Dear Arindam,
One way to identify scale breaks is formally to test the scale invariant
model as a null hypothesis, and prefer a model with a scale break as an
alternate (taking account of then extra parameters neede for the more
complex model) - see example at
http://www.geos.ed.ac.uk/homes/imain/igmpapers/publication61.pdf
Best wishes, Ian.
-----------------------------------
On 29/08/2016 07:40, ARINDAM SARKAR wrote:
> Respected All members,
>
> I have a query regarding the scale of self-similarity. If I conclude all
> of these suggestions,the gist becomes "the concept of self-similarity is
> applicable with in particular scale range". But problem is there is no
> any fixed scale range which can be applicable for a particular type of
> analysis. For example grain size analysis of cataclastic rock. In
> previous literatures, the scale range of self similarity is different
> for various analysis conducted through the different samples by
> different teachers. If you teachers kindly intimate me the solution,
> I'll be highly obliged.
>
> Thanking you,
> Regards
> Arindam Sarkar
>
> On Sat, Aug 27, 2016 at 8:37 PM, Natalie Deseta <[log in to unmask]
> <mailto:[log in to unmask]>> wrote:
>
> I agree with Dirk,
>
> Fractal relationships, or mean field theory are still applicable to
> geology. However, delimiting of the scaling of a particular fractal
> relationship is important. At certain scales there might be a rate
> or stepwise change in the system signalling a change in fractal
> paramteres.
>
> Example:
>
> Comminuated or ground up rock particles in shear zones exhibit a
> fractal relationship in terms of the particle size distribtuion.
> This reltationship breaks down when melt is formed in the shear
> zone. A new fractal relationship arises now due to the presence of
> melt and particle size range.
>
> The switch from one fractal relationship to another signals a change
> in the controls or conditions of the system.
>
> The issue of scaling is a common one underpinning a lot theoretical
> and experimental modelling in rheological and petrological studies.
> Often is it because we have misconceptions about the parameters
> controlling a process, or lack data.
>
> Cheers,
>
> Natalie Deseta
>
>
> On Aug 26, 2016 16:45, "Dirk Nieuwland" <[log in to unmask]
> <mailto:[log in to unmask]>> wrote:
>
> Maarten and Ijaz,
>
> It is always easy to ridicule something by taking extremes as an
> example of the general case.
> Usually it means that the person using that approach does niet
> really understand what he/she is talking about.
> To compare a mineral grain with mountain building is obviously
> an example of taking fractals to extremes beyond reasonable
> proportions.
>
> I have applied fractal theory frequently and successfully since
> about 1985, in oil and gas field development. The operational
> successes have demonstrated the reliability of fractal theory,
> provided it is used with care.
> Important is, to be very precise about the elements that are
> chosen to form part of a fractal family. In order to do this
> properly for natural fracture systems, one must in the first
> place understand fracture mechanics and the properties of
> natural fracture systems. Do not mix tension fractures and shear
> fractures and do not mix fractures of different fases (relative
> ages) of fracturing.
> Once one has done that properly, the fractal properties of the
> various populations (families) will be clear and can be used in
> a reliable way.
>
> Maarten mentions correctly that scale-independence may only be
> applicable over a limited range of scales, that seems OK and
> does not disqualify the use of fractals for such a range. A
> limited value is still a reliable value if it is used with
> common sense and with a sound fundamental understanding of the
> problem.
>
> Cheers, Dirk
>
> Dirk Nieuwland
> URL: www.newtec.nl <http://www.newtec.nl>
> T: +31 (0)71 5216892 <tel:%2B31%20%280%2971%205216892>
> M: +31 (0)621547949 <tel:%2B31%20%280%29621547949>
> E: [log in to unmask] <mailto:[log in to unmask]>
>
>
>> On 26 Aug 2016, at 16:08, Krabbendam, Maarten <[log in to unmask]
>> <mailto:[log in to unmask]>> wrote:
>>
>> Ijaz,
>>
>> Well, it does not work then, does it?
>> Rather, some features such as fractures are only
>> "scale-independent" over a limited range of scales.
>> Blanket physical theories only have limited values.......
>>
>> Maarten Krabbendam
>> BGS Scotland
>> Edinburgh EH14 4AP
>> Email: [log in to unmask] <mailto:[log in to unmask]>
>>
>>
>>
>> -----Original Message-----
>> From: Tectonics & structural geology discussion list
>> [mailto:[log in to unmask]
>> <mailto:[log in to unmask]>] On Behalf Of Ijaz Ahmad
>> Sent: 26 August 2016 14:19
>> To: [log in to unmask]
>> <mailto:[log in to unmask]>
>> Subject: Fractal/self-similar property--------A mineral grain
>> should display the property of mountain building. Right?
>>
>> Dear all
>> Theory of fractal describes the things being
>> scale-independent. This approach is also widely being used in
>> geology/geosciences worldwide. I want to have feed backs with
>> thanks.
>> Regards
>> ijaz
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>
>
>
>
> --
> /*Arindam Sarkar*/
> /*Doctoral Fellow (Ph.D.)*/
> /*Centre for Advanced Studies in Geology,
> University of Delhi, Delhi-7*/
> */Delhi,India/*/*
> Mob: +91 9717118391*/
--
Ian Main FRSE
Professor of Seismology and Rock Physics
Director of Research, School of Geosciences
http://www.geos.ed.ac.uk/homes/imain/
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.
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