# ادامة فروسوی داده‌های گرانی با استفاده از روش تکرار و تبدیل فوریه

نوع مقاله : مقاله تحقیقی‌ (پژوهشی‌)

نویسندگان

موسسه ژئوفیزیک، دانشگاه تهران، ایران

چکیده

محاسبه ادامۀ فروسوی داده‌های گرانی در صفحۀ افقی زیر زمین از روش تبدیل فوریه یک روش ناپایدار است. در این مقاله یک روش تکرار برای محاسبه ادامۀ فروسوی داده‌های گرانی در صفحۀ افقی که زیر سطح زمین قرار دارد عرضه می‌شود. روش تکرار با استفاده از برنامۀ رایانه‌ای نوشته شده و برای مدل‌های متفاوت بررسی می‏شود. سپس این روش با روش تبدیل فوریه برای محاسبه ادامۀ فروسوی داده‌های گرانی برای مدل مصنوعی مورد مقایسه قرار می‌‌گیرد. پس از آن مقدار کمی نوفه به مدل مصنوعی اضافه و ادامۀ فروسوی داده‌های گرانی از روش تکرار در صفحۀ افقی زیر زمین محاسبه‌  و میزان تغییرات میدان گرانی  بررسی  می‌شود. سپس ادامۀ فروسوی داده‌های گرانی با استفاده از روش تکرار برای مدل واقعی بررسی می‌شود. مشاهده می‌شود که روش تکرار برای محاسبه ادامۀ فروسوی داده‌های گرانی نسبت به روش تبدیل فوریه در فاصلۀ پایین‌تری از سطح زمین میدان گرانی را محاسبه می‌کند و میدان گرانی محاسبه شده به روش تکرار، پایداری خوبی نسبت به میدان گرانی محاسبه شده از روش تبدیل فوریه دارد.

کلیدواژه‌ها

عنوان مقاله [English]

### Calculation of the downward continuation of the gravity data using iterative and Fourier transform methods

نویسندگان [English]

• Maryam Aslanifar
• Vahid Ebrahimzade Ardestani
چکیده [English]

The downward continuation of the gravity data is one of the main issues of a geophysical data interpretation. Considering that the downward continuation of the gravity data is calculated on a plane under the ground and close to an anomaly, this gravity value could show the specifications of the anomaly better than the gravity anomaly on the ground. Factors such as shape, size and depth of the anomaly are determined by calculating the downward continuation of the gravity data.
The upward and downward continuation is usually calculated by the Fourier transform (FT) method. The upward continuation calculated from FT method  is stable. In this method, the upward continuation is calculated in a horizontal plane above the ground level. The higher frequencies (the shorter wavelengths) of the gravity data become damped in the calculation of the upward continuation. The amount of the downward continuation calculated by the FT method is unstable. The downward continuation is estimated in a horizontal plane lower than the ground level. The higher frequencies (the shorter wavelengths) of the gravity data are strengthened in the calculation of the downward continuation to a large extent which is a function of the downward continuation depth and the sampling interval. When the depth is several times bigger than the sampling interval, the downward continuation of the FT  method is divergent, because the exponential function is positive; therefore, the noise will be dominated and the anomaly shape will disappear.  Any existing and perhaps non-obvious errors in the measured data in the calculated field are very big and have unrealistic changes.
The iterative method for calculating the downward continuation is a new one. In this method, using a change of variable, the amount of the gravity on the ground level is attributed to the desired horizontal plane −on which the downward continuation of the gravity data is calculated− as an initial value of the gravity. The upward continuation of the initial value of the gravity data on the ground level is calculated (with a height equal to the depth of the downward continuation). The difference between the initial value of the gravity data on the desired horizontal plane and the amount of the upward continuation is added to the initial value. These calculations are placed in  a loop and the calculations of the loop are stopped when a predetermined accuracy is reached. Usually, the optimum downward continuation is gained after 100 to 200 iterations. The final value is placed as the amount of the downward continuation of the gravity data. This method is implemented in MATLAB and is run for the synthetic, synthetic with noise and real models. Considering that the amounts of the gravity data changes for the synthetic models and synthetic with noise models are low, the amount of the calculated gravity from the iterative method is stable. The limits of anomaly in the downward continuation of the studied models are preserved in all the forms, and the amount of the gravity near the horizontal planes of anomaly is greater than the gravity value at the ground level.

کلیدواژه‌ها [English]

• Downward continuation
• stable
• gravity data
• iterative method
• horizontal plane

#### مراجع

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