تعیین لبه‌های بی‌هنجاری‌های گرانی با استفاده از فیلتر ریخت‌شناسی ریاضی ارتقا یافته

نوع مقاله: مقاله تحقیقی‌ (پژوهشی‌)

نویسندگان

1 گروه ژئوفیزیک، دانشگاه آزاد اسلامی واحد تویسرکان، تویسرکان، ایران

2 گروه فیزیک زمین، مؤسسه ژئوفیزیک دانشگاه تهران، تهران، ایران

3 گروه ژئوفیزیک، دانشگاه آزاد اسلامی واحد همدان، همدان، ایران

چکیده

تشخیص لبه­های چشمه­های بی­هنجاری، یک ابزار ضروری در تفسیر داده­های میدان پتانسیل است. روش­های زیادی برای تشخیص لبه­ها وجود دارد که بسیاری از آنها شامل فیلترهای بالا گذر بر اساس مشتقات داده­های میدان پتانسیل است. در این مقاله از یک روش تشخیص لبه­ی جدید به نام فیلتر ریخت­شناسی ریاضی پیشرفته (Enhanced Mathematical Morphology) یا EMM استفاده می‌شود. فیلتر EMM به‌صورت نسبت فرسایش مشتق افقی کل به اتساع مشتق افقی کل و یا ترکیبی از این دو عملگر تعریف می­شود. این فیلتر می­تواند لبه­های منابع کم‌عمق و عمیق حتی با چگالی کم ­را به‌طور هم‌زمان نمایش دهد. فیلتر EMM به محاسبه مشتقات عمودی نیازی ندارد که همین امر باعث می‌شود این روش از نظر محاسباتی پایدار باشد. در این مقاله ضمن ارائه رابطه جدیدی برای فیلتر EMM، ابتدا این فیلتر به‌منظور اعتبار سنجی روش، بر روی داده­های مصنوعی با و بدون نوفه اجرا و سپس بر روی داده­های واقعی گنبد نمکی قم آزمایش شد و مرز بی­هنجاری معلوم گردید.

کلیدواژه‌ها


عنوان مقاله [English]

Edge detection of gravity anomalies by enhanced mathematical morphology filter

نویسندگان [English]

  • Mojtaba Babaei 1
  • Vahid Ebrahimzade Ardestani 2
  • Elham Amirian 3
1 Department of Geophysics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran
2 Department of Geophysics, University of Tehran, Tehran, Iran
3 Department of Geophysics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
چکیده [English]

Enhancement on the edges of the causative source is a tool in the interpretation of potential field data. There are many methods for recognizing the edges, most of which involve high pass filters based on derivatives of potential field data. In this paper, a new edge detection method is introduce, called the enhanced mathematical morphology (EMM) filter for interpretation of field data. The EMM filter uses the ratio of the erosion of the total horizontal derivative to the dilation of the total horizontal derivative to recognize the edges of the sources, and can display the edges of the bodies simultaneously. Edge detection of the potential field data has been widely used as a significant tool for geophysical exploration technologies, which can delineate the horizontal locations of causative sources. Normally, various high-pass filters are used to recognize the edges of the potential field data (Evjen 1936; Fedi and Florio 2001; Verduzco et al. 2004; Cooper and Cowan 2006; Cooper and Cowan 2011; Ma and Li 2012; Ma 2013).
The EMM filter uses the ratio of the erosion of THD to the dilation of THD to recognize the edges of the source. Mathematical morphology was developed by Matheron and Serra in 1964 (SERRA, 1983); which is an image analysis and recognition tool. The structuring element (SE) is a basic operator in mathematical morphology, used to interact with an image and to draw conclusions about how a shape fits or misses the shapes in the image. SE consists of a matrix of 0s and 1s that can have any arbitrary shape and size. The basic operations of mathematical morphology are dilation and erosion. Dilation is defined as the maximum value in the window ascertained by the SE. Erosion is defined as the minimum value in the window ascertained by the SE. The EMM filter is expressed as (Lili et al., 2013):
 
where imerode (F,SE) and imdilate (F,SE) represent the erosion and dilation of the THD, respectively.
In this paper, a new relationship is presented for EMM filter that is tested on synthetic data with and without noise as well as the real potential field data in Qom salt dome. The EMM method successfully delineates the edges of the causative sources, which gives better resolution of the deeper source than other filters, and can display the edges of the bodies in a more centralized way. In this article, a new relationship is defined for the EMM filter as:
 
 
The EMM filter was used to recognize the edges of the sources. It can display the edges of the shallow and deep bodies simultaneously. The EMM filter does not require the computation of vertical derivatives, which makes this method computationally stable. The EMM filter is tested on synthetic, and real potential field data in Qom salt dome and the edge detection was done with reasonable results.

کلیدواژه‌ها [English]

  • Edge detection
  • enhanced mathematical morphology
  • Filter
  • Erosion
  • dilation
  • Qom salt dom
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