An efficient algorithm for the Lp -norm joint inversion of gravity and magnetic data using the cross-gradient constraint is presented. The presented framework incorporates stabilizers that use Lp -norms ( 0≤p≤2 ) of the model parameters, and/or the gradient of the model parameters. The formulation is developed from standard approaches for independent inversion of single data sets, and, thus, also facilitates the inclusion of necessary model and data weighting matrices, for example, depth weighting and hard constraint matrices. Using the block Toeplitz Toeplitz block structure of the underlying sensitivity matrices for gravity and magnetic models, when data are obtained on a uniform grid, the blocks for each layer of the depth are embedded in block circulant circulant block matrices. Then, all operations with these matrices are implemented efficiently using 2-D fast Fourier transforms, with a significant reduction in storage requirements. The nonlinear global objective function is minimized iteratively by imposing stationarity on the linear equation that results from applying linearization of the objective function about a starting model. To numerically solve the resulting linear system, at each iteration, the conjugate gradient algorithm is used. This is improved for large scale problems by the introduction of an algorithm in which updatesmore »
This content will become publicly available on May 4, 2023
Large-scale focusing joint inversion of gravity and magnetic data with Gramian constraint
SUMMARY A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. The algorithm uses a non-linear Gramian constraint to impose correlation between the density and susceptibility of the reconstructed models. The global objective function is formulated in the space of the weighted parameters, but the Gramian constraint is implemented in the original space, and the non-linear constraint is imposed using two separate Lagrange parameters, one for each model domain. It is significant that this combined approach, using the two spaces provides more similarity between the reconstructed models. Moreover, it is shown theoretically that the gradient for the use of the unweighted space is not a scalar multiple of that used for the weighted space, and hence cannot be accounted for by adjusting the Lagrange parameters. It is assumed that the measured data are obtained on a uniform grid and that a consistent regular discretization of the volume domain is imposed. Then, the sensitivity matrices exhibit a block-Toeplitz-Toeplitz-block structure for each depth layer of the model domain, and both forward and transpose operations with the matrices can be implemented efficiently using two dimensional fast Fourier transforms. This makes it feasible to solve for large scale problems more »
- Award ID(s):
- 1913136
- Publication Date:
- NSF-PAR ID:
- 10340904
- Journal Name:
- Geophysical Journal International
- Volume:
- 230
- Issue:
- 3
- Page Range or eLocation-ID:
- 1585 to 1611
- ISSN:
- 0956-540X
- Sponsoring Org:
- National Science Foundation
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