Center of Mass Estimation of Simple Shaped Magnetic Bodies Using Eigenvectors of Computed Magnetic Gradient Tensor

نویسندگان

1 M.Sc. Graduated, Department of Physics, Faculty of Sciences, Razi University, Kermanshah, Iran

2 Assistant Professor, Department of Physics, Faculty of Sciences, Razi University, Kermanshah, Iran

3 Ph.D. Student, Department of Earth & Planetary Sciences, Macquarie University, Sydney, NSW

چکیده

Computed Magnetic Gradient Tensor (CMGT) includes the first derivatives of three components of magnetic field of a body. At the eigenvector analysis of Gravity Gradient Tensors (GGT) for a line of poles and point pole, the eigenvectors of the largest eigenvalues (first eigenvectors) point precisely toward the Center of Mass (COM) of a body. However, due to the nature of the magnetic field, it is shown that these eigenvectors for the similar shaped magnetic bodies (line of dipoles and point-dipole), in CMGT, are not convergent to COM anymore. Rather, in the best condition, when there is no remanent magnetization and the body is in the magnetic poles, their directions are a function of data point locations. In this study, by reduction to the pole (RTP) transformation and calculation of CMGT, a point is estimated that its horizontal components are exactly the horizontal components of the COM and its vertical component is a fraction of the COM vertical component. These obtained depth values are 0.56 and 0.74 of COM vertical components for a line of dipoles and point-dipole, respectively. To reduce the turbulent effects of noise, “Moving Twenty five Point Averaging” method and upward continuation filter are used. The method is tested on solitary and binary simulated data for bodies with varying physical characteristics, inclinations and declinations. Finally, it is imposed on two real underground examples; an urban gas pipe and a roughly spherical orebody and the results confirm the methodology of this syudy.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Center of Mass Estimation of Simple Shaped Magnetic Bodies Using Eigenvectors of Computed Magnetic Gradient Tensor

نویسندگان [English]

  • kurosh Karimi 1
  • Farzad Shirzaditabar 2
  • Arash Amirian 3
  • Ali Mansoobi 1
1 M.Sc. Graduated, Department of Physics, Faculty of Sciences, Razi University, Kermanshah, Iran
2 Assistant Professor, Department of Physics, Faculty of Sciences, Razi University, Kermanshah, Iran
3 Ph.D. Student, Department of Earth & Planetary Sciences, Macquarie University, Sydney, NSW
چکیده [English]

Computed Magnetic Gradient Tensor (CMGT) includes the first derivatives of three components of magnetic field of a body. At the eigenvector analysis of Gravity Gradient Tensors (GGT) for a line of poles and point pole, the eigenvectors of the largest eigenvalues (first eigenvectors) point precisely toward the Center of Mass (COM) of a body. However, due to the nature of the magnetic field, it is shown that these eigenvectors for the similar shaped magnetic bodies (line of dipoles and point-dipole), in CMGT, are not convergent to COM anymore. Rather, in the best condition, when there is no remanent magnetization and the body is in the magnetic poles, their directions are a function of data point locations. In this study, by reduction to the pole (RTP) transformation and calculation of CMGT, a point is estimated that its horizontal components are exactly the horizontal components of the COM and its vertical component is a fraction of the COM vertical component. These obtained depth values are 0.56 and 0.74 of COM vertical components for a line of dipoles and point-dipole, respectively. To reduce the turbulent effects of noise, “Moving Twenty five Point Averaging” method and upward continuation filter are used. The method is tested on solitary and binary simulated data for bodies with varying physical characteristics, inclinations and declinations. Finally, it is imposed on two real underground examples; an urban gas pipe and a roughly spherical orebody and the results confirm the methodology of this syudy.

کلیدواژه‌ها [English]

  • Computed Magnetic Gradient Tensor
  • Center of Mass
  • First Eigenvectors

Bell, R. E. and Hansen, R. O., 1998, The rise and fall of early oil field technology: The torsion balance gradiometer: The Leading Edge, 17, 81-83.

Beiki, M. and Pedersen, L. B., 2010, Eigenvector analysis of the gravity gradient tensor to locate geologic bodies. Geophysics, 75(6), I37–I49.

Beiki, M., Pedersen, L. B. and Nazi, H., 2011, Interpretation of aeromagnetic data using eigenvector analysis of pseudogravity gradient tensor. Geophysics, 76(3), L1–L10.

Blakely, R. J. and Simpson, R. W., 1986, Approximating edges of source bodies frommagnetic or gravity Anomalies. Geophysics, 51, 1494–1498.

Blakely, R. J., 1996, Potential Theory in Gravity and Magnetic Applications. Cambridge University press.

Blackburn, G., 1980, Gravity and magnetic surveys-Elura Orebody. Bull. Aust. Soc. Explor. Geophys, 11, 59-66

Chianese, D. and Lapenna, V., 2007, Magnetic probability tomography for environmental purposes: test measurements and field applications. J. Geophysics & Engineering, 4, 63-74.

Doll, W. E., Gamey, T. J., Beard, L. P. and Bell, D. T., 2006, Airborne vertical Magnetic gradient for near-surface applications. The Leading Edge, 25, 50–53.

Eppelbaum, L. V., 2015, Quantitative interpretation of magnetic anomalies from bodies approximated by thick bed models in complex environments. Environmental Earth Sciences, 74, 5971-5988.

Frahm, C. P., 1972, Inversion of the magnetic field gradient equation for a magnetic dipole field Naval Coastal Systems. Laboratory Informal Report NCSL, 135–172.

Gamey, T. J., Doll, W. E. and Beard, L. P., 2004, Initial design and testing of a full-tensor airborne SQUID magnetometer for detection of unexploded ordnance. SEG Expanded Abstracts, 23, 798-801.

Karimi Bavandpur, A. and Hajihosseini, A., 1999, 1:100000 geology map of Kermanshah. Geological Survey of Iran publications.

Karimi, K. and Shirzaditabar, F., 2017, Using the ratio of magnetic field to analytic signal of magnetic gradient tensor in determining the position of simple shaped magnetic anomalies. J. Geophysics & Engineering, 14, 769-779.

Mussett, A. E. and Aftab Khan, M., 2009, Looking into the Earth-An introduction to geological geophysics. Cambridge University Press.

Menke, W., 2012, Geophysical Data Analysis Discrete Inverse Theory MATLAB Edition. Academic Press.

Oruc, B., 2010, Location and depth estimation of point-dipole and line of dipoles using analytic signals of the magnetic gradient tensor and magnitude of vector components. J. Appl. Geophys, 70, 27–37.

Pedersen, L. B. and Rasmussen, T. M., 1990, The gradient tensor of potential field anomalies; some implications on data collection and data processing of maps. Geophysics, 55, 1558–1566.

Reford, M. S. and Sumner, J. S., 1964, Aeromagnetics. Geophysics, 29, 482–516.

Reid, A. B., Allsop, J. M., Granser, H., Millet, A. J. and Somerton, I. W., 1990, Interpretation in three dimensions using Euler deconvolution. Geophysics, 55(1), 80–91.

Schmidt, P. W. and Clark, D. A., 2000, Advantages of measuring the magnetic gradient tensor. Preview, 85, 26–30.

Schmidt, D. V. and Bracken, R. E., 2004, Field experiments with the tensor magnetic gradiometer system at Yuma Proving Ground. Arizona Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP), February, 2004.

Shaw, R. K., Agarwal, B. N. P. and Nandi, B. K., 2007, Use of Walsh transforms in estimation of depths of idealized sources from total-field magnetic anomalies. Computers and Geosciences, 33, 966–975.