Studia Geophysica et Geodaetica

, Volume 60, Issue 1, pp 69–90 | Cite as

Inversion of surface gravity data for 3-D density modeling of geologic structures using total variation regularization

  • Alireza Sobouti
  • Mahdi Motagh
  • Mohammad Ali Sharifi


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.


inverse gravimetric problem total variation regularization PP-TSVD algorithm genetic algorithm geologic structures 


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Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2015

Authors and Affiliations

  • Alireza Sobouti
    • 1
  • Mahdi Motagh
    • 1
    • 2
  • Mohammad Ali Sharifi
    • 1
    • 3
  1. 1.School of Surveying and Geospatial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.GFZ German Research Centre for GeosciencesPotsdamGermany
  3. 3.Research Institute of Geo-information Technology (RIGT), College of EngineeringUniversity of TehranTehranIran

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