Elastic Models of Deformation in Nature: Why Shouldn’t We Use The Present Day Fault Geometry?

Dee, Stephen J.¹, Brett Freeman², Graham Yielding², Peter Bretan² (1) Badley Geoscience Limited, Hundleby, Lincolnshire, United Kingdom (2) Badley Geoscience Ltd, Lincolnshire, United Kingdom

Elastic dislocation (ED) models of deformation associated with faults are used for the prediction of small-scale faults and fractures. Typically, a model will use a definition of fault displacement on the present day fault geometry (i.e. in the geologically deformed state) and forward model the strains on some observation surface. This approximation seems to be valid when the fault displacements are small. In reality, because the material bounding a dislocation deforms, the shape of the dislocation itself is also changed during deformation. Most boundary element and ED methods ignore this effect. As a consequence, during forward deformation, material points apparently move towards and can move through the fault plane which leads to problems in defining the strain field in close proximity to the fault.

Intuitively we argue that the fault geometry should be defined in the undeformed state i.e. the faults should have their geometry restored by applying the reverse of the elastic deformation prior to forward modelling. Unfortunately, this poses a new set of problems since a direct restoration, at the fault plane, is not possible mathematically. Instead, we define a bounding polyhedral surface for each fault which can be collapsed to the fault plane itself. Restoration of the bounding surface and subsequent collapse to a plane effectively yields a set of faults in their undeformed state.

We demonstrate that this is a more robust approach to locate predicted fracture intensities and we illustrate why this is important in determining fracture sweet spots in sub-surface models.