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

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 horizontalcomponents 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.

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

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 pointdipole), 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 pointdipole, 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.