Antonio Guillen

3D volumetric modelling of Cadomian terranes (Northern Brittany, France): an automatic method using Voronoı̈ diagrams

Abstract An automatic method based on the use of Voronoi diagrams is proposed for the 3D volumetric reconstruction of geological objects. It enables volumes to be constructed starting from the combined use of geological maps and cross-sections defined in multiple directions, and can also take into account incomplete information on geological interfaces and faults. The method is suitable for global modelling of a set of geological objects; it gives a consistent 3D volumic partition of space according to geological information contained in the maps and the cross-sections. The method is described and applied to modelling the main domains of the Cadomian collisional orogenic belt of Panafrican age in Northern Brittany (France). Thanks to the contrasting densities of the main units involved in the collisional process, the gravimetric effect of the volumic model can be calculated. Its comparison with the observed anomaly allows us to discuss the validity of the geological model. Although some improvements appear to be necessary, it is concluded that the method can make geological modelling more efficient through providing the possibility of rapidly testing many hypotheses.

Lithologic tomography: an application to geophysical data from the Cadomian belt of northern Brittany, France

Abstract A probabilistic description of subsurface lithologic structures can be established by inverting multidisciplinary geophysical data constrained by geological and geostatistical priors. The methodology is based on the joint modelling of several media properties and on a statistical description of the relationships between them. The information provided by the geophysical data and the geological and geostatistical priors is represented by probability density functions ( pdf ) that are combined into a posterior pdf composed by: (1) a prior pdf in the space of the primary (lithologic) model parameters, (2) a pdf of the secondary (physical) model parameters conditional to the primary model parameters and (3) a joint likelihood function that is the product of the independent likelihood functions for each observed geophysical field. Applying a Markov chain sampling method enables a large sample of joint models to be generated from the posterior pdf . The true configuration of the media is then determined from the representation of models pulled from the chain and the elaboration of statistics from the large sample of posterior joint models. The method was used to invert gravity and magnetic data jointly characterising the mass density field, the magnetic susceptibility field and the lithotype field along two 2-D sections of the geological units in the Cadomian belt of northern Brittany. Besides generating 10 6 joint models consistent with the observations and priors, some features of the joint models and the statistical tomographic images provided additional insights to the geologic configuration of the area. For example, the Main Cadomian Thrust shows an irregular geometry that could have resulted from the belt emplacement and/or from Variscan tectonism, and the Hercynian granitic intrusion shows a deep subsurface continuation. The cosimulation of magnetic susceptibility and mass density inside each lithologic region was performed according to a multivariate Gaussian model or a mixed multivariate Gaussian functions model that was developed specially to describe multimodal distributed properties.