Dear all,
Yes, there are a lot of pitfalls, but essentially the non-Euclidean or
'fractal' geometry introduced the mathematician Mandelbrot is a
qantitative expression of the geologist Lyell's observation of
scale-invariant or self-similar objects in geology. Neither claimed
scale-free geometry occurs on all scales (Mandelbrot explicitly says it
doesn't in natural systems in his book), though the bandwidth of scales
is often sufficient in practice to make easy identification of scale
difficult. This is why for example we teach new undergraduate students
in geology to add a scale bar or a hammer/lens cap/pencil to all
photographs or field sketches. As Maarten and Dirk have said, it can be
a practical as well as useful concept, if not pushed too far.
There is a more detailed discussion in the review and synthesis by
Bonnet et al. (2001)
http://www.geos.ed.ac.uk/homes/imain/igmpapers/rg2001.pdf
which cautions against the intrepretation of a fractal set based on a
narrow bandwidth of scales in the observations. [A 'narrow-band
fractal' is quite precisely an oxymoron (!)]
There is a discussion of how fractal geometry and scaling - in fracture,
faulting and earthquake populations - emerges spontaneously from the
underlying statistical mechanics of driven threshold systems at:
http://www.geos.ed.ac.uk/homes/imain/igmpapers/rg1996.pdf
Another interesting and much more recent observation is the amazing
bandwith (20 orders of magnitude in seismic moment) of stress drop in
acoustic emission and earthquakes compiled by Goodfellow and Young (2014):
http://civil.engineering.utoronto.ca/staff/professors/paul-young/acoustic-emission-source-parameters/
Best wishes, Ian.
--------------------------------
On 26/08/2016 18:50, Dirk Nieuwlan 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
> M: +31 (0)621547949
> 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]] 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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--
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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