Shape simulation and parameterization of model space using Voronoi tessellation: Implications in inversion

Geophysical model building consists of mainly describing geometry of the model and variation of physical properties. In several geophysical methods shape is dictated by the data itself, say for example in seismic, horizons are picked in the seismic data and they define the shape of the model. However, it is not so simple in several other geophysical measurements such as gravity and magnetic. In these cases based on some prior information a model is constructed. Often, in such cases stratified layered model is assumed because of computational simplicity and non-availability of detailed geological information. Inversion algorithms are used to refine the model geometry and the variation of the physical properties. Here, we present a method that describes the geometry of the model and assigns the physical properties to it using Voronoi tessellation. This method helps in generating realistic models and provides an efficient way to search the model space for parameter variation. This method has added advantages over the Cartesian geometry that it can define the geometry with few co-ordinates known as Voronoi centers. An application of the method has been demonstrated in modeling and inversion of gravity data.