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In this paper joint multifractal random walk approach is carried out to analyze
some petrophysical quantities for characterizing the petroleum
reservoir. These quantities include Gamma emission (GR), sonic
transient time (DT) and Neutron porosity (NPHI) which are collected
from four wells of a reservoir. To quantify mutual interaction of petrophysical quantities, joint
multifractal random walk is implemented. This approach is based on
the mutual multiplicative cascade notion in the multifractal
formalism and in this approach $L_0$ represents a benchmark to
describe the nature of cross-correlation between two series. The
analysis of the petrophysical quantities revealed that GR for all
wells has strongly multifractal nature due to the considerable
abundance of large fluctuations in various scales. The variance of probability distribution function,
$\lambda_{\ell}^2$, at scale $\ell$ and its intercept determine the
multifractal properties of the data sets sourced by probability density function. The value of
$\lambda_0 ^2$ for NPHI data set is less than GR's, however, DT
shows a nearly monofractal behavior, namely $\lambda_0 ^2\rightarrow
0$, so we find that $\lambda_0^2({\rm GR})>\lambda_0^2({\rm
NPHI})\gg\lambda_0^2({\rm DT})$. While, the value of
Hurst exponents can not discriminate between series GR, NPHI and DT.
Joint analysis of the petrophysical quantities for considered wells
demonstrates that $L_0$ has negative value for GR-NPHI confirming
that finding shaly layers is in competition with finding porous
medium while it takes positive value for GR-DT determining that
continuum medium can be detectable by evaluating the statistical
properties of GR and its cross-correlation to DT signal.\\
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