### Abstract

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimumstructure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

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

Pages (from-to) | 695-705 |

Number of pages | 11 |

Journal | Geophysical Journal International |

Volume | 213 |

Issue number | 1 |

DOIs | |

State | Published - Apr 1 2018 |

### Fingerprint

### Keywords

- Asia
- Gravity anomalies and Earth structure
- Inverse theory
- Numerical approximations and analysis

### ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology

### Cite this

*Geophysical Journal International*,

*213*(1), 695-705. https://doi.org/10.1093/gji/ggy014

**Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition.** / Vatankhah, Saeed; Renaut, Rosemary; Ardestani, Vahid E.

Research output: Contribution to journal › Article

*Geophysical Journal International*, vol. 213, no. 1, pp. 695-705. https://doi.org/10.1093/gji/ggy014

}

TY - JOUR

T1 - Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

AU - Vatankhah, Saeed

AU - Renaut, Rosemary

AU - Ardestani, Vahid E.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimumstructure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

AB - We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimumstructure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

KW - Asia

KW - Gravity anomalies and Earth structure

KW - Inverse theory

KW - Numerical approximations and analysis

UR - http://www.scopus.com/inward/record.url?scp=85052851334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052851334&partnerID=8YFLogxK

U2 - 10.1093/gji/ggy014

DO - 10.1093/gji/ggy014

M3 - Article

VL - 213

SP - 695

EP - 705

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 1

ER -