# کاربرد تحلیل مکان عدد موج در اکتشافات مغناطیس‌سنجی

نویسندگان

دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه شاهرود، شاهرود، ایران

چکیده

روش مغناطیس‌سنجیروشی رایج در اکتشاف ذخایر معدنی و هیدروکربن است. یکی از اهداف اساسی تفسیر داده‌های مغناطیسی،برآورد عمق یا محل منبع بی­هنجاری است که در حوزه مکان یا عدد موج صورت می‌گیرد. روش‌های گوناگونیدر هر دو حوزه معرفی شده‌اند که هرکدام دارای مزایا و معایبی هستند. یکی از روش‌های متداول، استفاده از طیف توان است. محاسبه طیف توان در حالت استاندارد به کمک تبدیل فوریه صورت می‌گیرد. برآورد عمق با استفاده از این روش، دارای دقت مناسب نیست و امکان جداسازی  بی­هنجاری­های مجاور را فراهم نمی‌آورد. در این مقاله از تبدیل موجک پیوسته با استفاده از موجک مادر مورلت برای برآورد طیف توان استفاده شده است. طیف توان حاصل به علت خواص تبدیل موجک پیوسته، هموار است و قابلیت تفکیک بی­هنجاری‌های مجاور را نیز دارد. نتایج برآورد عمق برای داده‌های مغناطیسی مصنوعی و واقعی، توانایی زیاد این روش را در برآورد عمق داده‌های میدان مغناطیسی نشان می‌دهد.

کلیدواژه‌ها

عنوان مقاله [English]

### Application of space-wavenumber analysis in magnetic exploration

نویسندگان [English]

• Amin Roshandel
• Ali Nejati Kalate
• Ali Moradzadeh
• Faramarz Dolati Ardejani
چکیده [English]

The magnetic method is a common tool in mining exploration, engineering geology and oil exploration. Depth estimation of potential field anomalies is an important step in the interpretation of the potential field data. There are various methods for depth estimation, which act in a space or wavenumber domain. Euler deconvolution is an automatic and conventional space-domain based method for depth estimation. The success of this approach depends on the choice of the two parameters, i.e. structural index and window length. Nowadays, wavelet transform is frequently used in geophysical data processing and interpretation. Cooper (2006) used the continuous wavelet transform of the derivative of the potential field data to estimate the depth of the potential source. This method is a qualitative approach and gives an estimate of the source depth by calculation of the similarity between the potential field data and the wavelet at different depths.
The Spector and Grant method is a common approach which acts on the wavenumber domain. Their method is based on the correlation between the wavenumber and anomaly depth. In this method, the depth of the anomaly can be estimated from the slope of the curve fitted to the logarithm of the potential field data power spectrum. In the Spector and Grant method the power spectrum of the potential field data is calculated by a standard Fourier transform. Fourier analysis has provided important visions into the interpretation of both local and regional effect. However, there is an intrinsic disadvantage in Fourier transform method: the kernel of Fourier transform is a sinusoidal function extended on the whole potential filed data interval, so that it uses global oscillations to analyze local ones. Due to its global approach, the Fourier power spectral density is inherently non-localized in space.
In this study, we used the continuous wavelet transform of the potential field data to compute the power spectral density of data. From a mathematical point of view, the continuous wavelet transform analysis does not use a global-space sinusoidal function but a space-wavenumber localized function called space-wavenumber wavelet. Unlike the Fourier analysis, the wavelet transform uses different wavelets and the success of the analysis often depends on the appropriate choice of the analyzing wavelet. We used the Morlet wavelet, due to its similarity with the potential filed data. The Morlet power spectral density is smoother than that of standard Fourier analysis and it can separate the two lateral and vertical anomalies.
The efficiency of this method is evaluated by applying it to both synthetic and real magnetic data. Synthetic models are considered with and without noise. The results of the synthetic example show that the space-wavenumber depth estimation method results in a more desirable estimation than the standard Fourier power spectral density. We use the mentioned methods to estimate the depth of the iron deposit of Ojat Abad located in the south of the Semnan-Damghan road.

کلیدواژه‌ها [English]

• Depth estimation
• continuous wavelet transform
• Morlet wavelet
• power spectrum

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