3-D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation

Saeed Vatankhah, Rosemary Renaut, Vahid E. Ardestani

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Sparse inversion of gravity data based on L1-norm regularization is discussed. An iteratively reweighted least squares algorithm is used to solve the problem. At each iteration the solution of a linear system of equations and the determination of a suitable regularization parameter are considered. The LSQR iteration is used to project the system of equations onto a smaller subspace that inherits the ill-conditioning of the full space problem. We show that the gravity kernel is only mildly to moderately ill-conditioned. Thus, while the dominant spectrum of the projected problem accurately approximates the dominant spectrum of the full space problem, the entire spectrum of the projected problem inherits the ill-conditioning of the full problem. Consequently, determining the regularization parameter based on the entire spectrum of the projected problem necessarily over compensates for the non-dominant portion of the spectrum and leads to inaccurate approximations for the full-space solution. In contrast, finding the regularization parameter using a truncated singular space of the projected operator is efficient and effective. Simulations for synthetic examples with noise demonstrate the approach using the method of unbiased predictive risk estimation for the truncated projected spectrum. The method is used on gravity data from the Mobrun ore body, northeast of Noranda, Quebec, Canada. The 3-D reconstructed model is in agreement with known drill-hole information.

Original languageEnglish (US)
Pages (from-to)1872-1887
Number of pages16
JournalGeophysical Journal International
Volume210
Issue number3
DOIs
StatePublished - Sep 1 2017

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estimators
Parameter estimation
Gravitation
inversions
gravity
gravitation
conditioning
Ores
iteration
Linear systems
Quebec
ore body
linear systems
Canada
norms
parameter estimation
inversion
minerals
operators
approximation

Keywords

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

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology

Cite this

3-D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation. / Vatankhah, Saeed; Renaut, Rosemary; Ardestani, Vahid E.

In: Geophysical Journal International, Vol. 210, No. 3, 01.09.2017, p. 1872-1887.

Research output: Contribution to journalArticle

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