### Abstract

We present an open source MATLAB package, IGUG, for 3D inversion of gravity data. The algorithm implemented in this package is based on methodology that was introduced by Bijani et al. (2015). A homogeneous subsurface body is modeled by an ensemble of simple point masses. The model parameters are the Cartesian coordinates of the point masses and their total mass. The set of point masses, assumed to each have the same mass, is associated to the vertices of a weighted complete graph in which the weights are computed by the Euclidean pairwise distances separating vertices. Kruskal's algorithm is used to solve the minimum spanning tree (MST) problem for the graph, yielding the reconstruction of the skeleton of the body described by the model parameters. The algorithm is stabilized using an equidistance function that restricts the spatial distribution of point masses and favors a homogeneous distribution for the subsurface structure. The non-linear global objective function for the model parameters comprises the data misfit term and the equidistance stabilization function. A regularization parameter λ is introduced to balance the two terms of the objective function, and reasonable physically-relevant bound constraints are imposed on the model parameters. A genetic algorithm is used to minimize the bound constrained objective function for a fixed λ, subject to the bound constraints. A new diagnostic approach is presented for determining a suitable choice for λ, requiring a limited number of solutions for a small set of λ. This contrasts the use of the L-curve which was suggested for estimating a suitable λ in Bijani et al. (2015). Simulations for synthetic examples demonstrate the efficiency and effectiveness of the implementation of the algorithm. It is verified that the constraints on the model parameters are not restrictive, even with less realistic bounds acceptable approximations of the body are still obtained. Included in the package is the script GMD.m which is used for generating synthetic data and for putting measurement data in the format required for the inversion implemented within IGUG.m. The script Diagnostic_Results.m is included within IGUG.m for analyzing and visualizing the results, but can also be used as a standalone script given import of prior results. The software can be used to verify the simulations and the analysis of real data that is presented here. The real data set uses gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada.

Original language | English (US) |
---|---|

Pages (from-to) | 19-29 |

Number of pages | 11 |

Journal | Computers and Geosciences |

Volume | 128 |

DOIs | |

State | Published - Jul 1 2019 |

### Fingerprint

### Keywords

- 3D inversion
- Equidistance function
- Graph theory
- Gravity
- Mobrun

### ASJC Scopus subject areas

- Information Systems
- Computers in Earth Sciences

### Cite this

*Computers and Geosciences*,

*128*, 19-29. https://doi.org/10.1016/j.cageo.2019.03.008

**IGUG : A MATLAB package for 3D inversion of gravity data using graph theory.** / Vatankhah, Saeed; Ardestani, Vahid Ebrahimzadeh; Niri, Susan Soodmand; Renaut, Rosemary; Kabirzadeh, Hojjat.

Research output: Contribution to journal › Article

*Computers and Geosciences*, vol. 128, pp. 19-29. https://doi.org/10.1016/j.cageo.2019.03.008

}

TY - JOUR

T1 - IGUG

T2 - A MATLAB package for 3D inversion of gravity data using graph theory

AU - Vatankhah, Saeed

AU - Ardestani, Vahid Ebrahimzadeh

AU - Niri, Susan Soodmand

AU - Renaut, Rosemary

AU - Kabirzadeh, Hojjat

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We present an open source MATLAB package, IGUG, for 3D inversion of gravity data. The algorithm implemented in this package is based on methodology that was introduced by Bijani et al. (2015). A homogeneous subsurface body is modeled by an ensemble of simple point masses. The model parameters are the Cartesian coordinates of the point masses and their total mass. The set of point masses, assumed to each have the same mass, is associated to the vertices of a weighted complete graph in which the weights are computed by the Euclidean pairwise distances separating vertices. Kruskal's algorithm is used to solve the minimum spanning tree (MST) problem for the graph, yielding the reconstruction of the skeleton of the body described by the model parameters. The algorithm is stabilized using an equidistance function that restricts the spatial distribution of point masses and favors a homogeneous distribution for the subsurface structure. The non-linear global objective function for the model parameters comprises the data misfit term and the equidistance stabilization function. A regularization parameter λ is introduced to balance the two terms of the objective function, and reasonable physically-relevant bound constraints are imposed on the model parameters. A genetic algorithm is used to minimize the bound constrained objective function for a fixed λ, subject to the bound constraints. A new diagnostic approach is presented for determining a suitable choice for λ, requiring a limited number of solutions for a small set of λ. This contrasts the use of the L-curve which was suggested for estimating a suitable λ in Bijani et al. (2015). Simulations for synthetic examples demonstrate the efficiency and effectiveness of the implementation of the algorithm. It is verified that the constraints on the model parameters are not restrictive, even with less realistic bounds acceptable approximations of the body are still obtained. Included in the package is the script GMD.m which is used for generating synthetic data and for putting measurement data in the format required for the inversion implemented within IGUG.m. The script Diagnostic_Results.m is included within IGUG.m for analyzing and visualizing the results, but can also be used as a standalone script given import of prior results. The software can be used to verify the simulations and the analysis of real data that is presented here. The real data set uses gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada.

AB - We present an open source MATLAB package, IGUG, for 3D inversion of gravity data. The algorithm implemented in this package is based on methodology that was introduced by Bijani et al. (2015). A homogeneous subsurface body is modeled by an ensemble of simple point masses. The model parameters are the Cartesian coordinates of the point masses and their total mass. The set of point masses, assumed to each have the same mass, is associated to the vertices of a weighted complete graph in which the weights are computed by the Euclidean pairwise distances separating vertices. Kruskal's algorithm is used to solve the minimum spanning tree (MST) problem for the graph, yielding the reconstruction of the skeleton of the body described by the model parameters. The algorithm is stabilized using an equidistance function that restricts the spatial distribution of point masses and favors a homogeneous distribution for the subsurface structure. The non-linear global objective function for the model parameters comprises the data misfit term and the equidistance stabilization function. A regularization parameter λ is introduced to balance the two terms of the objective function, and reasonable physically-relevant bound constraints are imposed on the model parameters. A genetic algorithm is used to minimize the bound constrained objective function for a fixed λ, subject to the bound constraints. A new diagnostic approach is presented for determining a suitable choice for λ, requiring a limited number of solutions for a small set of λ. This contrasts the use of the L-curve which was suggested for estimating a suitable λ in Bijani et al. (2015). Simulations for synthetic examples demonstrate the efficiency and effectiveness of the implementation of the algorithm. It is verified that the constraints on the model parameters are not restrictive, even with less realistic bounds acceptable approximations of the body are still obtained. Included in the package is the script GMD.m which is used for generating synthetic data and for putting measurement data in the format required for the inversion implemented within IGUG.m. The script Diagnostic_Results.m is included within IGUG.m for analyzing and visualizing the results, but can also be used as a standalone script given import of prior results. The software can be used to verify the simulations and the analysis of real data that is presented here. The real data set uses gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada.

KW - 3D inversion

KW - Equidistance function

KW - Graph theory

KW - Gravity

KW - Mobrun

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U2 - 10.1016/j.cageo.2019.03.008

DO - 10.1016/j.cageo.2019.03.008

M3 - Article

VL - 128

SP - 19

EP - 29

JO - Computers and Geosciences

JF - Computers and Geosciences

SN - 0098-3004

ER -