Generalized travel-time inversion on unstructured grids

We propose an extension to unstructured grids for the so-called generalized travel-time inversion method for inversion of production data. The framework of the inversion method applies directly to fully unstructured grids, but there are aspects regarding sensitivities and regularization that have to be addressed. First, we propose a generalized smoothing operator for the regularization to impose smooth modification on reservoir parameters. Second, to handle reservoir models with great heterogeneity in cell sizes, we investigate the use of rescaled sensitivities (average cell volume multiplied by local sensitivity density) in the inversion.We demonstrate the utility of our extensions on three synthetic cases in 2-D. First, we validate the inversion method by applying it to a reservoir model represented both on a Cartesian and on a refined triangular grid. Second, we apply the method for a highly unstructured grid with large differences in cell sizes. Third, we consider an example with faults and non-matching connections. All examples show that our method is able to match the data with the same quality as has been obtained earlier on structured grids and without degrading the realism of the reservoir parameters. Finally, we present a simple synthetic 3D case to illustrate that using rescaled sensitivities may be important to avoid unwanted grid-effects in models with strong variations in the thickness of the stratigraphic layers.