TY - JOUR
T1 - Investigation of lithological heterogeneities from velocity logs using EMD-Hölder technique combined with multifractal analysis and unsupervised statistical methods
AU - Amoura, Saliha
AU - Gaci, S.
AU - Barbosa, Sofia
AU - Farfour, Mohammed
AU - Bounif, Mohand A.
N1 - Funding Information:
We gratefully acknowledge the Algerian Ministry of Higher Education and Scientific Research for the scholarship under the Exceptional National Program (E.N.P) 2019/2020, the Departamento de Ci?ncias da Terra e GeoBioTec, FCT Universidade NOVA de Lisboa, the Algerian Institute of Petroleum (IAP) and the Geophysical Laboratory-FSTGAT (USTHB) to host and follow this research.
Funding Information:
We gratefully acknowledge the Algerian Ministry of Higher Education and Scientific Research for the scholarship under the Exceptional National Program (E.N.P) 2019/2020 , the Departamento de Ciências da Terra e GeoBioTec, FCT Universidade NOVA de Lisboa, the Algerian Institute of Petroleum (IAP) and the Geophysical Laboratory-FSTGAT (USTHB) to host and follow this research.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/1
Y1 - 2022/1
N2 - Well logging data are the main support of petrophysical information in petroleum engineering, and as many natural signals, they have deterministic component and noisy component. Conventional denoising methods depend on various filtering parameters, which increase the possibility of error and losing useful information in the signal. This research provides a well-controlled method to reduce noise, based on empirical mode decomposition (EMD) and regularity analysis indexed by the Hölder exponent (in short, EMD-Hölder). First, well velocity logs are handled as noisy signals, and decomposed into intrinsic mode functions (IMFs) for fast oscillations to slow oscillations via EMD, then regularity exponent is computed for each IMFs using wavelet leaders (WL) algorithm. The Hölder exponent (h) is one of the best metrics to quantify the singularity. The value of the Hölder exponent h = 0.5 characterizes the white noise of the analyzed signal, and any value h calculated from an intrinsic modal function IMF less than or equal to a predefined specific threshold, this IMF function is considered as noise, to be discarded while the reconstruction of the new denoised signal. To determine the multifractal properties of P- and S-wave velocities denoted Vp and Vs, respectively, a multifractal analysis was performed using the wavelet leaders (WL). The estimated multifractal parameters: scaling exponent τ (q), multifractal spectrum D(h), singularity strength h, and Hausdorff dimension D are used to quantify the non-stationarity and non-linearity of velocity, followed by an application of unsupervised statistical methods (a hierarchical clustering analysis, HCA, and principal component analysis, PCA) to establish a possible relationship between multifractal parameters and type of lithology (sandstone and clay). It is shown that the width of the multifractal spectra (Δh) estimated from well logs can be used as a lithological indicator of the studied geological formations.
AB - Well logging data are the main support of petrophysical information in petroleum engineering, and as many natural signals, they have deterministic component and noisy component. Conventional denoising methods depend on various filtering parameters, which increase the possibility of error and losing useful information in the signal. This research provides a well-controlled method to reduce noise, based on empirical mode decomposition (EMD) and regularity analysis indexed by the Hölder exponent (in short, EMD-Hölder). First, well velocity logs are handled as noisy signals, and decomposed into intrinsic mode functions (IMFs) for fast oscillations to slow oscillations via EMD, then regularity exponent is computed for each IMFs using wavelet leaders (WL) algorithm. The Hölder exponent (h) is one of the best metrics to quantify the singularity. The value of the Hölder exponent h = 0.5 characterizes the white noise of the analyzed signal, and any value h calculated from an intrinsic modal function IMF less than or equal to a predefined specific threshold, this IMF function is considered as noise, to be discarded while the reconstruction of the new denoised signal. To determine the multifractal properties of P- and S-wave velocities denoted Vp and Vs, respectively, a multifractal analysis was performed using the wavelet leaders (WL). The estimated multifractal parameters: scaling exponent τ (q), multifractal spectrum D(h), singularity strength h, and Hausdorff dimension D are used to quantify the non-stationarity and non-linearity of velocity, followed by an application of unsupervised statistical methods (a hierarchical clustering analysis, HCA, and principal component analysis, PCA) to establish a possible relationship between multifractal parameters and type of lithology (sandstone and clay). It is shown that the width of the multifractal spectra (Δh) estimated from well logs can be used as a lithological indicator of the studied geological formations.
KW - Empirical mode decomposition
KW - Lithological heterogeneities
KW - Multifractal spectrum
KW - Unsupervised statistical methods
KW - Velocity logs
KW - Wavelet leader
UR - http://www.scopus.com/inward/record.url?scp=85122511666&partnerID=8YFLogxK
U2 - 10.1016/j.petrol.2021.109588
DO - 10.1016/j.petrol.2021.109588
M3 - Article
AN - SCOPUS:85122511666
SN - 0920-4105
VL - 208
JO - Journal Of Petroleum Science And Engineering
JF - Journal Of Petroleum Science And Engineering
M1 - 109588
ER -