calcTensor(EBSD) vs. calcTensor(ODF) for seismic anisotropy

[Omero Felipe Orlandini]

Hello again, all! 

I have a simple question this time: when calcTensor(EBSD) is performed, does the orientation data remain fully discrete? I am mildly concerned that if the data remains totally discrete, then the resulting tensor will have an inaccurately high anisotropy due to orientation noise. However, it gets tricky using ODFs for the tensor calculation since the Gaussian smoothing (predictably) quite aggressively reduces the resulting seismic anisotropy.

Thank you!

[Luiz F. G. Morales]

Hi Phil

Whenever you want to calculate a contoured pole figure (including in these case the seismic properties that can be derived from the calcTensor), you will need to calculate an ODF and you will have to deal with your Gaussian smoothing. Nevertheless I am not entirely sure what you mean by “aggressively” reduction of seismic anisotropy. Indeed if during the calculation of your ODF you choose, lets say, a halfwidth of 1 degree and repeat the same calculation with a halfwidth of 10 degrees, the later will propably be less anisotropic. So, what is a proper value one can use to calculate the properties? I don’t really think there is a magical number in this case, a lot of people use a reasonable value of 10° (including myself), as it gives a good smoothing without interfering too much in the resuklts of velocities and anisotropies (and if you try 8° or 11, you will see the differences are rather minor). Nevertheless as mentioned by Rüdiger a couple of months ago, you may want to do some experiments with the calcKernel function and the methods implemented there

https://groups.google.com/forum/?fromgroups=#!topic/mtexmail/h8hDiUmhoZM

best

Luiz

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ETH Zürich
Luiz F. G. Morales
Scientific Center for Optical and Electron Microscopy (ScopeM)
HPT D 9
Auguste-Piccard-Hof 1
8093 Zurich, Switzerland
Phone +41 44 633 37 46
E-mail: luiz.m...@scopem.ethz.ch
URL: www.scopem.ethz.ch
URL: https://sites.google.com/site/luizfgmorales/
Skype: lfgmorales

[Omero Felipe Orlandini]

Hi Luiz! 

Ah ha, well let me show you what I mean by 'aggressively' reducing the seismic anisotropy - see attached files for some comparisons I did on one sample. The derivatives plot is only considering Vp and does not display the direct EBSD results. I've also done this sort of analysis for three other samples, and all behave the same way. 

It doesn't seem like there is any mathematical justification for picking one half-width or range of half-widths over another as there is no 'plateau' in the smoothing effect anywhere, and the net effect between a direct EBSD calcTensor and a 10-degree ODF calcTensor is ~1% reduction in Vp anisotropy (15% of the total anisotropy signal) although the 3-dimensional geometry of the anisotropy changes very little. I agree with your philosophy of choosing a half-width, but in this case it seems that 'good smoothing without interfering too much with the results' may be defined differently for a seismic anisotropy calculation than for a crystalline texture analysis. I am not sure exactly where the sweet spot is, from looking at the derivative of the effect and without a geological argument for a particular amount of orientation smoothing. Rüdiger's comment about generally never wanting to over-estimate a texture strength through inappropriate half-width selection is not quite as useful in the case of seismic anisotropy since the measure of seismic anisotropy is less qualitative than typical texture strength estimates - it seems both conceptually and mathematically much more sensitive to over-smoothing. 

Somehow, the calcTensor(EBSD) is sidestepping a lot (all?) of the smoothing effect, and I'm not quite sure how it is doing that or if it is intrinsically any more accurate to reality. 

Thank you!