Abstract
We develop an inversion procedure using the total variation (TV) regularization method as a stabilizing function to invert surface gravity data to retrieve 3-D density models of geologic structures with sharp boundaries. The developed inversion procedure combines several effective algorithms to solve the TV regularized problem. First, a matrix form of the gradient vector is designed using the Kronecker product to numerically approximate the 3-D TV function. The piecewise polynomial truncated singular value decomposition (PP-TSVD) algorithm is then used to solve the TV regularized inverse problem. To obtain a density model with depth resolution, we use a sensitivity-based depth weighting function. Finally, we apply the Genetic Algorithm (GA) to select the best combination of the PP-TSVD algorithm and the depth weighting function parameters. 3-D simulations conducted with synthetic data show that this approach produces sub-surface images in which the structures are well separated in terms of sharp boundaries, without the need of a priori detailed density model. The method applied to a real dataset from a micro-gravimetry survey of Gotvand Dam, southwestern Iran, clearly delineates subsurface cavities starting from a depth of 40 m within the area of the dam reservoir.
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Sobouti, A., Motagh, M. & Sharifi, M.A. Inversion of surface gravity data for 3-D density modeling of geologic structures using total variation regularization. Stud Geophys Geod 60, 69–90 (2016). https://doi.org/10.1007/s11200-014-0671-2
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DOI: https://doi.org/10.1007/s11200-014-0671-2