استفاده از عدد موج چند‌‌مدلی به‌‌منظور برآورد عمق توده‌های دایک و پله‌ای شیب‌دار از روی داده‌های مغناطیس‌سنجی

نوع مقاله: مقاله تحقیقی‌ (پژوهشی‌)

نویسندگان

1 دانشگاه صنعتی شاهرود، ایران

2 دانشکده مهندسی معدن و متالورژی دانشگاه یزد، ایران

چکیده

عدد موج محلی و عدد موج چندمدلی نشانگرهای مختلطی هستند که از سیگنال تحلیلی نتیجه می‌شوند. از این دو کمیت برای تفسیر داده‌های مغناطیسی دوبُعدی حاصل از مدل تماسی، صفحه نازک و استوانه افقی استفاده می‌‌شود. در این مقاله عدد موج چند‌‌مدلی بهبودیافته‌ای معرفی شده است که از آن برای برآورد عمق مدل دایک شیب‌دار و همچنین عمق تا وسط مدل پله‌ای شیب‌دار استفاده می‌شود. این روش روی داده‌های مغناطیسی دوبُعدی کاربرد دارد. بررسی رابطه عدد موج چندمدلی مدل‌های گوناگون منجر به توسعه تابع کلی می شود که فقط به عمق مدل وابسته است. در این مقاله با استفاده از روش برازش کمترین مربعات، عمق تا بالای توده‌ها برآورد می‌شود. این روش روی  داده‌های مغناطیس دوبُعدی مدل‌‌های دایک و پله‌ای شیب‌دار به کار برده شده است. همچنین این روش روی داده‌های نیم‌رخ‌‌ مغناطیس‌سنجی به طول 150 کیلومتر در گوشه شمال شرقی چهارگوش انارک به‌‌نحو موفقیت‌آمیز به کار برده شده است. در این بررسی دو توده دایکی‌‌شکل در عمق‌های 2800 و 3000 متری تشخیص داده شده است. این عمق‌ها درحکم نقطه شروع مدل‌سازی پیشرو تکراری مورد استفاده قرار گرفتند که در نتیجه، داده‌های نیم‌رخ‌‌ صحرایی با مدل زمین‌شناسی مناسبی برازش شد. همچنین به‌منظور مقایسه نتایج از روش تحلیل طیف انرژی استفاده شد. این روش نیز وجود دو توده در عمق را نشان می‌دهد که در عمق‌های 3500 و 2480 متری از سطح زمین واقع شده است.
 
 

کلیدواژه‌ها


عنوان مقاله [English]

Depth estimation of the 2-D magnetic subsurface bodies using multimodel wavenumbers

نویسندگان [English]

  • Kamal Alamdar 1
  • Abolghasem Kamkar-Rouhani 1
  • Abdul-hamid Ansar 2
چکیده [English]

An important problem in the interpretation of the magnetic data is the ability to understand the characteristics of the anomalous bodies that are the sources of the measured anomalies. A great deal can be interpreted by looking at the images of the magnetic data and its spatial derivatives. A quantitative interpretation of the magnetic data usually includes estimating dip, susceptibility, and most importantly, the depth to top of the sources of an anomalous magnetic response. Methods that exist for estimating depth work either on data recorded along a profile or data interpolated onto a regular grid. The advantage of the latter approach is that the resulting images are relatively simple and quick to produce, show regional structural patterns at the area under study, and are easily overlain on other geophysical and geological maps. However, many geophysical practitioners prefer to interpret individual profiles because finer sampling intervals generally lead to more accurate results. While this approach is considerably more laborious than using gridded data as its input, a richer understanding of the geology is resulted in this case. A variety of semiautomatic methods, based on using the derivatives of the magnetic anomalies, have been developed for the determination of causative source parameters such as boundary locations and depths. One of these techniques is the analytic signal method for magnetic anomalies initially used in its complex function form. It makes use of the Hilbert transform properties. Other methods for an automatic estimation of the source depth using profile data include the Naudy method, Werner deconvolution, Euler deconvolution, and the Phillips method. For these methods, the depth estimation procedure is applied to each point along the line. At those points where a source is detected, multiple solutions are returned, each based on a different assumed model. The interpreter must choose one of these solutions based on its understanding of geology or other complementary information from other geosciences data.
In recent years, we have shown the invention of some depth-estimation methods using the local wavenumber quantity. This quantity is one of the three attributes derived from the complex analytic signal. The local wavenumber is a spatial quantity (not to be confused with the Fourier wavenumber) and is analogous to the instantaneous frequency used in the analysis of temporal series. Thurston and Smith (1997) have employed the local wavenumber to estimate the depth of 2-D thin sheets and contacts, using a priori information (typically the judgment of the interpreter) to determine which model is more appropriate. This method was subsequently generalized by introducing the concept of a multimodel wavenumber (The term multimodel applies because this quantity gives the same result disregard of the source being a horizontal cylinder, a thin sheet, or a contact). However, in the case of dipping dyke model or slipping step model, the conventional multimodel wavenumber is a combination of a bell-shaped function and terms dependent on the dimensions of the source which complicate a quantitative analysis particularly the depth estimation. To extend the applicability of this method, we must define a quantity that has a bell-shaped functional form, but independent of the source dimensions, when the source of the magnetic response is either a dipping thick dyke or a sloping finite step.
In this paper, we document a further broadening of the applicability scope to include the dipping thick dykes and finite sloping steps by introducing an additional multimodel wavenumber called improved multimodel wavenumber. As in Thurston and Smith (1997) and Smith et al. (1998), we assume that the sources are two dimensional. We also present a new method to estimate the source depth using profile data as input. This method is based on the least-squares fitting of both the conventional and improved multimodel wavenumber from different geometry sources.
We illustrate this technique using synthetic 2-D magnetic data from a dipping dyke model and a slipping step model on a 150-km-long line of aeromagnetic data from the Northwestern part of Anarak quadrangle yielding two thick dykes between the depths of 2800 and 3000m. Using this solution as a starting point in the iterative forward modeling exercise, the measured data were in reasonable agreement with the model.
 
 

کلیدواژه‌ها [English]

  • local wavenumber
  • multimodel wavenumber
  • dipping Dyke
  • slipping step
  • Anarak
Gay, S. P., 1963, Standard curves for the interpretation of magnetic anomalies over long tabular bodies: Geophysics, 28, 161–200.

Grant, F. S., and West, G. F., 1965, Interpretation Theory in Applied Geophysics: 2nd edition, McGraw-Hill Book Co, 458p.

Hartman, R. R., Teskey, D. J., and Friedberg, J. L., 1971, A system for rapid digital aeromagnetic interpretation: Geophysics, 36, 891–918.

Jain, S., 1976, An automatic method of direct interpretation of magnetic profiles: Geophysics, 41, 531–545..

Nabighian, M. N., 1972, The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: Its properties and use for automated interpretation: Geophysics, 37, 507– 517

Naudy, H., 1971, Automatic determination of depth on aeromagnetic profiles: Geophysics, 36, 717–722.

Phillips, J. D., 1979, ADEPT: A program to estimate depth to magnetic basement from sampled magnetic profiles: U.S. Geol. Survey Open- File Report, 79-367.

Smith, R. S., Thurston, J. B., Dai, T., and MacLeod, I. N., 1998, ISPITM—The improved source parameter imaging method: Geophys. Prosp., 46; 141–151.

Taner, M. T., Koehler, F., and Sheriff, R. E., 1979, Complex seismic trace analysis: Geophysics, 44, 1041–1063.

Thompson, D. T., 1982, EULDPH—A new technique for making computer-assisted depth estimates from magnetic data: Geophysics, 47, 31–37.

Thurston, J. B., and Smith, R. S., 1997, Automatic conversion of magnetic data to depth, dip, and susceptibility contrast using the SPI(TM) method: Geophysics, 62, 807–813.