Pure and Applied Geophysics

, Volume 175, Issue 12, pp 4389–4409 | Cite as

An Improved 3D Joint Inversion Method of Potential Field Data Using Cross-Gradient Constraint and LSQR Method

  • Farshad Joulidehsar
  • Ali MoradzadehEmail author
  • Faramarz Doulati Ardejani


The joint interpretation of two sets of geophysical data related to the same source is an appropriate method for decreasing non-uniqueness of the resulting models during inversion process. Among the available methods, a method based on using cross-gradient constraint combines two datasets is an efficient approach. This method, however, is time-consuming for 3D inversion and cannot provide an exact assessment of situation and extension of anomaly of interest. In this paper, the first attempt is to speed up the required calculation by substituting singular value decomposition by least-squares QR method to solve the large-scale kernel matrix of 3D inversion, more rapidly. Furthermore, to improve the accuracy of resulting models, a combination of depth-weighing matrix and compacted constraint, as automatic selection covariance of initial parameters, is used in the proposed inversion algorithm. This algorithm was developed in Matlab environment and first implemented on synthetic data. The 3D joint inversion of synthetic gravity and magnetic data shows a noticeable improvement in the results and increases the efficiency of algorithm for large-scale problems. Additionally, a real gravity and magnetic dataset of Jalalabad mine, in southeast of Iran was tested. The obtained results by the improved joint 3D inversion of cross-gradient along with compacted constraint showed a mineralised zone in depth interval of about 110–300 m which is in good agreement with the available drilling data. This is also a further confirmation on the accuracy and progress of the improved inversion algorithm.


LSQR method LB algorithm compact constraint JalalAbad mine gravity and magnetic inversion 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Farshad Joulidehsar
    • 1
  • Ali Moradzadeh
    • 1
    Email author
  • Faramarz Doulati Ardejani
    • 1
  1. 1.School of Mining Engineering, College of EngineeringUniversity of TehranTehranIran

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