عنوان مقاله [English]
Recently, interpretation of causative sources using components of the gravity gradient tensor (GGT) has had a rapid progress. Assuming N as the structural index, components of the gravity vector and gravity gradient tensor have a homogeneity degree of -N and - (N+1), respectively. In this paper, it is shown that the eigenvalues, the first and the second rotational invariants of the GGT (I1 and I2) are homogeneous with the homogeneity degree of - (N+1), -2(N+1) and -3(N+1), respectively. Furthermore, the product of M homogeneous functions with a homogeneity degree of - (N+1) itself is homogeneous with the degree of –M(N+1), and their summation do not change the homogeneity degree. Therefore, the Euler deconvolution of these functions can be used to estimate the location and type of the source, simultaneously. The advantage of using Euler deconvolution of invariants compared to other methods that use invariants is that the only parameters involved in location approximation are invariants and their derivatives. Therefore, it is completely independent of the orientation of the coordinate system as well as having little sensitivity to random noise. In this study, the model is tested on synthetic models with and without noise. Finally, application of the method has been demonstrated on measured gravity gradient tensor data set from the Blatchford Lake area, Southeast of Yellowknife, Northern Canada.
Beiki, M., 2010, Analytic signals of gravity gradient tensor and their application to estimate source location: Geophysics, 75(6), I59-I74.
Beiki, M., Clark, D. A., Austin, J. R., and Foss, C. A., 2012, Estimating source location using normalized magnetic source strength calculated from magnetic gradient tensor data: Geophysics, 77(6), J23-J37.
Beiki, M., Keating, P., and Clark, D. A., 2014, Interpretation of magnetic and gravity gradient tensor data using normalized source strength–A case study from McFaulds Lake, Northern Ontario, Canada: Geophysical prospecting, 62(5), 1180-1192.
Beiki, M., and Pedersen, L.B., 2012, Comment on “Depth Estimation of Simple Causative Sources from Gravity Gradient Tensor Invariants and Vertical Component” by B. Oruç in Pure Appl. Geophys, 167 (2010), 1259–1272: Pure and applied geophysics, 169(1-2), 275-277.
Birkett, T. C., Richardson, D. G. and Sinclair, W. D., 1994, Gravity modelling of the Blatchford Lake intrusive suite, Northwest Territories: in, WD Sinclair and DG Richardson, eds, Studies of rare metal deposits in the Northwest Territories: Geological Survey of Canada, Bulletin, 475, 5-16.
Geological Survey of Canada., 2011, Airborne geophysical surveys, gravity gradiometer and magnetic data, Blatchford Lake Area; Geological Survey of Canada, Open File 6955.
Clark, D. A., 2012, New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength: Exploration Geophysics, 43(4), 267-282.
Davidson, A., 1978, The Blachford Lake intrusive suite: an Aphebian plutonic complex in the Slave Province, Northwest territories: Current Research Geological Survey of Canada Paper, 78(1), 119-127.
Davidson, A., 1981, Petrochemistry of the Blatchford Lake complex. District of Mackenzie: Geological Survey of Canada Open File, 764.
Davidson, A., 1982, Petrochemistry of the Blanchford Lake complex near Yellowknife, Northwest Territories.
Hoffman, P., and Kurfurst, D., 1988, Geology and tectonics. East Arm of Great Slave Lake, Northwest Territories: Geological Survey of Canada, Map A, 1628, 2.
Mikhailov, V., Pajot, G., Diament, M., and Price, A., 2007, Tensor deconvolution: A method to locate equivalent sources from full tensor gravity data: Geophysics, 72(5), I61-I69.
Mickus, K. L. and Hinojosa, J. H., 2001, The complete gravity gradient tensor derived from the vertical component of gravity: a Fourier transform technique: Journal of Applied Geophysics, 46(3), 159-174.
Nabighian, M. N., 1984, Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations. Geophysics, 49(6), 780-786.
Oruç, B., 2010, Depth estimation of simple causative sources from gravity gradient tensor invariants and vertical component: Pure and applied geophysics, 167(10), 1259-1272.
Pedersen, L., and Rasmussen, T., 1990, The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps: Geophysics, 55(12), 1558-1566.
Phillips, J. D., Hansen, R. O., and Blakely, R. J., 2007, The use of curvature in potential-field interpretation: Exploration Geophysics, 38, 111–119.
Pilkington, M., and Beiki, M., 2013, Mitigating remanent magnetization effects in magnetic data using the normalized source strength: Geophysics, 78(3), J25-J32.
Pinckston, D. R., 1989, Mineralogy of the Lake Zone Deposit, Thor Lake, Northwest Territories.
Reid, A. B., Allsop, J., Granser, H., Millett, A. T., and Somerton, I., 1990, Magnetic interpretation in three dimensions using Euler deconvolution: Geophysics, 55(1), 80-91.
Reid, A. B., Ebbing, J., and Webb, S. J., 2014, Avoidable Euler Errors–the use and abuse of Euler deconvolution applied to potential fields: Geophysical Prospecting, 62(5), 1162-1168.
Roest, W. R., Verhoef, J., and Pilkington, M., 1992, Magnetic interpretation using the 3-D analytic signal: Geophysics, 57(1), 116-125.
Sanchez, V., Sinex, D., Li, Y., Nabighian, M., Wright, D., and Smith, D. V., 2005, Processing and inversion of magnetic gradient tensor data for UXO applications: Paper presented at the Symposium on the Application of Geophysics to Engineering and Environmental Problems 2005.
Trueman, D., Pedersen, J., and Jorre, L., 1984, Geology of the Thor Lake Beryllium Deposits, An Update: Contribution to the Geology of Northwest Territories, 1, 115-120.
Wilson, H., 1985, Analysis of the magnetic gradient tensor: Defence Research Establishment Pacific: Technical Memorandum, 8, 5-13.
Zhang, C., Mushayandebvu, M. F., Reid, A. B., Fairhead, J. D., and Odegard, M. E., 2000, Euler deconvolution of gravity tensor gradient data: Geophysics, 65(2), 512-520.
Zhou, W., 2016, Depth estimation method based on the ratio of gravity and full tensor gradient invariant: Pure and Applied Geophysics, 173(2), 499-508.