Araştırma Makalesi
BibTex RIS Kaynak Göster

Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü

Yıl 2024, Cilt: 12 Sayı: 1, 121 - 133, 26.01.2024
https://doi.org/10.29130/dubited.1100533

Öz

Düşey elektrik sondajı (DES) verilerinin ters çözümü doğrusal olmayan bir problem olması nedeniyle zor bir işlemdir. Bu çalışmada, genelleştirilmiş regresyon sinir ağlarının özdirenç problemine uygulanabilirliği araştırılmıştır. Genelleştirilmiş regresyon sinir ağları (GRNN) ile düşey elektrik sondajı verilerinin ters çözümü test edilmiştir. Sinir ağı düz çözüm ile oluşturulan yapay verilerle eğitilmiştir. Ağ hem eğitim seti içinde bulunmayan diğer yapay veriler ile hem de arazi verisi ile test edilmiştir. Ayrıca GRNN parametresi olan yayılım parametresi de farklı değerler kullanılarak karşılaştırılmıştır. En düşük hata oranını veren yayılım parametresi kullanılmıştır. Yapay veriler 3 tabakalı modellerdir. Arazi verisi ise 4 tabakalı olarak değerlendirilmiştir. GRNN çıktısı yapay verilerde 3 tabakalı model için 3 özdirenç ve 2 tabaka kalınlığı olmak üzere 5 parametredir. Arazi verisinde ise 4 tabakalı bir model için 4 özdirenç ve 3 tabaka kalınlığı olmak üzere 7 parametredir. GRNN ile ters çözüm sonuçları çok düşük hata oranları ile başarılı olmuştur. DES verilerinin kalınlık ve özdirenç kestirimleri için GRNN yöntemi performansı yüksek bir oranda başarılı olmuştur.

Kaynakça

  • O. Koefoed, Geosounding principles, 1. Resistivity sounding measurements, 1st ed., Amsterdam, Netherlands: Elsevier, 1979.
  • W.K. Kosinski and E.K. William, "Geoelectric soundings for predicting aquifer properties." Groundwater, vol. 19, no. 2, pp. 163-171, 1981.
  • A.A. Zohdy, "A new method for the automatic interpretation of Schlumberger and Wenner sounding curves." Geophysics vol. 54, no. 2, pp. 245-253, 1989.
  • S. Maiti, G. Gupta, V.C. Erram and R.K. Tiwari, "Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach." Nonlinear Processes in Geophysics, vol. 18, no. 2, pp. 179-192, 2011.
  • C.L. Pekeris, "Direct method of interpretation in resistivity prospecting." Geophysics, vol. 5, no. 1, pp. 31-42, 1940.
  • S.M. Argilo, "Two computer programs for the calculation of standard graphs for resistivity prospection." Geophysical Prospecting, vol. 15, pp. 71-91, 1967.
  • G. Kunetz and J.P. Rocroi. "Traitement Automatique des Sondages Electriques Automatic Processing of Electrical Soundings." Geophysical Prospecting, vol. 18, no. 2, pp. 157-198, 1970.
  • D.P. Ghosh, "The application of linear filter theory to the direct interpretation of geoelectrical resistivity sounding measurements." Geophysical Prospecting, vol. 19, no. 2, pp. 192-217, 1971.
  • J. R. Inman, “Resistivity inversion with ridge regression.” Geophysics, vol. 40, no. 5, pp. 798-817, 1975.
  • H.K. Johansen, “A man/computer interpretation system for resistivity soundings over a horizontally strafified earth.” Geophysical Prospecting, vol. 25, no.4, pp 667-691, 1977.
  • E. Szaraniec, “Direct resistivity interpretation by accumulation of layers.” Geophysical Prospecting, vol. 28, no. 2, pp. 257-268, 1980.
  • J. Chyba, “On the interpretation of resistivity soundings by the least‐squares method.” Geophysical Prospecting, vol. 31, no. 5, pp. 795-799, 1983.
  • M.A. Meju, “An effective ridge regression procedure for resistivity data inversion.” Computers & Geosciences, vol. 18, no. 2-3, pp. 99-118, 1992.
  • Y. Meheni, R. Guérin, Y. Benderitter and A. Tabbagh, “Subsurface DC resistivity mapping: approximate 1-D interpretation.” Journal of Applied Geophysics, vol. 34, no. 4, pp. 255-269, 1996.
  • B.B. Bhattacharya and M.K. Sen, “Use of VFSA for resolution, sensitivity and uncertainty analysis in 1D DC resistivity and IP inversion.” Geophysical Prospecting, vol. 51, no. 5, pp. 393-408, 2003.
  • M.K. Jha, S. Kumar and A. Chowdhury, “Vertical electrical sounding survey and resistivity inversion using genetic algorithm optimization technique.” Journal of Hydrology, vol. 359, no. 1-2, pp. 71-87, 2008.
  • J.L.F. Martínez, E.G. Gonzalo, J.P.F. Álvarez, H.A. Kuzma and C.O.M. Pérez, “PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case.” Journal of Applied Geophysics, vol. 71, no. 1, pp. 13-25, 2010.
  • W.A. Sandham and D.J. Hamilton, “Inverse theory, artificial neural networks.” in Gupta H.K. (eds) Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. Springer, 2021, pp. 796-807.
  • H.M. El-Kaliouby, M.M. Poulton and E.A. El Diwany, “Inversion of coincident loop TEM data for layered polarizable ground using neural networks.” In SEG Technical Program Expanded Abstracts, Society of Exploration Geophysicists, 1999, pp. 259-262.
  • C. Calderón‐Macías, M.K. Sen and P.L. Stoffa, “Artificial neural networks for parameter estimation in geophysics.” Geophysical Prospecting, vol. 48, no. 1, pp. 21-47, 2000.
  • V. Spichak and I. Popova, “Artificial neural network inversion of magnetotelluric data in terms of three-dimensional earth macroparameters.” Geophysical Journal International, vol. 142, no. 1, pp. 15-26, 2000.
  • M. Van der Baan and C. Jutten, “Neural networks in geophysical applications.” Geophysics, vol. 65, no. 4, pp. 1032-1047, 2000.
  • M.M. Poulton, Computational neural networks for geophysical data processing. 1st ed., vol. 30, USA, Elsevier, 2001.
  • M.M. Poulton, “Neural networks as an intelligence amplification tool: A review of applications.” Geophysics, vol. 67, no. 3, pp. 979-993, 2002.
  • L. Zhang, M.M. Poulton and T. Wang, “Borehole electrical resistivity modeling using neural networks.” Geophysics, vol. 67, no. 6, pp. 1790-1797, 2002.
  • D.J. Bescoby, G.C. Cawley and P.N. Chroston, “Enhanced interpretation of magnetic survey data from archaeological sites using artificial neural networks.” Geophysics, vol. 71, no. 5, pp. 45-53, 2006.
  • M.A. Al-Garni, “Interpretation of some magnetic bodies using neural networks inversion.” Arabian Journal of Geosciences, vol. 2, no. 2, pp. 175-184, 2009.
  • H.M. El-Kaliouby and M.A Al-Garni, “Inversion of self-potential anomalies caused by 2D inclined sheets using neural networks.” Journal of Geophysics and Engineering, vol. 6, no. 1, pp. 29-34, 2009.
  • G. El‐Qady and K. Ushijima, “Inversion of DC resistivity data using neural networks.” Geophysical Prospecting, vol. 49, no. 4, pp. 417-430, 2001.
  • Y. Srinivas, A.S Raj, D.H. Oliver, D. Muthuraj and N. Chandrasekar, “A robust behavior of Feed Forward Back propagation algorithm of Artificial Neural Networks in the application of vertical electrical sounding data inversion.” Geoscience Frontiers, vol. 3, no. 5, pp. 729-736, 2012.
  • S. Maiti, V.C. Erram, G. Gupta and R.K. Tiwari, “ANN based inversion of DC resistivity data for groundwater exploration in hard rock terrain of western Maharashtra (India).” Journal of Hydrology, vol. 464, pp. 294-308, 2012.
  • S. Maiti, G. Gupta, V.C. Erram and R.K. Tiwari, “Delineation of shallow resistivity structure around Malvan, Konkan region, Maharashtra by neural network inversion using vertical electrical sounding measurements.” Environmental Earth Sciences, vol. 68 no. 3, pp. 779-794, 2013.
  • A.S. Raj, Y. Srinivas, D.H. Oliver and D. Muthuraj, “A novel and generalized approach in the inversion of geoelectrical resistivity data using Artificial Neural Networks (ANN).” Journal of Earth System Science, vol. 123, no. 2,pp. 395-411, 2014.
  • D.F. Specht, “Probabilistic neural networks.” Neural networks, vol. 3, no. 1, pp. 109-118 1990.
  • D.F. Specht, “A general regression neural network.” IEEE transactions on neural networks, vol. 2, no. 6, pp. 568-576, 1991.
  • J. Ferahtia, K. Baddari, N. Djarfour and A.K. Kassouri, “Incorporation of a non-linear image filtering technique for noise reduction in seismic data.” Pure and Applied Geophysics, vol. 167, no. 11, pp. 1389-1404, 2010.
  • N. Djarfour, J. Ferahtia, F. Babaia, K. Baddari, E.A. Said and M. Farfour, “Seismic noise filtering based on generalized regression neural networks.” Computers & Geosciences, vol. 69, pp. 1-9, 2014.
  • A.A. Konate, H. Pan, N. Khan and J.H. Yang, “Generalized regression and feed-forward back propagation neural networks in modelling porosity from geophysical well logs.” Journal of Petroleum Exploration and Production Technology, vol. 5, no. 2, pp. 157-166, 2015.
  • J. Wiszniowski, “Applying the general regression neural network to ground motion prediction equations of induced events in the Legnica-Głogów copper district in Poland.” Acta Geophysica, vol. 64, no. 6, pp. 2430-2448, 2016.
  • K. Ji, Y. Ren, R. Wen, C. Zhu, Y. Liu and B. Zhou, “HVSR-based Site Classification Approach Using General Regression Neural Network (GRNN): Case Study for China Strong Motion Stations.” Journal of Earthquake Engineering, pp. 1-23, 2021.
  • A.A. Garrouch, “Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements.” Geophysics, 83(1), MR1-MR14, 2018.
  • J. Wiszniowski, “Application of Focal Plane Directions for Estimating Ground Motion Models with General Regression Neural Networks.” Pure and Applied Geophysics, 1-11, 2022.
  • F. Zhou, Z. Chen, L. Ma, H. Liu, and G. Fang, “Applying machine learning for rapid and automatic characterizations of concrete rebars based on EMI and GPR data.” In Geophysical Research Abstracts, Vol. 21, 2019.
  • S. Haykin, Neural Networks-A Comprehensive Foundation, 3rd ed. New Jersey, USA: Pearson Education, Inc., 2009.
  • M.H. Beale, M.T. Hagan and H.B. Demuth, Neural network toolbox. User’s Guide, MathWorks, 2, 77-81, 2010.
  • P.D. Wasserman, Advanced methods in neural computing. John Wiley & Sons Inc., 1993.
  • A.T. Başokur, Düşey elektrik sondajı verilerinin yorumu. JFMO Eğitim Yayınları., 2010.
  • E. Pekşen, T. Yas and A. Kıyak, “1-D DC resistivity modeling and interpretation in anisotropic media using particle swarm optimization.” Pure and Applied Geophysics, vol. 171, no. 9, pp. 2371-2389, 2014.

Inversion of Vertical Electrical Sounding Data by Using General Regression Neural Network

Yıl 2024, Cilt: 12 Sayı: 1, 121 - 133, 26.01.2024
https://doi.org/10.29130/dubited.1100533

Öz

The inversion of vertical electrical sounding (VES) data is a difficult task, since it is a non-linear problem. In this study, the general regression neural network approach was investigated to solve vertical electrical sounding inverse problems. The general regression neural network (GRNN) was tested to inversion of vertical electrical sounding data. The neural network was trained with synthetic data sets created by forward modeling. The network was tested both with another set of synthetic data and with field data. In addition, the spread parameter which is the GRNN parameter was compared using different values. The spread parameter giving the lowest error rate was used. Synthetic data are 3 layers models. Field data was inverted as 4 layers. The GRNN output is 5 parameters which are 3 resistivity and 2 layer thickness for the 3-layer model in synthetic data. In field data, there are 7 parameters which are 4 resistivity and 3 layer thickness for a 4-layer model. Inversion results of GRNN were successful with very low error rates. The GRNN method was successful with a high performance rate for estimation of the thickness and resistivity of VES data.

Kaynakça

  • O. Koefoed, Geosounding principles, 1. Resistivity sounding measurements, 1st ed., Amsterdam, Netherlands: Elsevier, 1979.
  • W.K. Kosinski and E.K. William, "Geoelectric soundings for predicting aquifer properties." Groundwater, vol. 19, no. 2, pp. 163-171, 1981.
  • A.A. Zohdy, "A new method for the automatic interpretation of Schlumberger and Wenner sounding curves." Geophysics vol. 54, no. 2, pp. 245-253, 1989.
  • S. Maiti, G. Gupta, V.C. Erram and R.K. Tiwari, "Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach." Nonlinear Processes in Geophysics, vol. 18, no. 2, pp. 179-192, 2011.
  • C.L. Pekeris, "Direct method of interpretation in resistivity prospecting." Geophysics, vol. 5, no. 1, pp. 31-42, 1940.
  • S.M. Argilo, "Two computer programs for the calculation of standard graphs for resistivity prospection." Geophysical Prospecting, vol. 15, pp. 71-91, 1967.
  • G. Kunetz and J.P. Rocroi. "Traitement Automatique des Sondages Electriques Automatic Processing of Electrical Soundings." Geophysical Prospecting, vol. 18, no. 2, pp. 157-198, 1970.
  • D.P. Ghosh, "The application of linear filter theory to the direct interpretation of geoelectrical resistivity sounding measurements." Geophysical Prospecting, vol. 19, no. 2, pp. 192-217, 1971.
  • J. R. Inman, “Resistivity inversion with ridge regression.” Geophysics, vol. 40, no. 5, pp. 798-817, 1975.
  • H.K. Johansen, “A man/computer interpretation system for resistivity soundings over a horizontally strafified earth.” Geophysical Prospecting, vol. 25, no.4, pp 667-691, 1977.
  • E. Szaraniec, “Direct resistivity interpretation by accumulation of layers.” Geophysical Prospecting, vol. 28, no. 2, pp. 257-268, 1980.
  • J. Chyba, “On the interpretation of resistivity soundings by the least‐squares method.” Geophysical Prospecting, vol. 31, no. 5, pp. 795-799, 1983.
  • M.A. Meju, “An effective ridge regression procedure for resistivity data inversion.” Computers & Geosciences, vol. 18, no. 2-3, pp. 99-118, 1992.
  • Y. Meheni, R. Guérin, Y. Benderitter and A. Tabbagh, “Subsurface DC resistivity mapping: approximate 1-D interpretation.” Journal of Applied Geophysics, vol. 34, no. 4, pp. 255-269, 1996.
  • B.B. Bhattacharya and M.K. Sen, “Use of VFSA for resolution, sensitivity and uncertainty analysis in 1D DC resistivity and IP inversion.” Geophysical Prospecting, vol. 51, no. 5, pp. 393-408, 2003.
  • M.K. Jha, S. Kumar and A. Chowdhury, “Vertical electrical sounding survey and resistivity inversion using genetic algorithm optimization technique.” Journal of Hydrology, vol. 359, no. 1-2, pp. 71-87, 2008.
  • J.L.F. Martínez, E.G. Gonzalo, J.P.F. Álvarez, H.A. Kuzma and C.O.M. Pérez, “PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case.” Journal of Applied Geophysics, vol. 71, no. 1, pp. 13-25, 2010.
  • W.A. Sandham and D.J. Hamilton, “Inverse theory, artificial neural networks.” in Gupta H.K. (eds) Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. Springer, 2021, pp. 796-807.
  • H.M. El-Kaliouby, M.M. Poulton and E.A. El Diwany, “Inversion of coincident loop TEM data for layered polarizable ground using neural networks.” In SEG Technical Program Expanded Abstracts, Society of Exploration Geophysicists, 1999, pp. 259-262.
  • C. Calderón‐Macías, M.K. Sen and P.L. Stoffa, “Artificial neural networks for parameter estimation in geophysics.” Geophysical Prospecting, vol. 48, no. 1, pp. 21-47, 2000.
  • V. Spichak and I. Popova, “Artificial neural network inversion of magnetotelluric data in terms of three-dimensional earth macroparameters.” Geophysical Journal International, vol. 142, no. 1, pp. 15-26, 2000.
  • M. Van der Baan and C. Jutten, “Neural networks in geophysical applications.” Geophysics, vol. 65, no. 4, pp. 1032-1047, 2000.
  • M.M. Poulton, Computational neural networks for geophysical data processing. 1st ed., vol. 30, USA, Elsevier, 2001.
  • M.M. Poulton, “Neural networks as an intelligence amplification tool: A review of applications.” Geophysics, vol. 67, no. 3, pp. 979-993, 2002.
  • L. Zhang, M.M. Poulton and T. Wang, “Borehole electrical resistivity modeling using neural networks.” Geophysics, vol. 67, no. 6, pp. 1790-1797, 2002.
  • D.J. Bescoby, G.C. Cawley and P.N. Chroston, “Enhanced interpretation of magnetic survey data from archaeological sites using artificial neural networks.” Geophysics, vol. 71, no. 5, pp. 45-53, 2006.
  • M.A. Al-Garni, “Interpretation of some magnetic bodies using neural networks inversion.” Arabian Journal of Geosciences, vol. 2, no. 2, pp. 175-184, 2009.
  • H.M. El-Kaliouby and M.A Al-Garni, “Inversion of self-potential anomalies caused by 2D inclined sheets using neural networks.” Journal of Geophysics and Engineering, vol. 6, no. 1, pp. 29-34, 2009.
  • G. El‐Qady and K. Ushijima, “Inversion of DC resistivity data using neural networks.” Geophysical Prospecting, vol. 49, no. 4, pp. 417-430, 2001.
  • Y. Srinivas, A.S Raj, D.H. Oliver, D. Muthuraj and N. Chandrasekar, “A robust behavior of Feed Forward Back propagation algorithm of Artificial Neural Networks in the application of vertical electrical sounding data inversion.” Geoscience Frontiers, vol. 3, no. 5, pp. 729-736, 2012.
  • S. Maiti, V.C. Erram, G. Gupta and R.K. Tiwari, “ANN based inversion of DC resistivity data for groundwater exploration in hard rock terrain of western Maharashtra (India).” Journal of Hydrology, vol. 464, pp. 294-308, 2012.
  • S. Maiti, G. Gupta, V.C. Erram and R.K. Tiwari, “Delineation of shallow resistivity structure around Malvan, Konkan region, Maharashtra by neural network inversion using vertical electrical sounding measurements.” Environmental Earth Sciences, vol. 68 no. 3, pp. 779-794, 2013.
  • A.S. Raj, Y. Srinivas, D.H. Oliver and D. Muthuraj, “A novel and generalized approach in the inversion of geoelectrical resistivity data using Artificial Neural Networks (ANN).” Journal of Earth System Science, vol. 123, no. 2,pp. 395-411, 2014.
  • D.F. Specht, “Probabilistic neural networks.” Neural networks, vol. 3, no. 1, pp. 109-118 1990.
  • D.F. Specht, “A general regression neural network.” IEEE transactions on neural networks, vol. 2, no. 6, pp. 568-576, 1991.
  • J. Ferahtia, K. Baddari, N. Djarfour and A.K. Kassouri, “Incorporation of a non-linear image filtering technique for noise reduction in seismic data.” Pure and Applied Geophysics, vol. 167, no. 11, pp. 1389-1404, 2010.
  • N. Djarfour, J. Ferahtia, F. Babaia, K. Baddari, E.A. Said and M. Farfour, “Seismic noise filtering based on generalized regression neural networks.” Computers & Geosciences, vol. 69, pp. 1-9, 2014.
  • A.A. Konate, H. Pan, N. Khan and J.H. Yang, “Generalized regression and feed-forward back propagation neural networks in modelling porosity from geophysical well logs.” Journal of Petroleum Exploration and Production Technology, vol. 5, no. 2, pp. 157-166, 2015.
  • J. Wiszniowski, “Applying the general regression neural network to ground motion prediction equations of induced events in the Legnica-Głogów copper district in Poland.” Acta Geophysica, vol. 64, no. 6, pp. 2430-2448, 2016.
  • K. Ji, Y. Ren, R. Wen, C. Zhu, Y. Liu and B. Zhou, “HVSR-based Site Classification Approach Using General Regression Neural Network (GRNN): Case Study for China Strong Motion Stations.” Journal of Earthquake Engineering, pp. 1-23, 2021.
  • A.A. Garrouch, “Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements.” Geophysics, 83(1), MR1-MR14, 2018.
  • J. Wiszniowski, “Application of Focal Plane Directions for Estimating Ground Motion Models with General Regression Neural Networks.” Pure and Applied Geophysics, 1-11, 2022.
  • F. Zhou, Z. Chen, L. Ma, H. Liu, and G. Fang, “Applying machine learning for rapid and automatic characterizations of concrete rebars based on EMI and GPR data.” In Geophysical Research Abstracts, Vol. 21, 2019.
  • S. Haykin, Neural Networks-A Comprehensive Foundation, 3rd ed. New Jersey, USA: Pearson Education, Inc., 2009.
  • M.H. Beale, M.T. Hagan and H.B. Demuth, Neural network toolbox. User’s Guide, MathWorks, 2, 77-81, 2010.
  • P.D. Wasserman, Advanced methods in neural computing. John Wiley & Sons Inc., 1993.
  • A.T. Başokur, Düşey elektrik sondajı verilerinin yorumu. JFMO Eğitim Yayınları., 2010.
  • E. Pekşen, T. Yas and A. Kıyak, “1-D DC resistivity modeling and interpretation in anisotropic media using particle swarm optimization.” Pure and Applied Geophysics, vol. 171, no. 9, pp. 2371-2389, 2014.
Toplam 48 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Doğukan Durdağ 0000-0002-9995-9865

Ertan Pekşen 0000-0002-3515-1509

Yayımlanma Tarihi 26 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Durdağ, D., & Pekşen, E. (2024). Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü. Duzce University Journal of Science and Technology, 12(1), 121-133. https://doi.org/10.29130/dubited.1100533
AMA Durdağ D, Pekşen E. Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü. DÜBİTED. Ocak 2024;12(1):121-133. doi:10.29130/dubited.1100533
Chicago Durdağ, Doğukan, ve Ertan Pekşen. “Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları Ile Ters Çözümü”. Duzce University Journal of Science and Technology 12, sy. 1 (Ocak 2024): 121-33. https://doi.org/10.29130/dubited.1100533.
EndNote Durdağ D, Pekşen E (01 Ocak 2024) Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü. Duzce University Journal of Science and Technology 12 1 121–133.
IEEE D. Durdağ ve E. Pekşen, “Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü”, DÜBİTED, c. 12, sy. 1, ss. 121–133, 2024, doi: 10.29130/dubited.1100533.
ISNAD Durdağ, Doğukan - Pekşen, Ertan. “Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları Ile Ters Çözümü”. Duzce University Journal of Science and Technology 12/1 (Ocak 2024), 121-133. https://doi.org/10.29130/dubited.1100533.
JAMA Durdağ D, Pekşen E. Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü. DÜBİTED. 2024;12:121–133.
MLA Durdağ, Doğukan ve Ertan Pekşen. “Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları Ile Ters Çözümü”. Duzce University Journal of Science and Technology, c. 12, sy. 1, 2024, ss. 121-33, doi:10.29130/dubited.1100533.
Vancouver Durdağ D, Pekşen E. Düşey Elektrik Sondajı Verilerinin Genelleştirilmiş Regresyon Sinir Ağları ile Ters Çözümü. DÜBİTED. 2024;12(1):121-33.