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Fractal Fract
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Fractals in Geosciences: Theory and Applications
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Fractals in Geosciences: Theory and Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 6379

Special Issue Editors

Dr. Orietta Nicolis

E-Mail Website
Guest Editor
Facultad de Ingenieria, Universidad Andres Bello, Viña del, Mar 2520000, Chile
Interests: time series models; spatial and spatial-temporal models; machine learning methods; big data; computer science; wavelet-transforms; fractional and multifractal processes
Dr. Said Gaci

E-Mail Website
Guest Editor
Department of Geology, Geophysics & Reservoir, Algerian Institute of Petroleum (IAP), Sonatrach, Boumerdes 35000, Algeria
Interests: exploration geophysics; seismic prospecting; signal processing

Special Issue Information

Dear Colleagues,

Fractals are gaining an increasing interest in various fields of the Geosciences, and are receiving a large number of applications in each field. This Special Issue aims to collect scientific research connected to this topic, and thus to highlight the contribution of fractals in earth sciences. Moreover, it will be of interest to involve a broader range of audiences from various scientific communities, being mindful of their potential merits to stimulate more original applications.

The Issue will cover the following applications and other relevant topics:

  • Well logging;
  • Oil/gas reservoir characterization;
  • Geostatistics;
  • Analysis of geomagnetic activity;
  • Hydrology and hydrogeology;
  • Signal and image processing analysis of geosciences data;
  • Topographical modeling;
  • Probabilistic and statistical analysis in Geosciences

Dr. Orietta Nicolis
Dr. Said Gaci
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal
  • fractional
  • multifractal
  • scaling
  • fractional brownian motion
  • geosciences
  • geostatistics

Published Papers (3 papers)

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Research

18 pages, 2327 KiB  
Article
Signal-Noise Identification for Wide Field Electromagnetic Method Data Using Multi-Domain Features and IGWO-SVM
by Xian Zhang, Diquan Li, Jin Li, Bei Liu, Qiyun Jiang and Jinhai Wang
Fractal Fract. 2022, 6(2), 80; https://doi.org/10.3390/fractalfract6020080 - 31 Jan 2022
Cited by 5 | Viewed by 1805
Abstract
Noise tends to limit the quality of wide field electromagnetic method (WFEM) data and exploration results. The existing WFEM denoising methods lack the signal identification process and are only able to filter or eliminate abnormalities in the time or frequency domain, which easily [...] Read more.
Noise tends to limit the quality of wide field electromagnetic method (WFEM) data and exploration results. The existing WFEM denoising methods lack the signal identification process and are only able to filter or eliminate abnormalities in the time or frequency domain, which easily leads to the loss of more abundant real data and to low data quality. Thus, we built the WFEM data sample library to extract the multi-domain features. Then, neighborhood search and location sharing were used to improve the grey wolf optimizer (IGWO) algorithm. The support vector machine (SVM) parameters were optimized by IGWO to train multi-domain features, and an IGWO-SVM data model was generated. We used the data model to quantitatively test the WFEM signal and noise in the simulation and measured data. This method can effectively identify the WFEM signal and noise, eliminate the identified noise, and use the identified signal to reconstruct the effective data. Finally, the digital coherence technique was used to extract the spectrum amplitude of the effective frequency points. The experiments demonstrated the advantage of the convergence of IGWO algorithms and the comparison of the SVM parameters optimization techniques. The proposed method can quickly and effectively search the optimal SVM parameters, significantly improve the identification effect of WFEM signal noise, and completely remove the abnormal noise waveform in the reconstructed data. The more stable electric field curves in the results verify the effectiveness of the algorithm design and optimized identification method. Full article
(This article belongs to the Special Issue Fractals in Geosciences: Theory and Applications)
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14 pages, 4086 KiB  
Article
Unified Scale Theorem: A Mathematical Formulation of Scale in the Frame of Earth Observation Image Classification
by Christos G. Karydas
Fractal Fract. 2021, 5(3), 127; https://doi.org/10.3390/fractalfract5030127 - 17 Sep 2021
Cited by 5 | Viewed by 1896
Abstract
In this research, the geographic, observational, functional, and cartographic scale is unified into a single mathematical formulation for the purposes of earth observation image classification. Fractal analysis is used to define functional scales, which then are linked to the other concepts of scale [...] Read more.
In this research, the geographic, observational, functional, and cartographic scale is unified into a single mathematical formulation for the purposes of earth observation image classification. Fractal analysis is used to define functional scales, which then are linked to the other concepts of scale using common equations and conditions. The proposed formulation is called Unified Scale Theorem (UST), and was assessed with Sentinel-2 image covering a variety of land uses from the broad area of Thessaloniki, Greece. Provided as an interactive excel spreadsheet, UST promotes objectivity, rapidity, and accuracy, thus facilitating optimal scale selection for image classification purposes. Full article
(This article belongs to the Special Issue Fractals in Geosciences: Theory and Applications)
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12 pages, 2150 KiB  
Article
A Grey System Approach for Estimating the Hölderian Regularity with an Application to Algerian Well Log Data
by Said Gaci and Orietta Nicolis
Fractal Fract. 2021, 5(3), 86; https://doi.org/10.3390/fractalfract5030086 - 2 Aug 2021
Cited by 2 | Viewed by 1487
Abstract
The Hölderian regularity is an important mathematical feature of a signal, connected with the physical nature of the measured parameter. Many algorithms have been proposed in literature for estimating the local Hölder exponent value, but all of them lead to biased estimates. This [...] Read more.
The Hölderian regularity is an important mathematical feature of a signal, connected with the physical nature of the measured parameter. Many algorithms have been proposed in literature for estimating the local Hölder exponent value, but all of them lead to biased estimates. This paper attempts to apply the grey system theory (GST) on the raw signal for improving the accuracy of Hölderian regularity estimation. First, synthetic logs data are generated by the successive random additions (SRA) method with different types of Hölder functions. The application on these simulated signals shows that the Hölder functions estimated by the GST are more precise than those derived from the raw data. Additionally, noisy signals are considered for the same experiment, and more accurate regularity is obtained using signals processed using GST. Second, the proposed technique is implemented on well log data measured at an Algerian exploration borehole. It is demonstrated that the regularity determined from the well logs analyzed by the GST is more reliable than that inferred from the raw data. In addition, the obtained Hölder functions almost reflect the lithological discontinuities encountered by the well. To conclude, the GST is a powerful tool for enhancing the estimation of the Hölderian regularity of signals. Full article
(This article belongs to the Special Issue Fractals in Geosciences: Theory and Applications)
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