ESTIMATION OF LAYER PARAMETERS USING VERY FAST SIMULATED ANNEALING METHOD IN ELECTRICALLY ANISOTROPIC MEDIA

Öz

In this study, electrical anisotropy was investigated in horizontal and vertical directions. Strike and dip angles were examined with theoretical examples regarding of anisotropy in the horizontal direction. A square electrode array was preferred for this purpose. In general; when we plot the apparent resistivity data calculated in an electrically isotropic medium in the polar diagram, the shape of the apparent resistivity curve is circle. However, a flower shape was observed in an electrically anisotropic medium using apparent resistivity values in the polar diagram. In the second part of this work, the electrical anisotropy in the vertical direction was investigated. Schlumberger electrode array was used for examination of the anisotropy in the vertical direction. In the case of electrical anisotropic media, the theoretical data for layered structures were calculated and plotted. Then we explained that how layer parameters estimated from the theoretical curves using very fast simulated annealing method. Estimation of layer parameters were calculated by the method proposed in this study using the vertical electric sounding field data. Finally, these estimated results were compared with the result predicted value using the particle swarm optimization method with the same data set previously.

Anahtar Kelimeler

• Electrical anisotropy,Very fast simulated annealing,Global optimization,Square array,Vertical electrical sounding

ELEKTRİKSEL YÖN BAĞIMLI ORTAMLARDA ÇOK HIZLI TAVLAMA BENZETİMİ YÖNTEMİ İLE TABAKA PARAMETRELERİNİN BELİRLENMESİ

Öz

Bu çalışmada elektriksel anizotropi yatay ve düşey yönde incelenmiştir. Yatay yönde anizotropinin doğrultu ve eğimle değişimi teorik örneklerle araştırılmıştır. Bu amaç için kare elektrot dizilim kullanılmıştır. Genel olarak, elektriksel izotrop ortamlarda hesaplanan görünür özdirenç verilerini kutupsal koordinatlarda çizdiğimizde çember,  anizotrop olan ortamlarda ise çiçek yapısı şekli gözlenmiştir. Bu çalışmanın ikinci kısmında düşey yönde elektriksel anizotropi incelenmiştir. Düşey yönde anizotropi incelenirken Schlumberger elektrot dizilimi kullanılmıştır. Elektriksel olarak anizotrop olan ortamlarda tabakalı yapılar için teorik veriler hesaplanmış ve çizilmiştir. Daha sonra teorik eğrilerden tabaka parametreleri çok hızlı tavlama benzetimi yöntemi ile hesaplanmıştır.  Düşey elektrik sondaj arazi verilerinden önerilen yöntem ile tabaka parametreleri kestirilmiştir. Sonuçlar daha önce aynı veri setini kullanıp parçacık sürü optimizasyonu ile kestirilen tabaka parametreleri ile karşılaştırılmıştır. 

Anahtar Kelimeler

• Elektriksel anizotropi,Çok hızlı tavlama benzetimi,Global en iyileme,Kare dizilim,Düşey elektrik sondajı

Kaynakça

1. Alkan, H., Balkaya, Ç., 2018. Parameter estimation by Differential Search Algorithm from horizontal loop electromagnetic (HLEM) data, Journal of Applied Geophysics. 149(2), 77–94.
2. Balkaya, Ç., 2013. An implementation of differential evolution algorithm for inversion of geoelectrical data, Journal of Applied Geophysics. 98(11), 160-175.
3. Başokur, A.,T., 2015. Türev tabanlı parametre kestirim yöntemleri. TMMOB Jeofizik Mühendisleri Odası yayını, Ankara.
4. Başokur, A.,T., 2010. Düşey elektrik sondajı verilerinin yorumu. TMMOB Jeofizik Mühendisleri Odası yayını, Ankara.
5. Başokur, A.,T., Akca, İ., Siyam, N., 2007. Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method, Geophysical Prospecting. 55 (3), 393-406.
6. Fernandez-Alvarez, J.,P., Fernandez-Martinez, J.,L., Menendez-Perez, C.,O., 2008. Feasibility analysis of the use of binary genetic algorithms as importance samplers application to a 1-D DC resistivity inverse problem. Mathematical Geosciences, 40 (4), 375–408.
7. Fernández Martinez, J.L., Garcia Gonzalo, E., Fernández Álvarez, J.P., Kuzma, H.A., Menéndez Pérez, C.O., 2010. PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case, Journal of Applied Geophysics. 71(1), 13-25.
8. Göktürkler, G., Balkaya, Ç., Ekinci, Y., L., Turan, S., 2016, Uygulamalı jeofizikte metasezgiseller, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 22(6), 563-580.

9. Grant, F.S. West, G.F. , 1965. Interpretation theory in applied geophysics. McGraw-Hill, New York.
10. Greenhalgh, S., A., Marescot, L., Zhou, B., Greenhalgh, M., Wiese, T., 2009. Electric potential and Frechet derivatives for a uniform anisotropic medium with a tilted axis of symmetry. Pure and Applied Geophysics, 166 (4), 673–699.
11. Habberjam, G., M., 1972. The effects of anisotropy on square array resistivity measurements. Geophysical Prospecting, 20 (2), 249–266.
12. Habberjam, G., M., 1975. Apparent resistivity, anisotropy and strike measurements. Geophysical Prospecting, 23 (2), 211–247.
13. Herwanger, J., V., Pain, C., C., Binley, A., De Olivereira, C., R., E., Wortington, M., H., 2004. Anisotropic resistivity tomography. Geophysical Journal International, 158 (2), 409–425.
14. Ingber, L., 1989. Very fast simulated reannealing. Mathematical and Computer Modeling, 12 (8), 967 –993.
15. Kara, K., B., Pekşen, E., 2018. Anizotropik ortamda bir boyutlu DC verilerinin VFSA yöntemi ile ters çözümü. 7.Yerelektrik Çalıştayı Bildiri Özler Kitapçığı, 21-23. http://calistay.sdu.edu.tr/yerelektrik2018/img/YEC7_bildiri_ozleri.pdf , 5 Ağustos 2018.
16. Keller, G., V., Frischknecht, F., C., 1966. Electrical methods in geophysical prospecting. Permagon, New York.
17. Kim, J., Yi, M., Cho, S., Son, J., Song, W., 2006. Anisotropic cross hole resistivity tomography for ground safety analysis of a high-storied building over an abandoned mine. Journal of Environmental Engineering Geophysics, 11 (4), 225–235.
18. Kirkpatrick, S., Gelatt, C., D., Jr., Vecchi, M., P., 1983. Optimization by simulated annealing. Science, 220 (4598), 671–680.
19. Koefoed, O., 1979. Geosounding principles resistivity sounding measurements. Elsevier, Amsterdam.
20. Lane, J., W., Haeni, F., P., Watson, W., M., 1995. Use of a square‐array direct‐current resistivity method to detect fractures in crystalline bedrock in New Hampshire. Groundwater, 33 (3), 476–485.
21. Li, Y., Spitzer, K., 2005. Finite element resistivity modelling for three-dimensional structures with arbitrary anisotropy. Physics of the Earth and Planetary Interiors, 150 (1–3), 15–27.
22. Loke, M.H., 2018. Tutorial : 2-D and 3-D electrical imaging surveys. https://www.geotomosoft.com/downloads.php, 5 August 2018.
23. Maillet, R., 1947. The fundamental equations of electrical prospecting. Geophysics, 12 (4), 529–556.
24. Pain, C., Herwanger, J., Saunders, J., Wortington, M., Oliveira, C., 2003. Anisotropic resistivity inversion. Inverse Problems, 19 (5), 1081–1111.
25. Pekşen, E., Yas, T., Kıyak, A., 2014. 1-D DC Resistivity modeling and interpretation in anisotropic media using particle swarm optimization. Pure and Applied Geophysics, 171 (9), 2371–2389.
26. Pekşen, E.,Yas, T., 2018. Resistivity inversion of transversely isotropic media. Turkish Journal of Earth Sciences, 27 (2) 152–166.
27. Pervago, E., Mousatov, A., Shevnin, V., 2006. Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order. Geophysical Prospecting, 54 (5), 651–661.
28. Sen, M., Stoffa, P., 2013. Global optimization methods in geophysical inversion. Elsevier, Amsterdam.
29. Sharma, S., P., 2011. VFSARES- a very fast simulated annealing Fortran program for interpretation of 1-D DC resistivity sounding data from various electrode arrays. Computer and Geosciences, 42 (C), 177–188.
30. Shaw, R., Srivastava, S., 2007, Particle swarm optimization: a new tool to invert geophysical data, Geophysics. 72 (2), F75–F83.
31. Taylor, R., W., Fleming, A., H., 1988. Characterizing jointed systems by azimuthal resistivity surveys. Ground Water, 26 (4), 464474.
32. Telford, W., M., Geldart, L., P., Sheriff, R.,E., 1990. Applied geophysics. Cambridge University Press, Cambridge.
33. Yang, X., S., 2010. Engineering optimization: An introduction with metaheuristic applications. Wiley, New Jersey.
34. Yeboah-Forson, A., Whitman, D., 2014. Electrical resistivity characterization of anisotropy in the Biscayne Aquifer. Groundwater, 52 (5), 728–736.
35. Yin, C., Wiedelt, P., 1999. Geoelectrical fields in layered earth with arbitrary anisotropy. Geophysics, 64 (2), 426–434.
36. Zhou, B., Greenhalgh, M., Greenhalgh, S., A., 2009. 2.5/3-D resistivity modelling in anisotropic media using Gaussian quadrature grids. Geophysical Journal International, 176 (1), 63–80.