Model-Based Probabilistic Inversion Using Magnetic Data

Abstract

Considering the inherent uncertainty of structural geological models, the non-uniqueness of geophysical inverse problems, and the growing availability of data, there is a need for methods that combine different types of data and allow for updating knowledge in a consistent way. By making use of the development of efficient, gradient-based MCMC algorithms, probabilistic inversion provides a tool for this. To test to what extent we can reduce the uncertainty of an initial geological model, we integrate geological modelling into a Bayesian inverse framework. Additional information can then be included in this inverse framework through likelihood functions.
The proposed methodology is tested on a geological model of the structurally complex Kevitsa deposit in Finnish Lapland. By starting with an initial interpretation-based 3D geological model, we define the uncertainties in our geological model by means of probability density functions. Magnetic data and geological interpretations of borehole data are used to define geophysical and geological likelihoods respectively. To use the magnetic data in the inference, the mathematical description of the magnetic forward calculation is implemented for a 3D voxelised space, linking the geophysical data through magnetic rock properties to the uncertain structural parameters. The result of the inverse problem is presented in the form of probability distributions and ensembles of the realised models through visual analysis. The former is a statistical consideration of the results, whereas the latter is a visual representation for direct interpretation in a geological sense. The uncertainties in these visual representations are best presented by means of information entropy, which allows for a quantitative analysis. The results show that well-defined likelihood functions can reduce uncertainties in geological models and build on the complementary strength of different types of data. Where probabilistic inversion inherently provides uncertainty analysis, finding a single representative solution is less trivial. Therefore we conclude that the strength of the used methodology mainly lies in data integration and uncertainty quantification.