Fuzzy c-mean clustering joint inversion of magnetotelluric (MT) and gravity data-sets using unstructured tetrahedral meshes

Minimum-structure, or Occam’s, style of inversion deals with the fundamental non-uniqueness of the inverse problem by finding the simplest Earth model that reproduces the observations. As an additional consequence of this approach, minimum-structure inversion is also reliable and robust. Because of these reasons, it has been extensively utilized in mineral and petroleum exploration problems, and lithospheric studies. The method has been adapted and extended in many ways to obtain more reliable and realistic models of the Earth’s subsurface. Joint inversion of geophysical data-sets is one of the most important extensions of minimum-structure inversion. This method can reduce the non-uniqueness of the inverse problem by combing two, or more, different geophysical data-sets in a single inverse problem. Different geophysical methods have different sensitivity to different physical properties, hence, it is hoped that the null space for one type of data can be spanned by the other.

Joint inversion algorithms can be divided into two main categories, structural-based and petrophysical-based joint inversion methods, depending on the coupling measure used between the physical property models. We have adopted the fuzzy c-mean (FCM) clustering technique which is a petrophysical-based method to jointly invert MT and gravity data-sets. The optimization of this method is not as challenging as for structural-based approaches. We have also performed constrained FCM clustering for independent MT and gravity inversions to compare the constructed models of this method with the joint inversion, and independent MT and gravity inversions. The FCM clustering method makes effective use of statistical petrophysical data which may exist in complex geological structures, or can be anticipated, to encourage the inverted physical property values to move towards the a priori petrophysical data as target clusters.

The capabilities of the joint and constrained FCM clustering inversion are evaluated on synthetic and real examples. The constructed density and conductivity models from the joint inversion have a more plausible representation of the true model’s geometry and have a reasonable range of the recovered physical property values compared to the independent constrained FCM clustering technique and independent unconstrained MT and gravity inversions.

Keywords: Fuzzy c-mean clustering, Gravity, Joint inverse problem, MT, Unstructured tetrahedral mesh