DETERMINATION OF THE ELASTIC CONSTANTS OF ANISOTROPIC SOLIDS FROM GROUP VELOCITIES MEASURED IN SYMMETRY DIRECTIONS

1996 ◽  
Vol 10 (02) ◽  
pp. 235-246 ◽  
Author(s):  
KWANG YUL KIM ◽  
ARTHUR G. EVERY ◽  
WOLFGANG SACHSE
Keyword(s):  
Group Velocity ◽  
Elastic Constants ◽  
Symmetry Axis ◽  
Symmetry Plane ◽  
Orthorhombic Symmetry ◽  
Easy Method ◽  
Novel Method ◽  
Complete Set ◽  
Wave Normal

We present in this article a novel method of determining all three elastic constants of cubic crystals from a single broadband waveform propagating in the [001] direction. The method can be easily extended to media of orthorhombic symmetry whose symmetry plane quasitransverse (QT) group velocity sheet is folded across the symmetry axis. The usefulness of these formulas lies in providing a very convenient and easy method of determining all the elastic constants of a medium from the rays propagating in the principal symmetry directions of the medium. Particular emphasis is given to the so-called oblique-mode QT rays with group velocity lying along a symmetry axis but with wave normal lying away from that axis in a symmetry plane. Through the use of these oblique modes the need to make off-axis measurements to obtain a complete set of elastic constants is circumvented. Moreover, we describe a method of clarifying the ambiguity that arises; with which symmetry plane is the wave normal of an oblique-mode QT ray propagating in the symmetry axis associated. Further, we show how the effect of a finite rise time source can be corrected for in the determination of a mixed index elastic constant.

Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1803-1817 ◽  
Author(s):  
Andrey Bakulin ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Fractured Reservoirs ◽  
Symmetry Plane ◽  
P Wave ◽  
Single Fracture ◽  
Orthorhombic Symmetry ◽  
Weak Anisotropy ◽  
Horizontal Symmetry ◽  
Vertical Symmetry Plane ◽  
Vertical Fractures

Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between the anisotropic parameters defined in the vertical symmetry planes. Subsequently, the fracture weaknesses, which carry information about the density and content of the fracture network, can be estimated in the same way as for fracture‐induced transverse isotropy with a horizontal symmetry axis (HTI media) examined in our previous paper (part I). The parameter estimation procedure can be based on the azimuthally dependent reflection traveltimes and prestack amplitudes of P-waves alone if an estimate of the ratio of the P- and S-wave vertical velocities is available. It is beneficial, however, to combine P-wave data with the vertical traveltimes, NMO velocities, or AVO gradients of mode‐converted (PS) waves. In each vertical symmetry plane of the model with two orthogonal fracture sets, the anisotropic parameters are largely governed by the weaknesses of the fractures orthogonal to this plane. For weak anisotropy, the fracture sets are essentially decoupled, and their parameters can be estimated by means of two independently performed HTI inversions. The input data for this model must include the vertical velocities (or reflector depth) to resolve the anisotropic coefficients in each vertical symmetry plane rather than just their differences. We also discuss several criteria that can be used to distinguish between the models with one and two fracture sets. For example, the semimajor axis of the P-wave NMO ellipse and the polarization direction of the vertically traveling fast shear wave are always parallel to each other for a single system of fractures, but they may become orthogonal in the medium with two fracture sets.

Determination of 1,2-Benzisothiazolin-3-One in Paper for Food Packaging by Fluorescence Spectroscopy

2014 ◽  
Vol 633-634 ◽  
pp. 329-332
Author(s):  
Jia Yue Sun ◽  
Qiu Mei Di ◽  
Qi Guang Xu ◽  
Liu Han
Keyword(s):  
Fluorescence Spectroscopy ◽  
Food Packaging ◽  
Correction Coefficient ◽  
Method Detection Limit ◽  
Easy Method ◽  
Food Package ◽  
Novel Method ◽  
Limit Detection ◽  
Hydrothermal Extraction

A novel method has been developed to detect 1,2-benzisothiazolin-3-one (BIT) in paper for food packaging by hydrothermal extraction coupled with fluorescence spectroscopy in paper for food package. Parameters affecting fluorescence intensity have been evaluated, including the pH of solvents and the effect of surfactants. It turned out to be that fluorescent spectroscopy was a sensitive and easy method to determine BIT in paper package. The regression equation obtained was liner, and the correction coefficient was 99.9%, the limit detection (LOD) was 25.3μg/L, method detection limit (MDL) was 0.25mg/kg, which turned out that this method was sensitive and precise to determine BIT in food package.

Die experimentelle Ermittlung der elastischen Konstanten höherer Ordnung

1960 ◽  
Vol 15 (12) ◽  
pp. 1056-1067 ◽  
Author(s):  
Alfred Seeger ◽  
Otto Buck
Keyword(s):  
Elastic Constants ◽  
Experimental Methods ◽  
Theory Of Elasticity ◽  
Polycrystalline Copper ◽  
Third Order ◽  
Numerical Work ◽  
The Third ◽  
Third Order Elastic Constants ◽  
Complete Set

The application of the non-linear theory of elasticity to solid state problems has recently become of increasing importance. For numerical work the knowledge of the third-order elastic constants is required. The present paper compiles the various experimental methods for the experimental determination of these constants and derives, where required, the formulae for the evaluation of the experiments. We give a critical compilation of the available data on third-order elastic constants. A complete set is given for germanium single crystals (6 constants) and for polycrystalline copper and iron (3 constants).

scholarly journals Resonant Ultrasound Spectroscopy: Sensitivity Analysis for Anisotropic Materials with Hexagonal Symmetry

2021 ◽  
pp. 1-20
Author(s):  
Christopher Sevigney ◽  
Onome Scott-Emuakpor ◽  
Farhad Farzbod
Keyword(s):  
Elastic Constants ◽  
Material Properties ◽  
Free Vibrations ◽  
Hexagonal Symmetry ◽  
Resonant Ultrasound Spectroscopy ◽  
Cubic Symmetry ◽  
Complete Set ◽  
Resonant Ultrasound ◽  
Non Destructive

Abstract Resonance ultrasound spectroscopy (RUS) is a non-destructive technique for evaluating elastic and an-elastic material properties. The frequencies of free vibrations for a carefully crafted sample are measured, and material properties can be extracted from this. In one popular application, the determination of monocrystal elasticity, the results are not always reliable. In some cases, the resonant frequencies are insensitive to changes in certain elastic constants or their linear combinations. Previous work has been done to characterize these sensitivity issues in materials with isotropic and cubic symmetry. This work examines the sensitivity of elastic constant measurements by the RUS method for materials with hexagonal symmetry, such as titanium-diboride. We investigate the reliability of RUS data and explore supplemental measurements to obtain an accurate and complete set of elastic constants.

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