Two-Dimensional Multifractional Brownian Motion- Based Investigation of Heterogeneities from a Core Image - Advances in Data, Methods, Models and Their Applications in Geoscience - page 113

(a)

(b) (c)

(d) (e)

Fig. 1. Used bidimensional analyzing wavelets:

Morlet wavelet (  0x =  0y =5.).

Spatial representation: (a) real part (b) imaginary part

Fourier transform representation (c)

Mexican hat.

Spatial representation (d)

Fourier transform representation (e)

3.3.2 Generalized two-dimensional multiple filter technique
The 1D MFT was initially suggested by Dziewonski et al. (1969). It consists on carrying out a
decomposition using a Gaussian filter:

2

 

kk
k

 

n

 



 

Gkk (, )  e

 

(13)

n

n

where k is a variable center angular frequency (or wavenumber) of the filter Gkk (, )

n

, and

n

 is a shaping parameter of the filter.
In order to overcome the poor ''time'' and ''low-frequency'' domains resolution toward the
low frequencies, Li (1997) suggests a varying quality factor Q and a varying bandwidth Δk :

   kk k  . Lnk ()

n

(14)

2 1

Where  is a constant, k 1 and k 2 are the - 3 dB points of the Gaussian filter.