A compressed sensing based 3D resistivity inversion algorithm for hydrogeological applications

Ranjan, Shashi and K B V N, Phanindra and Peddinti, Srinivasa Rao and J, Adinarayana (2018) A compressed sensing based 3D resistivity inversion algorithm for hydrogeological applications. Journal of Applied Geophysics, 151. pp. 318-327. ISSN 0926-9851

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Image reconstruction from discrete electrical responses pose a number of computational and mathematical challenges. Application of smoothness constrained regularized inversion from limited measurements may fail to detect resistivity anomalies and sharp interfaces separated by hydro stratigraphic units. Under favourable conditions, compressed sensing (CS) can be thought of an alternative to reconstruct the image features by finding sparse solutions to highly underdetermined linear systems. This paper deals with the development of a CS assisted, 3-D resistivity inversion algorithm for use with hydrogeologists and groundwater scientists. CS based l1-regularized least square algorithm was applied to solve the resistivity inversion problem. Sparseness in the model update vector is introduced through block oriented discrete cosine transformation, with recovery of the signal achieved through convex optimization. The equivalent quadratic program was solved using primal-dual interior point method. Applicability of the proposed algorithm was demonstrated using synthetic and field examples drawn from hydrogeology. The proposed algorithm has outperformed the conventional (smoothness constrained) least square method in recovering the model parameters with much fewer data, yet preserving the sharp resistivity fronts separated by geologic layers. Resistivity anomalies represented by discrete homogeneous blocks embedded in contrasting geologic layers were better imaged using the proposed algorithm. In comparison to conventional algorithm, CS has resulted in an efficient (an increase in R2 from 0.62 to 0.78; a decrease in RMSE from 125.14 Ω-m to 72.46 Ω-m), reliable, and fast converging (run time decreased by about 25%) solution.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Article
Uncontrolled Keywords: Compressed sensing, Geophysics, Hydrogeology, Image reconstruction, Resistivity inversion
Subjects: Civil Engineering
Divisions: Department of Civil Engineering
Depositing User: Team Library
Date Deposited: 26 Mar 2018 11:44
Last Modified: 26 Mar 2018 11:44
URI: http://raiith.iith.ac.in/id/eprint/3846
Publisher URL: http://doi.org/10.1016/j.jappgeo.2018.02.008
OA policy: http://www.sherpa.ac.uk/romeo/issn/0926-9851/
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