Sparse norm and Cross-gradient inversions of gravity and magnetic data sets utilizing open-source resources in Python (Case study: Hematite ore body in Jalal Abad area (Iran))

Document Type : Research Article


Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran.


The gravity and the magnetic data sets are utilized to model the Hematite ore body. The cross-gradient joint inversion is used to invert the data sets simultaneously. To discretize the model space, the advanced meshing algorithm (Octree mesh) has been applied. The sparse norm and cross-gradient inversion modules in Python, accessible through Simulation and Parameter Estimation in Geophysics (SimPEG, version 0.17.0) website, have been applied to the inversion process. The sparse norm inversions do not provide reasonable results, particularly for the gravity data set. The estimated density contrasts through the inversion process are very low and unrealistic and on the other hand, the north-south cross sections do not represent a real image from the subsurface sources. The magnetic modeling results obtained through sparse norm inversion also show unrealistic characters, particularly for the 3-dimensional figure of the subsurface anomaly.
The cross-gradient inversion acts quite successfully for both gravity and magnetic models in spite of high noise level in gravity data and the weak signal of magnetic data. The results are in good agreement with geological evidences and also former geophysical survey in the survey area. The priority of cross-gradient inversion of gravity and magnetic data sets to separate inversion is quite clear, despite the weak magnetic signal.


Main Subjects

Ardestani, V.E., Dominique, F., & Oldenburg, D. (2021). Gravity and Magnetic Processing and Inversion Over the Mahallat Geothermal System Using Open Source Resources in Python. Pure and Applied Geophysics, 178. doi:10.1007/s00024-021-02763-6.
Cockett, R., Kang, S., Heagy, L.J., Pidlisecky, A., & Oldenburg, D.W., (2015). SimPEG: an open source framework for simulation and gradient based parameter estimation in geophysical applications. Comput. Geosci. 85, 142–154. 10.1016/j.cageo.2015.09.015. S009830041530056X.
Gallardo, L.A. (2004). Joint two-dimensional inversion of geoelectromagnetic and seismic refraction data with cross-gradients constraint. University of Lancaster.
Gallardo, L.A., & Meju, M.A. (2004). Joint two‐dimensional DC resistivity and seismic travel time inversion with cross‐gradients constraints. Journal of Geophysical Research: Solid Earth, 109 (B3).
Green, P.J. (1984). Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and some Robust and Resistant Alternatives. J. R. Statist. Soc., 46(2), 149-192.
Haber, E., & Heldmann, S. (2007). An octree multi grid method for quast-static Maxvell’s equations with highly discontinuous coefficients. J. Comput. Phy., 65, 324-337.
Jones, E., Oliphant, T., & Peterson, P. (2001). {SciPy}: open-source scientific tools for {Python}. URL ⟨⟩.
Jolidehsar, F., Moradzadeh A., & Dolati ardehjani, F. (2021). 3-D sparse joint inversion of cross-gradient using smoothness constraint for gravity and magnetic data sets of iron deposit of Jalal abad mine. Journal of Mining Engineering (JME), 15(49),  67-88.
Oldenburg, D.W., & Li, Y. (2005). Inversion for Applied Geophysics: A Tutorial, pp. 89–150 (Chapter 5). URL ⟨⟩.
Pluff, D. (1976). Gravity and Magnetic fields of polygonal prisms and application to magnetic terrain corrections. Geophysics, 41, 727-41.
Rao, D.B, & Babu, N.R. (1991). A rapid method for three-dimensional modeling of magnetic anomalies,. Geophysics, 56, 1729-37.
Tikhonov A.V., & Arsenin V.Y. (1977). Solution of ill-posed problems: John Wiley & Sons, Inc.
Zhou, J., Meng, X., Guo, L., & Zhang, S. (2015). Threedimensional cross-gradient joint inversion of gravity and normalized magnetic source strength data in the presence of remanent magnetization. Journal of Applied Geophysics, 119, 51-60.