new improvement in interpretation of gravity gradient tensor data using eigenvalues and invariants: an application to blatchford lake, northern canada

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.

New Improvement in Interpretation of Gravity Gradient Tensor Data Using Eigenvalues and Invariants: An Application to Blatchford Lake, Northern Canada

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.