Comparison of trimmed mean, Empiric Mode Decomposition and robust regression methods for filtering VLF data with outliers

Öz

Very Low Frequency (VLF) electromagnetic method is widely implemented to determine shallow conductivity distribution of subsurface. Collected VLF data are usually aperiodic and consequently non-linear filtering techniques are often used for eliminating noise in VLF data. In this study, several non-linear filtering methods are implemented on synthetic and field data to determine methods performing better in case of outliers in data. In contrary of synthetic studies, the true subsurface model is unknown for the field data. Hence, VLF-R and Electrical Resistivity Tomography data, which are also collected over the same measuring profile, are also interpreted and their results are assumed as better representations of the subsurface. Applications on noisy synthetic and field datasets showed that the robust regression performs better than the other techniques in case of data with outliers.

Anahtar Kelimeler

• VLF
• Empiric Mode Decomposition
• robust regression
• trimmed mean
• inversion

Aykırı değerler içeren VLF verilerinin süzgeçlenmesinde budanmış ortalama, Empirik Mod Ayrışımı ve dayanıklı regresyon yöntemlerinin karşılaştırılması

Öz

Çok Düşük Frekans (VLF) elektromanyetik yöntem , yeraltının sığ iletkenlik dağılımının belirlenmesi için sıklıkla uygulanır. Toplanan VLF verileri genelde aperiyodiktir ve bu nedenle doğrusal olmayan süzgeçleme yöntemleri VLF verilerinin gürültüden arındırılması için sıklıkla uygulanmaktadır. Bu çalışmada, aykırı değerler içeren verilerin değerlendirilmesinde daha başarılı yöntemlerin belirlenmesi için farklı doğrusal olmayan süzgeçler kuramsal ve gürültülü arazi verilerine uygulanmıştır. Kuramsal verilerin aksine, arazi verilerinde gerçek yeraltı modeli bilinemediği için, aynı ölçüm hattı üzerinde farklı zamanda toplanmış VLF-R ve Elektrik Rezistivie Tomografisi verileri değerlendirilmiştir ve sonuçları yeraltının daha doğru bir temsili olarak kabul edilmiştir. Kuramsal ve arazi verileri üzerinde gerçekleştirilen uygulamalarda, aykırı değerler içeren verilerde dayanıklı regresyonun diğer yöntemlere göre daha başarılı olduğunu göstermiştir.

Anahtar Kelimeler

• VLF
• Empirik Mod Ayrışımı
• dayanıklı regresyon
• budanmış ortalama
• ters çözüm

Kaynakça

1. Bayrak, M., Şenel, L., 2012. Two-dimensional resistivity imaging in the Kestelek boron area by VLF and DC resistivity methods. Journal of applied geophysics, Cilt. 82, 1-10. https://doi.org/10.1016/j.jappgeo.2012.03.010
2. Drahor, M.G., Berge, M.A., 2006. Geophysical investigations of the Seferihisar geothermal area, Western Anatolia, Turkey. Geothermics, Cilt. 35, 302-320.https://doi.org/10.1016/j.geothermics.2006.04.001
3. Olesen, O., Henkel, H., Lile, O.B., Mauring, E., Ronning, J.S., 1992. Geophysical inverstigations of the Stuoragurra postglacial fault, Finnmark, northern Norway. Journal of Applied Geophysics., Cilt. 29, 95-118. https://doi.org/10.1016/0926-9851(92)90001-2
4. Yamaguchi, S., Murakami, S., Inokuchi, H., 2001., Resistivity mapping using the VLF-MT method around surface fault ruptures of the 1995 Hyogo-ken Nanbu earthquake, Japan. The Island Arc, Cilt.. 10, 296–305. https://doi.org/10.1111/j.1440-1738.2001.00328.x
5. Gürer, A., Bayrak, M., Gürer, Ö.F., 2009. A VLF survey using current gathering phenomena for tracing buried faults of Fethiye–Burdur Fault Zone, Turkey. Journal of Applied Geophysics, Cilt. 68, 437-447. https://doi.org/10.1016/j.jappgeo.2009.03.011
6. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., Liu, H. H. , 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: mathematical, physical and engineering sciences, 454(1971), 903-995. https://doi.org/10.1098/rspa.1998.0193
7. Jeng, Y., Lin, M. J., Chen, C. S., & Wang, Y. H., 2007. Noise reduction and data recovery for a VLF-EM survey using a nonlinear decomposition method. Geophysics, Cilt. 72(5), F223-F235. https://doi.org/10.1190/1.2752561
8. Bahri, A. S., Warnana, D. D., Santos, F. A. M., & Santosa, B. J., 2014. Fast, simultaneous and robust VLF-EM data denoising and reconstruction via multivariate empirical mode decomposition. Computers & Geosciences, Cilt. 67, 125-138. https://doi.org/10.1016/j.cageo.2014.03.007

9. Bahri, A. S., & Santosa, B. J., 2015. Application of Multivariate EMD to Improve Quality VLF-EM Data: Synthetic and Fields Data. Applied Mechanics and Materials, Cilt. 771, 170-173, Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/AMM.771.170
10. Verardi, V., & Croux, C., 2009. Robust regression in Stata. The Stata Journal, Cilt. 9(3), 439-453. https://doi.org/10.1177/1536867X0900900306
11. Ebrahimi, A., Sundararajan, N., & Babu, V. R., 2019. A comparative study for the source depth estimation of very low frequency electromagnetic (VLF-EM) signals. Journal of Applied Geophysics, Cilt. 162, 174-183. https://doi.org/10.1016/j.jappgeo.2019.01.007
12. Karcıoğlu, G., 2019. Near-surface resistivity structure near avcilar landslide in Istanbul, Turkey by 2D inversion of VLF data. Journal of Applied Geophysics, Cilt. 163, 73-83. https://doi.org/10.1016/j.jappgeo.2019.02.012
13. Kumar, S., Pal, S. K., & Guha, A., 2020. Very low frequency electromagnetic (VLF-EM) study over Wajrakarur kimberlite Pipe 6 in Eastern Dharwar Craton, India. Journal of Earth System Science, Cilt. 129(1), 1-10. https://doi.org/10.1007/s12040-020-1367-3
14. Sungkono, Santosa, B. J., Bahri, A. S., Santos, F. M., & Iswahyudi, A., 2017. Application of Noise-Assisted Multivariate Empirical Mode Decomposition in VLF-EM Data to Identify Underground River. Advances in Data Science and Adaptive Analysis, Cilt. 9(01), 1650011. https://doi.org/10.1142/S2424922X1650011X
15. Candansayar, M. E., 2008. Two‐dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least‐squares solution with singular value decomposition algorithms. Geophysical Prospecting, Cilt. 56(1), 141-157. https://doi.org/10.1111/j.1365-2478.2007.00668.x
16. Özyıldırım, Ö., Candansayar, M. E., Demirci, İ., & Tezkan, B., 2017. Two-dimensional inversion of magnetotelluric/radiomagnetotelluric data by using unstructured mesh. Geophysics, Cilt. 82(4), E197-E210. https://doi.org/10.1190/geo2016-0378.1
17. Özyıldırım, Ö., Demirci, İ., Gündoğdu, N. Y., & Candansayar, M. E., 2020. Two dimensional joint inversion of direct current resistivity and radiomagnetotelluric data based on unstructured mesh. Journal of Applied Geophysics, Cilt. 172, 103885. https://doi.org/10.1016/j.jappgeo.2019.103885
18. Triggs B., McLauchlan P.F., Hartley R.I., Fitzgibbon A.W., 2000. Bundle Adjustment — A Modern Synthesis. In: Triggs B., Zisserman A., Szeliski R. (eds) Vision Algorithms: Theory and Practice. IWVA 1999. Lecture Notes in Computer Science, vol 1883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44480-7_21
19. Stromberg, A., 2004. Why write statistical software? The case of robust statistical methods. Journal of Statistical Software, Cilt. 10(5), 1-8.
20. Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Jarrod Millman, K., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., ..., van Mulbregt, P., and SciPy 1.0 Contributors, 2020. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nat. Methods, 17, 261–272. https://doi.org/10.1038/s41592-019-0686-2
21. Constable, S. C., Parker, R. L., & Constable, C. G., 1987. Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, Cilt. 52(3), 289-300. doi: 10.1190/1.1442303
22. de Groot-Hedlin, C., & Constable, S., 1990. Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics, Cilt. 55(12), 1613-1624. doi: 10.1190/1.1442813