وارون‌سازی دو بعدی داده‌های مغناطیس‌سنجی با استفاده از قیدهای فشردگی و وزن‌دهی عمقی: دو مطالعه موردی روی داده‌های لوله انتقال گاز و داده‌های آثار باستانی

نوع مقاله : پژوهشی

نویسندگان

1 دانشجوی دکتری، گروه فیزیک زمین، مؤسسه ژئوفیزیک، دانشگاه تهران، تهران، ایران

2 دانشیار، گروه ژئوفیزیک، دانشکدۀ مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

چکیده

آشکارسازی سازه­های زیرسطحی همواره یکی از مسائل مورد بحث در تأمین امنیت و نگهداری تأسیسات مدفون و برخی اکتشافات ژئوفیزیکی بوده است. بنابراین نیاز ضروری به روش­های غیر­مخرب برای آشکار­سازی این گونه اهداف زیرسطحی کاملاً مشهود می‌باشد. از این رو برای تهیه نقشه این سازه­ها می­توان از روش­های ژئوفیزیکی مناسب، بدون هرگونه تخریبی در سطح زمین بهره گرفت. با وارون­سازی داده‌های ژئوفیزیکی می­توان پارامترهای هندسی مانند عمق، موقعیت افقی و خواص فیزیکی مانند خودپذیری مغناطیسی بی‌هنجاری‌های زیرسطحی را تعیین کرد. در روش مغناطیس­سنجی، مسأله وارون‌سازی دارای عدم‌یکتایی جبری و عدم‌یکتایی تئوریکی است. همچنین تغییرات کم در مقدار داده‌ها به‌دلیل وجود نوفه، باعث تغییرات شدیدی در تخمین پارامترهای مدل می‌شود. برای رفع این مشکلات می‌توان از قیدهای مختلف و اطلاعات اولیه بهره گرفت. در این پژوهش، الگوریتم وارون‌سازی کمینه طول وزن‌دار منظم‌سازی‌شده و دو قید فشردگی و وزن‌دهی عمقی استفاده شده است. برای بررسی کارایی الگوریتم، از داده‌های مصنوعی حاصل از مدل دایک قائم و مدل دو دایک شیب­دار استفاده شده است. نتایج به‌دست آمده، دلالت بر تفکیک­پذیری بالای الگوریتم مورد نظر داشته به‌نحوی که شیب و تباین چگالی آن نزدیک به مدل اصلی هستند. برای بررسی کارایی عملی الگوریتم پیشنهادی، این الگوریتم بر روی داده‌های برداشت‌شده لوله انتقال گاز در منطقه قلعه شوکت شهرستان شاهرود و داده‌های آثارباستانی ناحیه‌ای از شهر سوخته پمپئی اعمال شده است. نتایج حاصل از وارون­سازی با استفاده از این الگوریتم، بازیابی قابل‌قبولی از واقعیت زیر سطح را نشان می­دهند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

2-D inversion of magnetic data using compactness and depth weighting constraints: two case studies on gas transmission pipe and archeological data

نویسندگان [English]

  • Ramin Varfinezhad 1
  • Saeed Parnow 1
  • Abolghasem Kamkar Rouhani 2
1 Ph.D. Student, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran
2 Associate Professor, Department of Geophysics, School of Mining, Petroleum & Geophysics Engineering, Shahrood University Technology, Shahrood, Iran
چکیده [English]

Magnetic surveys have been used for a wide range of studies such as oil and gas exploration, mining applications and mapping bedrock topography. Inversion of magnetic data is the most important step in the interpretation of magnetic anomalies. Due to the existence of 2-D geological structures such as fracture zones, faults, dikes, rift zones and anticlines, 2-D inversion of magnetic data is very practical. Magnetic data inversion has two main problems about non-uniqueness and instability of the solution which can be obviated by using constraints and a priori information. Non-uniqueness is the consequence of two ambiguities: I) following Gauss theorem, there are many equivalent sources that can produce the same known field at the surface (theoretical ambiguity), II) since the parameterization of the problem is such that there are more unknowns than observations, the system does not provide enough information in order to uniquely determine model parameters (algebraic ambiguity). Every measurement of data on the earth’s surface contains some noise which imposes a large amount of changes on the inverse solution, therefore the problem is also ill-posed. There are many constraints including compactness, minimization of inertia around an axis or a point, depth weighting etc. Different combinations of these constraints in the objective function lead to different algorithms each of which are appropriate for some cases. In this paper, an inversion algorithm based on inserting a combination of compactness and depth weighting constraints in the regularized weighted minimum length solution is introduced. Compactness constraint, introduced by Last and Kubic, tries to minimize the area of the anomalous body in 2-D. Depth weighting function, introduced by Li and Oldenberg, is utilized to counteract the natural decay of kernel, so all the cells have an equal probability during the inversion. The subsurface is discretized into many horizontal prisms with infinite length in one direction, which is required for 2-D modeling, and the susceptibility of each prism is assumed to be constant. Model parameters, susceptibilities contrast, is also limited between a lower and upper bound. This algorithm was programmed in MATLAB software and its efficiency was investigated by applying it on synthetic models and real data. The first synthetic model is a vertical dyke and inversion process was done for free-noise and noisy data and in both cases recovered models were satisfactory. The second model was composed of two parallel dip dykes in different depths which is a complex synthetic case. Inverting free-noise data leads to the well recovering true model. Reconstructed model obtained from noisy data actually represented an acceptable model. Therefore, results of synthetic cases were promising enough and convince us in order to apply the algorithm on real cases. Finally, the algorithm was applied on two real data sets: i) real data of the buried metallic pipes for gas transmission in Qaleh-Showkat area, Shahrood, ii) an archeological data profile of an area in old Pompeii city near Naples in Italy. This profile intersects three walls. Inversion result of the first data set using this algorithm represents an anomaly at 35 m from the start point of profile with depth to top of about 1 m and its high recovered susceptibility value was suggestive of iron or steel pipe. The derived model from archeological data were suggestive of four anomalies: the first weak anomaly was not related to any of the three walls, the horizontal and vertical extensions of the second and third anomalies were in good agreement with the first two walls and the fourth one at the end of the profile has a great difference range depth with the third wall. One main reason can be related to the imperfect profile at the end where it is not being backed to the background value.

کلیدواژه‌ها [English]

  • magnetometry
  • inversion
  • compactness
  • depth weighting
  • synthetic model
حسینی، م.، 1388، برداشت، پردازش و تفسیر داده های رادار نفوذی به زمین (GPR) در منطقه شاهرود و مقایسه نتایج آن با نتایج ژئومغناطیس در منطقه مزبور، پایان­نامه ارشد، دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود.
Aster, R. C., Borchers, B. and Thurber, C. H, 2005, Parameter estimation and inverse problems, Elsevier Academic Press.
Blakely, R. J., 1996, Potential Theory in Gravity and Magnetic Applications, Cambridge University Press.
Boulanger, O. and Chouteau, M., 2001, Constraints in 3D gravity inversion, Geophys. Prospect., 49, 265-280.
Cella, F. and Fedi, M., 2012, Inversion of potential field data using the structural index as weighting function rate decay, Geophys. Prospect, 60, 313-336.
Fedi, M., 2007, DEXP: A fast method to determine the depth and the structural index of potential fields sources, Geophysics, 72, 1-11.
Fedi, M. and Florio, G., 2009, Quarta T. Multiridge analysis of potential fields: geometrical method and reduced Euler deconvolution, Geophysics, 74, 53-65.
Hsu, S. K., Sibuet, J. C., and Shyu, C. T., 1996, High-resolution detection of geologic boundaries from potential-field anomalies: An enhanced analytic signal technique, Geophysics, 61(2), 373-386.
Keating, P. and Pilkington, M., 2004, Euler deconvolution of the analytic signal and its application to magnetic interpretation, Geophysical prospecting, 52, 165-182.
Last, B. J. and Kubik, K., 1983, Compact gravity inversion, Geophysics, 48, 713-721.
Li, Y. and Oldenburg, D. W, 1996, 3-D inversion of magnetic data, Geophysics, 61, 394-408.
Menke, W., 2012, Geophysical data analysis, discrete inverse theory, Elsevier Academic Press.
Nabighian, M. N., Grauch, V. J. S., Hansen, R. O., LaFehr, T. R., Li, Y., Peirce, J. W. and Ruder, M. E., 2005, The historical development of the magnetic method in exploration, Geophysics, 70(6), 33-61.
Nabighian, M. N., and Hansen, R. O., 2001, Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform, Geophysics, 66(6), 1805-1810.
Paoletti, V., Ialongo, S., Florio, G., Fedi, M. and Cella, F., 2013, Self-constrained inversion of potential fields, Geophysical Journal International, 195(2), 854-869.
Pilkington, M., 2009, 3D magnetic data-space inversion with sparseness constraints, Geophysics, 74, 7-15.
Pilkington, M., 1997, 3-D magnetic imaging using conjugate gradients, Geophysics, 62, 1132–1142.
Phillips, J. D., Hansen, R. O. and Blakely, R., 2007, The use of curvature in potential field interpretation, Explor. Geophys. 38, 111-119.
Salem, A. and Ravat, D., 2003, A combined analytic signal and Euler method (AN-EUL) for automatic interpretation of magnetic data, Geophysics, 68, 1952–1961.
Silva, J. B. C. and Barbosa, V. C. F., 2006, Interactive gravity inversion, Geophysics, 71, 1-9.
Stavrev, P. and Reid, A. B., 2007, Degrees of homogeneity of potential fields and structural indices of Euler deconvolution, Geophysics, 72, 1-12.
Thurston, J. B. and Smith, R. S., 1997, Automatic conversion of magnetic data to depth, dip, susceptibility contrast using the SPI method, Geophysics 62, 807-813.
Vatankhah, S., Renaut, R. A. and Ardestani, E. V., 2014, Regularization parameter estimation for underdetermined problems by the χ2 principle with application to 2D focusing gravity inversion, Inverse Problems, 30, 085001-085009.