We use a new, mechanically based volumetric structural restoration tool to investigate the mechanics of fault-related folding using natural examples imaged in three-dimensional (3-D) seismic data. The restoration technique is based on a finite element approach that simultaneously restores folding and faulting while allowing rock properties to spatially vary during restoration. We apply these techniques to two types of structures, detachment and shear fault-bend folds, where mechanical layering is a significant factor in their development. Our examples include a detachment anticline from the Caspian Sea and a shear fault-bend fold from the deep-water Niger Delta, both of which contain syntectonic growth horizons that help to constrain the restorations. Restorations of the detachment fold most closely match displacement fields specified in the kinematic forward models when materials are defined as incompressible and rigid, yet the variation of mechanical strength in restorations is perhaps more compatible with the growth of natural structures as recorded by syntectonic growth strata. This analysis shows that the restorations of the detachment fold favor a combination of both kink-band migration and limb rotation folding mechanisms. Numerical simulations of the growth shear fault-bend fold also closely match the displacement field prescribed by the kinematics of shear fault-bend fold models when weak basal units and bedding-plane slip surfaces, enabling flexural slip, are incorporated in the model. The results demonstrate that these techniques can be used to provide full 3-D restorations that closely match established two-dimensional kinematic theories, yet allow constraint of 3-D displacement fields and strain patterns in complex structures.

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