Full-waveform inversion of Crosshole GPR data: Implications for porosity estimation in chalk

The Maastrichtian-Danian chalk is a widely distributed hydrocarbon and groundwater reservoir rock in north-western Europe. Knowledge of lateral and vertical heterogeneity and porosity variation in this type of rock is essential, since they critically determine the reservoir properties. We have collected a densely sampled crosshole ground-penetrating radar (GPR) dataset from a highly heterogeneous section of the chalk and inverted it with a full-waveform inversion (FWI) approach. To date, successful crosshole FWI has only been reported for a handful of GPR field data, none of which include strongly heterogeneous environments like the one considered in this study. Testing different starting models shows that all FWI results converge to very similar subsurface structures indicating that the results are robust with regard to local variations in the permittivity starting models and are not very sensitive to the conductivity starting models. Compared to their ray-based counterparts, the obtained FWI models show significantly higher resolution and improved localization of fine-scale heterogeneity. The final FWI permittivity tomogram was converted to a bulk porosity model using the Complex Refractive Index Model (CRIM) and comparisons with plug sample porosities and televiewer image logs verify that variations in the obtained permittivity are related to facies and lithology changes. The inferred porosity varies from 30 to 54%, which is consistent with values in the chalk cores from the investigated boreholes and in agreement with other studies conducted in similar rocks onshore. Moreover, porosities vary significantly over scales of less than a meter both laterally and vertically. The FWI constrains porosity variation with decimeter scale resolution in our 5 m (horizontally) by 10 m (vertically) model section bridging the gap between what is measured on the core sample scale and the scale typical of hydrogeophysical field experiments conducted to characterize fluid flow in the subsurface. The results provide complementary knowledge to traditional chalk reservoir characterization.