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

آشکارسازی سازه های زیرسطحی همواره یکی از مسائل مورد بحث در تامین امنیت و نگهداری تاسیسات مدفون و برخی اکتشافات ژئوفیزیکی بوده است. بنابراین نیاز ضروری به روش های غیر مخرب برای آشکار سازی این گونه اهداف زیرسطحی کاملاً مشهود می‌باشد. از این رو برای تهیه نقشه این سازه ها می توان از روش های ژئوفیزیکی مناسب، بدون هرگونه تخریبی در سطح زمین بهره گرفت. با وارون سازی داده‌های ژئوفیزیکی می توان پارامترهای هندسی مانند عمق، موقعیت افقی و خواص فیزیکی مانند خودپذیری مغناطیسی بی‌هنجاری‌های زیرسطحی را تعیین کرد. در روش مغناطیس سنجی، مساله 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 شیب دار استفاده شده است. نتایج به‌دست آمده، دلالت بر تفکیک پذیری 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 وارون سازی با استفاده از این الگوریتم، بازیابی قابل‌قبولی از واقعیت زیر سطح را نشان می دهند.

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

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 2D geological structures such as fracture zones, faults, dikes, rift zones and anticlines, 2D inversion of magnetic data is very practical. Magnetic data inversion has two main problems about nonuniqueness and instability of the solution which can be obviated by using constraints and a priori information. Nonuniqueness 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 illposed. 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 2D. 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 2D 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 freenoise 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 freenoise 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 QalehShowkat 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.