Dear list members
I got good references on the issue together with
a work on "Scaling properties of the coefficient
of variation" of Peter Bossew and a PhD. thesis
on geostatistics of Joao Felipe.
Below the references have been reported.
I found particularly easy to follow the work of
Malamhud who gives a quite clear synthesis
of the relationships between variogram, fractal
dimension, spectral analysis, etc
.
From what I see there are strong analogies
between time series and spatial data.
Then, looking at the wavelet techniques I have
the feeling of strong similarities with the
application of dispersion variance and also with
the increments of order k of the generalized covariances
theory.
B. D. Malamud and D. L. Turcotte, Self-Affine
Time Series: I. Generation and Analyses,pp. 190
Bruno, R., Raspa, G., 1989. Geostatistical characterization of
fractal models of surfaces. In: Armstrong, M. (Ed.),
Geostatistics. Kluwer Academic, Dordrecht, pp. 7789.
Burrough, P.A., 1981. Fractal dimensions of landscapes and
other environmental data. Nature 294, 240242.
Burrough, P.A., 1983. Multiscale sources of spatial variation in
soil. I. The application of fractal concepts to nested levels of
soil variation. Journal of Soil Science 34, 577597.
Butler, J.B., Lane, S.N., Chandler, J.H., 2001. Characterization
of the structure of river-bed gravels using two-dimensional
fractal analysis. Mathematical Geology 33, 301330.
Klinkenberg, B., 1992. Fractals and morphometric measures: is
there a relationship? Geomorphology 5, 520.
Yang, Z.Y., Di, C.C., 2001. A directional method for directly
calculating the fractal parameters of joint surface roughness.
International Journal of Rock Mechanics and Mining
Sciences 38, 12011210.
Chaos in geology and Geophysics. (Cambridge University Press)
Jens Feder's book "Fractals"
At 19.32 14/03/2009, Gregoire Dubois wrote:
Hello Gustavo,
if you use Burrough's approach (deriving the fractal dimension from
the log-log plot of the variogram) then it is relatively
straightforward: instead of using the slope of the log-log plot of the
variogram in 1D, you do the same from the 2D semivariogram, but....you
have to make the assumption that the the 2D omnidirectional variogram
is identical to the one obtained 1D, hence, you should make sure that
you are in a situation in which you have no trends and anisotropies.
Cheers
Gregoire
On Wed, Mar 11, 2009 at 2:34 PM, Gustavo Vasques
<gmvasq...@yahoo.com.br> wrote:
>
> Dear Sebastiano and list,
>
> I am also interested in this topic, and have
another question related to it.
>
> Is there a simple way to calculate the
fractal dimension from a continuous point
variable that is distributed NOT on a transect,
but rather at discontinuous (i.e. random) locations in a 2D study area?
>
> Thank you,
>
> Gustavo Vasques
>
> --- Em qua, 11/3/09, seba <sebastiano.trevis...@libero.it> escreveu:
>
>> De: seba <sebastiano.trevis...@libero.it>
>> Assunto: AI-GEOSTATS: variogram and fractals
>> Para: ai-geostats@jrc.it
>> Data: Quarta-feira, 11 de Março de 2009, 6:48
>> Dear list members
>>
>> I'm trying to find some bibliography about the
>> relationships
>> between variograms and fractals. I know that there is a
>> relationship between the exponent of a power variogram
>> model and the fractal
>> dimensions, but I would like to know more.
>> In particular I'm trying to find a paper or a book that
>> gives a comprensive and intuitive picture of the issue.
>> Thank you in advance.
>> Sebastiano T.
>>
>>
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