Karşılıklı kuyu yer radarı verilerinin modellenmesi

Öz

Uygulamalı jeofiziğin girişimsel olmayan elektromanyetik yöntemlerinden biri olan yer radarı sığ yeraltının oldukça yüksek çözünürlükle görüntülenmesi için yaygın olarak kullanılmaktadır. Bir yer radarı çalışmasında iki önemli unsur olan çözünürlük ve derinlik, zeminlerin su, kil, çözülebilir tuz içeriklerinden ve antenin merkez frekansından etkilenir. Elektriksel iletkenliğin yüksek olduğu alanlarda istenilen çözünürlük ve hedeflenen derinlikte iyi bir yeraltı görüntüsü elde etmek zor olabilir. Bu nedenle, karşılıklı kuyu dizilimine dayanan bir yer radarı çalışması daha detaylı bir yeraltı radar hız dağılımının elde edilmesi için iyi bir alternatif yaklaşım olabilir. Bu çalışmada, karşılıklı kuyu yer radarı veri kümelerinin tomografik ters çözümü için gerekli olan ilk varış seyahat süreleri Maxwell denklemlerinin zaman ortamı sonlu farklar ve gridlenmiş bir hız alanı boyunca Eikonal denkleminin sonlu farklar çözümünden hesaplanmıştır. Modellemede iki kuramsal yeraltı modeli kullanılmıştır. İlk modelde yeraltı iki tabakadan oluşmaktadır. İkinci model tekdüze bir ortam içerisinde gömülü düşük ve yüksek hızlı bloklar içermektedir. Yer-hava arayüzeyinin modellemedeki etkisi ve bir kuyu içi radar çalışmasında kuyuların derinliği ve mesafesi arasındaki oranının önemi test çalışmalarında gösterilmiştir. Tüm alıcı konumlarında zamanda kaydedilmiş elektrik alanın düşey bileşenini (Ez) içeren radargramlar zaman ortamı sonlu farklar modellemesinden elde edilmiştir. Farklı derinlikteki kaynak konumları için seyahat süresi kontur haritaları hızlı bir sonlu farklar Eikonal çözücüsünden elde edilmiştir. Daha sonra, minimum seyahat süresine sahip ışın yolları alıcıdan kaynağa en dik iniş doğrultusunda izlenerek hesaplanmıştır. Sonuç olarak, her iki modelleme yaklaşımından elde edilen seyahat süreleri birbirleriyle oldukça uyumludur. Zaman ortamı sonlu farklar modellemesi ilk varışlarla ilişkili dalga fazlarının belirlenmesi ve değerlendirilmesi için önemli bir araçtır. Diğer taraftan, Eikonal denklemi temelli modelleme ilk varış sürelerinin doğrudan hesaplanması için oldukça etkili bir yaklaşım sunmaktadır.

Anahtar Kelimeler

• Eikonal çözücü,Modelleme,Karşılıklı kuyu,Seyahat zamanı,Sonlu farklar,Yer radarı

Modeling of crosshole ground-penetrating radar data

Abstract

The ground-penetrating radar (GPR) that is one of the non-invasive electromagnetic methods of applied geophysics is widely used to image shallow subsurface with extremely high resolution. The resolution and depth being two important aspects in a GPR survey are affected by the water, clay, soluble salt contents of soils and the center frequency of antenna. It may be difficult to obtain a good subsurface image at desired resolution and targeted depth in the areas characterized by high electrical conductivity. Therefore, a GPR survey based on the crosshole configuration can be a good alternative approach to achieve more detailed subsurface radar velocity distribution. In this study, first-arrival traveltimes being essential for tomographic inversion of crosshole GPR data sets were calculated by a finite-difference time-domain (FDTD) solutions of Maxwell’s equations and finite-difference solution of the Eikonal equation throughout a gridded velocity field. Two theoretical subsurface models were used in modeling. In the first model, the subsurface divided into two layers. The second model includes low- and high-velocity blocks embedded in a homogenous medium. The effect of ground-air interface in modeling and the importance of the ratio between separation and depth of boreholes in a crosshole radar survey were also shown during the test studies. Radargrams consisting of the vertical component of the electric field (Ez) recorded in time at the entire receiver locations were acquired from FDTD modeling. Traveltime contour maps for source locations with different depths were obtained from a fast finite-difference Eikonal solver. Raypaths having the minimum traveltime were then calculated by following the steepest gradient direction from the receiver to the transmitter. As a result, the first-arrival traveltimes obtained from both modeling approaches are quite compatible with each other. FDTD modeling is an important tool to determine and evaluate of the wave phases corresponding to the first arriving wave. On the other hand, Eikonal-equation-based modeling presents an approach being highly effective for directly computing first-arrival traveltimes.

Keywords

• Eikonal solver,Modeling,Crosshole,Traveltime,Finite differences,Ground-penetrating radar

References

1. Murray T, Booth A, Rippin DM. “Water-content of glacier-Ice: Limitations on estimates from velocity analysis of surface ground-penetrating radar surveys”. Journal of Environmental and Engineering Geophysics, 12(1), 87-99, 2007.
2. Singh KK, Kulkarni AV, Mishra VD. “Estimation of glacier depth and moraine cover study using ground penetrating radar (GPR) in the Himalayan region”. Journal of the Indian Society of Remote Sensing, 38(1), 1-9, 2010.
3. Gizzi FT, Loperte A, Satriani A, Lapenna V, Masini N, Proto M. “Georadar investigations to detect cavities in a historical town damaged by an earthquake of the past”. Advances in Geosciences, 24, 15-21, 2010.
4. Şeren A, Babacan AE, Gelişli K, Öğretmen Z, Kandemir R. “An investigation for potential extensions of the karaca cavern using geophysical methods”. Carbonates Evaporites, 27(3), 321-329, 2012.
5. Nouioua I, Boukelloul ML, Fehdi C, Baali F. “Detecting sinkholes using ground penetrating radar in Drâa Douamis, Cherea Algeria: A case study”. Electronic Journal of Geotechnical Engineering, 18, 1337-1349, 2013.
6. Conyers LB. “Innovative ground-penetrating radar methods for archaeological mapping”. Archaeological Prospection, 13(2), 139-141, 2006.
7. Piro S, Campana S. “GPR investigation in different archaeological sites in Tuscany (Italy). Analysis and comparison of the obtained results”. Near surface Geophysics, 10, 47-56, 2012.
8. Neal A. “Ground-penetrating radar and its use in sedimentology: principles, problems and progress”. Earth-Science Reviews, 66(3-4), 261-330, 2004.

9. Huisman JA, Hubbard SS, Redman JD, Annan AP. “Measuring soil water content with ground penetrating radar: A review”. Vadose Zone Journal, 2(4), 476-491, 2003.
10. Turesson A. “Water content and porosity estimated from ground-penetrating radar and resistivity”. Journal of Applied Geophysics, 58(2), 99-111, 2006.
11. Daniels DJ. Ground Penetrating Radar. 2nd ed. London, United Kingdom, The Institute of Electrical Engineers, 2004.
12. Benedetto A, Pajewski L. Civil Engineering Applications of Ground Penetrating Radar. Switzerland, Springer International Publishing, 2015.
13. Knight R. “Ground penetrating radar for environmental applications”. Annual Review of Earth Planetary Sciences, 29, 229-255, 2001.
14. Porsani JL, Filho WM, Elis VR, Shimeles F, Dourado JC, Moura HP. “The use of GPR and VES in delineating a contamination plume in a landfill site: a case study in SE Brazil”. Journal of Applied Geophysics, 55(3-4), 199-209, 2004.
15. Novo A, Lorenzo H, Rial FI, Solla M. “3D GPR in forensics: Finding a clandestine grave in a mountainous environment”. Forensic Science International, 204(1-3), 134-138, 2011.
16. Capizzi P, Martorana R, Messina P, Cosentino PL. “Geophysical and geotechnical investigations to support the restoration project of the roman ‘Villa del Casale’, Piazza Armerina, Sicily, Italy”. Near Surface Geophysics, 10(2), 145-160, 2012.
17. Kadioglu S. Imaging and Radioanalytical Techniques in Interdisciplinary Research - Fundamentals and Cutting Edge Applications. Editor: Kharfi F. Transparent 2d/3d Half Bird’s-Eye View of Ground Penetrating Radar Data Set in Archaeology and Cultural Heritage, 107-138, Rijeka, Croatia, Intech, 2013.
18. Pérez-Gracia V, Caselles JO, Clapés J, Martinez G, Osorio R. “Non-destructive analysis in cultural heritage buildings: Evaluating the Mallorca cathedral supporting structures”. NDT & E International, 59, 40-47, 2013.
19. Butnor JR, Barton C, Day FP, Johnsen KH, Mucciardi AN, Schroeder R, Stover DB. Measuring Roots. Editor: Mancuso S. Using Ground-Penetrating Radar to Detect Tree Roots and Estimate Biomass, 213-245, Berlin, Germany, Springer Berlin Heidelberg.
20. Zhu S, Huang C, Su Y, Sato M. “3D ground penetrating radar to detect tree roots and estimate root biomass in the field”. Remote Sensing, 6(6), 5754-5773, 2014.
21. Nicolotti G, Socco LV, Martinis R, Godio A, Sambuelli L. “Application and comparison of three tomographic techniques for detection of decay in trees”. Journal of Arboriculture, 29(2), 66-78, 2003.
22. Fisher E, McMechan GA, Annan AP. “Acquisiton and processing of wide-aperture ground-penetrating radar data”. Geophysics, 57(3), 495-504, 1992.
23. Topp CG, Davis JL, Annan AP. “Electromagnetic determination of soil water content: Measurements in coaxial transmission lines”. Water Resource Research, 16(3), 574-582, 1980.
24. Göktürkler G, Balkaya Ç. “Traveltime tomography of crosshole radar data without ray tracing”. Journal of Applied Geophysics, 72(4), 213-224, 2010.
25. Sato M, Miwa T. “Polarimetric borehole radar system for fracture measurement”. Subsurface Sensing Technologies and Applications, 1(1), 161-175, 2000.
26. Serzu MH, Kozak ET, Lodha GS, Everitt RA, Woodcock DR. “Use of borehole radar techniques to characterize fractured granitic bedrock at AECL's underground research laboratory”. Journal of Applied Geophysics, 55(1-2), 137-150, 2004.
27. Hubbard SS, Peterson JE, Roberts J, Wobber F. “Estimation of permeable pathways and water content using tomographic radar data”. The Leading Edge, 16(11), 1623-1628, 1997.
28. Peterson JE, Majer E, Knoll MD. “Hydrogeological property estimation using tomographic data at the Boise hydrogeophysical research site”. Proceedings SAGEEP’99, Oakland, CA, USA, 14-18 March 1999.
29. Rucker DF, Ferré TPA. “Correcting water content measurement errors associated with critically refracted first arrivals on zero offset profiling borehole ground penetrating radar profiles”. Vadose Zone Journal, 3(1), 278-287, 2004.
30. Tronicke J, Tweeton DR, Dietrich P, Appel E. “Improved crosshole radar tomography by using direct and reflected arrival times”. Journal of Applied Geophysics, 47(2), 97-105, 2001.
31. Wikipedia. “First Break Picking”. https://en.wikipedia.org/wiki/First_break_picking (27.11.2015).
32. Yee KS. “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media”. IEEE Transactions on Antennas and Propagation, 14(3), 302-307, 1966.
33. Taflove A, Brodwin ME. “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations”. IEEE Transactions on Microwave Theory and Technique, 23(8), 623-630, 1975.
34. Taflove A. “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures”. Wave Motion, 10(6), 547-582, 1988.
35. Taflove A, Hagness SC. Computational Electrodynamics: The Finite-difference Time-domain Method. 3rd ed. London, United Kingdom, Artech House Publishers, 2005.
36. Taflove A, Simpson J. Computational Electrodynamics: The Finite-difference Time-domain Method. Editors: Taflove A, Hagness SC. Introduction to Maxwell’s Equations and the Yee Algorithm, 51-106, London, United Kingdom, Artech House Publishers, 2005.
37. Červený V. Seismic Tomography - With Applications in Global Seismology. Editor: Nolet G. Ray Tracing Algorithms in Three-dimensional Laterally varying Layered Structures, 99-133. Dordrecht, Holland, Springer, 1987.
38. Červený V. Seismic Ray Theory. New York, USA, Cambridge University Press, 2001.
39. Vidale J. “Finite-difference calculation of travel-times”. Bulletin of the Seismological Society of America, 78(6), 2062-2076, 1988.
40. Vidale JE. “Finite-difference calculation of traveltimes in three dimensions”. Geophysics, 55(5), 521-526, 1990.
41. Podvin P, Lecomte I. “Finite-difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools”. Geophysical Journal International, 105(1), 271-284, 1991.
42. Afnimar, Koketsu K. “Finite difference traveltime calculation for head waves travelling along an irregular interface”. Geophysical Journal International, 143(3), 729-734, 2000.
43. Balkaya Ç. Karşılıklı Kuyu Yer Radarı Verisinin İki Boyutlu Seyahat Zamanı Tomografisi. Doktora Tezi, Dokuz Eylül Üniversitesi, İzmir, Türkiye, 2010.
44. Balkaya Ç, Akçığ Z, Göktürkler G. “A comparison of two travel-time tomography schemes for crosshole radar Data: Eikonal-equation-based Inversion versus ray-based inversion”. Journal of Environmental and Engineering Geophysics, 15(4), 203-218, 2010.
45. Wang F, Liu S, Qu X. “Crosshole radar tomographic inversion without ray tracing”. 14th International Conference on Ground Penetrating Radar, Shanghai, China, 4-8 June 2012.
46. Wang F, Liu S, Qu X. “Ray based crosshole radar traveltime tomography using Multistencils Fast Marching Method”. 11th SEGJ International Symposium, Yokohama, Japan, 18-21 November 2013.
47. Wang F, Liu S, Qu X. “Ray-based crosshole radar traveltime tomography using MSFM method”. Proceedings of the 15th International Conference on Ground Penetrating Radar, Brussels, Belgium, 30 June - 4 July 2014.
48. Wang F, Liu S, Qu X. “Crosshole radar traveltime tomographic inversion using the fast marching method and the iteratively linearized scheme”. Journal of Environmental and Engineering Geophysics, 19(4), 229-237, 2014.
49. Blindow N, Eisenburger D, Illich B, Petzold H, Richter T. Environmental Geology. Editors: Knödel K, Lange G, Voight H-J. Ground Penetrating Radar, 283-335, Hannower, Germany, Springer Berlin Heidelberg New York, 2007.
50. Reynolds JM. An Introduction to Applied and Environmental Geophysics. Chichester, United Kingdom, John Wiley & Sons Ltd, 1997.
51. Parkhomenko EI. Electrical Properties of Rocks. New York, USA, Plenum Press, 1967.
52. Clement WP, Barrash W. “Crosshole radar tomography in a fluvial aquifer near Boise, Idaho”. Journal of Environmental and Engineering Geophysics, 11(3), 171-184, 2006.
53. Wang D, McMechan GA. “Finite-difference modeling of borehole ground penetrating radar data”. Journal of Applied Geophysics, 49(3), 111-127, 2002.
54. Annan AP. Hydrogeophysics. Editors: Rubin Y, Hubbard SS. GPR Methods for Hydrogeological Studies, 185-213, Dordrecht, The Netherlands, Springer, 2005.
55. Annan AP. Ground Penetrating Radar Principles, Procedures & Applications. Mississauga, On, Canada, Sensors & Software Inc., 2004.
56. Giannopoulos A. “Modelling ground penetrating radar by GprMax”. Construction and Building Materials, 19(10), 755-762, 2005.
57. Belina FA, Ernst JR, Holliger K. “Inversion of crosshole seismic data in heterogeneous environments: Comparison of waveform and ray-based approaches”. Journal of Applied Geophysics, 68(1), 85-94, 2009.
58. Ernst JR, Green AG, Maurer H, Holliger K. “Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data”. Geophysics, 72(5), J53-J64, 2007.
59. Holliger K, Bergmann T. “Numerical modeling of borehole georadar data”. Geophysics, 67(4), 1249-1257, 2002.
60. Chen HW, Huang TM. “Finite-difference time-domain simulation of GPR data”. Journal of Applied Geophysics, 40(1-3), 139-163, 1998.
61. Irving J, Knight R. “Numerical modeling of ground-penetrating radar in 2-D using MATLAB”. Computers & Geosciences, 32(9), 1247-1258, 2006.
62. Georgakopoulos SV, Birtcher CR, Balanis CA, Renaut RA. “Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration, Part 1: Theory”. IEEE Antennas and Propagation Magazine, 44(1), 134-142, 2002.
63. Harris FJ. “On the use of windows for harmonic analysis with the discrete Fourier transform”. Proceedings of the IEEE, 66(1), 51-83, 1978.
64. Chen YH, Chew WC, Oristaglio ML. “Application of perfectly matched layers to the transient modeling of subsurface EM problems”. Geophysics, 62(6), 1730-1736, 1997.
65. Roden JA, Gedney SD. “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media”. Microwave and Optical Technology Letters, 27(5), 334-339, 2000.
66. Mo LW, Harris JM. “Finite-difference calculation of direct-arrival traveltimes using the eikonal equation”. Geophysics, 67(4), 1270-1274, 2002.
67. Aldridge DF, Oldenburg DW. “Two-dimensional tomographic inversion with finite-difference traveltimes”. Journal of Seismic Exploration, 2, 257-274, 1993.
68. Hole JA, Zelt BC. “3-D finite-difference reflection travel-times”. Geophysical Journal International, 121(2), 427-434, 1995.
69. Lecomte I, Gjoystdal H, Dahle A, Pedersen OC. “Improving modelling and inversion in refraction seismics with a first-order Eikonal solver”. Geophysical Prospecting, 48(3), 437-454, 2000.
70. Qin FH, Luo Y, Olsen KB, Cai WY, Schuster GT. “Finite-difference Solution of the Eikonal equation along expanding wavefronts”. Geophysics, 57(3), 478-487, 1992.
71. Ammon CJ, Vidale JE. “Tomography without rays”. Bulletin of the Seismological Society of America, 83(2), 509-528, 1993.