2D and 3D restoration of complexe geological structures and deformation modeling

The following example is taken from a sandbox experiment (McClay, 1990). Fig. 1a shows the result of a listric normal fault model with sedimentation. The model was triangulated (Fig. 1b) and restored by removing the upper sedimentary layers one by one. The top of the next upper sedimentary layer is constrained to be horizontal and the base of the model is constrained to follow the shape of the listric basal fault. The faults are constrained to stay in contact with no friction. The elastic properties are homogeneous in the model. No other constraints are imposed so for each step the faults are free to accommodate any slip until the model equilibrates (ΣF=0) and the elastic deformations are minimized. We have mapped the picture of the sandbox experiment from McClay (1990) onto the model using the texture mapping tool, so we are able to follow the deformation of the layers during each steps of the restoration (see Fig. 2).

Figure 1: Sandbox model of a listric normal fault (from McClay, 1990). (a) Photograph of the final state of the sandbox model. (b) Finite element mesh of the sandbox model.

Figure 2: Cross section restoration of the sandbox model. The picture has been colorized and mapped onto the finite element mesh of the initial state. In the next 6 restoration states (see animation) , the picture was deformed according to the translation, rotation and straining of the finite element mesh. The last image is the restored initial state.

The following example is an illustration of how a complexly deformed (folded and faulted) surface can be restored in one go with no addition of artificial discontinuities. Here, the horizon is constrained to unfold onto a datum horizontal surface while the faults are constrained to close and accommodate shear in order to minimize the elastic deformation during the restoration process. Where fault slip directions are known, they are used as an additional constraint. If there is lateral variation of facies, this could be approximated by varying the mechanical properties of the model. In this example the mechanical properties are homogeneous with a Poisson's ratio of 0.25 and a Young's modulus of 50 GPa.

Figure 1: (a) Initial surface with finite element mesh. Red lines show the constrained slip directions. (b) Restored horizon with unfolding and unfaulting. (c) Initial surface geometry with iso-contours of computed differential strain (e₁-e₃)/2 during restoration. Strain concentration may indicate bad consistency of the geological interpretation.

Here we illustrate how true 3D unfolding can be achieved. The top of the layer is constrained to unfold onto a datum horizontal surface while the rest of the volume is free to move is the x, y and z directions in order to minimize the elastic deformation during the restoration process. If there is lateral and vertical variation of facies, this could be model by varying the mechanical properties of the model. In this example the mechanical properties are homogeneous with a Poisson's ratio of 0.25 and a Young's modulus of 50 GPa. A benefit of restoring true 3D Geological structures using geomecanics, compared to other existing kinematics methods, is that one can compute stresses and strains within the deformed layers and these could be related to smaller scale fractures and faults, which might have a large economic impact.

Figure 2: (a) 3D geometry of the layer to unfold. (b) Discretization of the layer with tetrahedra. (c) Restored layer. (d) Initial surface geometry with computed retro-deformation. Computed stresses and strains could be related to secondary fractures and faults caused by folding.