Multiscale spatial analysis of fracture arrangement and pattern reconstruction using Ripley's K-function

This work presents novel multiscale spatial data analytics using Ripley's K-function, as a measure of spatial interaction, to study one-dimensional arrangement of fractures. Fracture spatial arrangements are classified into clustered, anticlustered, or indistinguishable from random by testing statistical significance of the calculated Ripley's K-function. Characterizations of fracture arrangements are performed as a function of length scale and position. Analysis of the K-function along the study interval identifies where fracture clustering and anticlustering occur. A simulation technique is also introduced here to statistically reconstruct spatial arrangements and to generate fracture realizations that are spatially similar to the fractures observed in the field. With this simulation technique, one can also fill spatial gaps in fracture measurements where data are absent, unreliable, or unused. Synthetic as well as field-measured 1D fracture datasets are used for testing and demonstration. Methods introduced in this work can be readily applied to fracture datasets observed in outcrops, borehole image logs, and cores.

Automated summary

This work presents novel multiscale spatial data analytics using Ripley's K-function to study the arrangement of one-dimensional fractures. The statistical significance of the calculated Ripley's K-function is used to classify fracture spatial arrangements. Characterizations of fracture arrangements as a function of length scale and position are performed. A simulation technique is introduced to reconstruct spatial arrangements and generate fracture realizations similar to the observed fractures. Synthetic and field-measured fracture datasets are used for testing and demonstration. These methods can be applied to fracture datasets observed in various geological settings.