A method of stiffnessTensor.
the speeds of the three elastic plane waves in a direction and their polarisations, the eigenvalues and eigenvectors of the Christoffel tensor
Syntax
vp, vs1, vs2, pp, ps1, ps2 = velocity(C, n)
In the direction n, or at a list of them.
vp, vs1, vs2, pp, ps1, ps2 = velocity(C, n, density=rho)
With another density than the tensor’s.
vp, vs1, vs2, pp, ps1, ps2 = velocity(C)
As functions on the sphere and axis fields.
vp, vs1, vs2, pp, ps1, ps2 = velocity(C, harmonic=True)
As harmonic expansions.
Description
The Christoffel tensor of the direction n is C_ijkl n_j n_l; its eigenvalues divided by the density are the squared speeds of the quasi longitudinal wave, vp, and of the two shear waves, vs1 the faster, vs2 the slower, its eigenvectors the polarisations, the directions in which the particles move. A stiffness in GPa and a density in g/cm^3 give speeds in km/s. A compliance tensor is inverted first.
The result is a named tuple, so velocity(C, n).vp picks one entry. Without a direction the speeds are functions on the sphere, evaluated where they are asked, and the polarisations axis fields; with harmonic=True they are sampled once on a quadrature grid and expanded. MATLAB’s velocity(C, n, rho) passes the density third, which is taken too.
Input
C |
stiffnessTensor in GPa, or complianceTensor |
n |
vector3d, the propagation directions |
Keywords
| keyword | default | description |
|---|---|---|
density |
None |
the density in g/cm^3; by default the density stored on the tensor, else 1 |
harmonic |
False |
expand the functions of a call without a direction in spherical harmonics instead of evaluating them where they are asked |
bandwidth |
48 |
the harmonic degree of these expansions |
Output
vp, vs1, vs2 |
the speeds of the p wave and of the faster and slower s wave in km/s; S2Fun without a direction |
pp, ps1, ps2 |
vector3d, the polarisations of the three waves; S2AxisField without a direction |
See also
energyVector, ChristoffelTensor, plotSeismicVelocities, WaveVelocities
MATLAB’s stiffnessTensor.velocity
source
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/stiffnessTensor.velocity_py.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.