitly in a hydraulic fracture simulator would require a prohibitively fine mesh. To avoid such a scenario, a suitable homogenization, which would represent the effect of multiple layers in an average sense, should be performed. We consider a sample variation of elastic properties and minimum horizontal stress versus depth that has more than a hundred layers. We evaluate methodologies to homogenize the stress and the elastic properties. The elastic response of a layered material is found to be equivalent to that of a transversely isotropic material, and the explicit relations for the effective parameters are obtained. To illustrate the relevance of the homogenization procedure for hydraulic fracturing, the propagation of a plane strain hydraulic fracture in a finely layered shale is studied. To reduce the complexity of the numerical model, elastic layering is neglected and only the effect of the stress layers is analyzed. The results demonstrate the ability of the homogenized stress model to accurately capture the hydraulic fracture behavior using a relatively coarse mesh. This result is obtained by using a special asymptotic solution at the tip element that accounts for the local stress variation near the tip, which effectively treats the material at the tip element as nonhomogenized.

Sign in / Sign up

Export Citation Format

Share Document