Systems and processes for building multiple equiprobable coherent geometrical models of the subsurface

A system configured to perturb an initial three-dimensional (3D) geological model including a fault using a 3D vector field, the system comprising:

• a memory to store the initial 3D geological model;
• and
• a processor configured to generate a coherent 3D vector field comprising 3D vectors, wherein each 3D vector of the 3D vector field is associated with a node of the initial 3D geological model and has a magnitude within a range of uncertainty of the node of the initial 3D geological model including the fault and to apply the coherent 3D vector field to the initial 3D geological model associated therewith to generate a perturbed 3D model, wherein the perturbed 3D model differs from the initial 3D geological model by a displacement defined by the 3D vector field associated with nodes having uncertain values, wherein the processor is configured to generate the 3D vector field to be coherent such that the divergence of the 3D vector field is greater than (−1) and less than ( 3/2);and
• a display to display the perturbed 3D model.