Hydrocarbon resource and risk assessments rely on subsurface structure maps generated from the interpretation of seismic reflection and well data. Commonly, the uncertainty in these maps is poorly quantified and communicated, primarily because there has not been a holistic workflow that addresses all aspects of structural interpretation uncertainty, including the geological hypotheses underlying a structure map. Unquantified and uncommunicated uncertainty can lead to exploration well failures or poorly designed field development plans. Here, we present three parallel workflows that quantify structural interpretation uncertainty by addressing the following questions. (1) How much does a structure map rely on a conceptual geologic model in its creation? (2) What is the three-dimensional positional uncertainty range of the horizon and faults in a structure map, given a choice in conceptual geological model? (3) What is the uncertainty in the conceptual geologic model itself? The products of these workflows are a series of maps that, in summation, address these aspects of structural interpretation uncertainty and can be used to uncertainty in development scenarios.

To overcome the non-physical limitations to 2D structural restoration tools, efforts are being made toward developing 3D mechanics-based methods, which respect both mass and linear momentum conservations. 3D methods remove many common assumptions in 2D techniques that are often violated in nature, such as line-length and area conservation or constant boundary condition (BC) displacement. However, 3D restorations have challenges of their own that must be overcome to produce accurate, physical representations of rock deformation. One of the greatest challenges is choosing geologically and physically reasonable BCs. These are often based on accepted geometric assumptions, such as flattening and unfolding a datum horizon while simultaneously removing fault offset. However, these BCs, as based on kinematic hypotheses, may lead to unphysical configurations. In addition, non-physical BCs are …

Methods to quantify deformation and reverse the process of strain as a mode to illustrate geologic evolution through time have been previously used for a number of decades. Early efforts on the quantification of bed reconstruction were completed either by manually weighing the sections on delicate

Volumetric restoration can provide crucial insights into the structural evolution of three-dimensional (3-D) petroleum systems. A major limitation to its widespread application is the need to include complex architectures and realistic mechanics such as flexural slip. We apply an implicit approach that allows for, including unconformities, thin and/or pinched-out layers in the models but that cannot explicitly localize slip along horizons. To take advantage of this approach while accounting for flexural slip in 3-D restoration, we investigate new geomechanical properties. We consider flexural slip folding as a result of stacked rigid and thin weak layers, which can be modeled using transversely isotropic properties. We compare restorations of an anticline using transversely isotropic properties, isotropic properties, and a stack of rigid isotropic layers with nonfrictional slip between the layers. Our results show that transversely isotropic properties reasonably approximate flexural slip folding. We use these new tools to model the evolution of a complex system located in the Niger Delta toe. The system includes a detachment fold, a fault-bend fold, and a structural wedge formed in series. Growth stratigraphy and erosional surfaces delimit the kinematics of deformation. Regional erosive surfaces, 3-D gradients of fault slip, and vertical variations in mechanical strength motivated the use of our new restoration techniques. Restoring two growth units results not only in reinforcing the interpretation that the area is behaving as a deforming thrust sheet at critical taper, but also in highlighting coeval activity on both the hinterland structures and the toe of the thrust belt.

Thierry Adate Philip Allen Martin Appold Stefan Back David Barbeau Catherine Baudon Christian Berndt Richard Berry Claudia Bertoni Giovanni Bertotti Roderic Bosboom Dan Bosence Erdin Bozkurt Marita Bradsaw Douglas Burbank Peter Burgess Sebastien Carretier Alan Carroll Andrew Carter Cristian Carvajal Guillaume Caumon William Cavazza Blaine Cecil David Chapman Ole Clausen Sierd Cloetingh Domenico Cosentino Isabelle Coutand Salvatore Critelli Federico Dávila Gregory Davis Bernard Delcaillau Alex Densmore Claudio Di Celma Enrico Dinelli Rebecca Dorsey Francesco Dramis Brandon Dugan Gregor Eberli Eva Enkelmann Paul Fitzgerald Kerry Gallagher Daniel Garcı́a-Castellanos Beatriz Garcia-Fresca Eduardo Garzanti Annette George Christoph Glotzbach Didier Granjeon Carine Grelaud Richard Groshong Chris Guzofski Gary Hampson Mark Harris Adrian Hartley Peter Haughton William Helland-Hansen George Hilley Gregory Hoke Frank Horvath Mads Huuse Pascale Huyghe Raymond Ingersoll Xavier Janson Cari Johnson Teresa Jordan Flemming Jørgensen Ian Kane Paul Kapp Albert Kettner Eric Kirby Peter Koenigshof Barry Kohn Michelle Kominz Wouter Krijgsman Scot Krueger Gary Lash Daniel Le Heron Mike Leeder Andrew Leier Shaofeng Liu Lidia Lonergan Adriano Mazzini Stefano Mazzoli Paul Meijer Qing-Ren Meng Neil Mitchell Julien Moreau Chris Morley Frederic Mouthereau Cornel Olariu Michael Oskin Chris Paola Ivan Petrinovic Mike Pope Daniel Praeg Nereo Preto David Pyles Jeffrey Rahl Victor Ramos Robert Ratliff

Mechanics-based restoration has been seen by some in the structural geology community as a panacea – a new technology that melds the retrodeformational merits of kinematic balancing with principles of continuum mechanics. The method has been touted for its ability to simulate complex 3D systems without assumptions of plane strain, allowing for heterogeneous fault slip distributions and mechanical interaction of fault segments. It has been suggested as a means to predict distributions of geologic strain and associated small-scale structures; however, we demonstrate that the kinematics of restoration models may differ significantly from forward deformation. Restoration models are governed by boundary conditions that are different from the forces driving forward geologic deformation. Models may be improved by supplementing restoration boundary conditions with loads that attempt to reverse tectonic strain, but unphysical artifacts persist. Mechanics-based restoration may be an appropriate tool for traditional applications of kinematic models including validation of structural interpretation and modeling geometric evolution; however, more subtle features, particularly strain distribution, should be treated with skepticism. Restoration models may provide insights to the initial configuration of forward mechanical models with physically appropriate boundary conditions and non-linear material behavior. Forward models provide the best means for simulating deformation and predicting subsidiary structures.

The northward migration of the Mendocino triple junction has resulted in a fundamental modification of the crust of coastal California. As a consequence of viscous coupling between the southern edge of the Gorda slab and the base of the North American crust beneath the Coast Ranges of central and northern California, the crust of coastal California was first thickened and then thinned. This viscous coupling and ephemeral crustal thickening has produced a distinctive pattern Of Uplift that allows us to map the three-dimensional extent of crustal modification. This pattern of crustal deformation has combined with the strain field of the developing Sari Andreas fault system to produce the observed pattern of near-surface deformation. The rapid rise in heat flow south of the triple junction observed in the northern Coast Ranges is a direct consequence of development and removal of the crustal welt that migrated with the triple junction.

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.

We evaluate a new 3D structural restoration method, which employs simple elastic constitutive relations, by applying it to a series of mechanical forward models and natural examples. The restoration method uses standard finite element approaches to minimizing total strain energy imposed on a model by restoration of a geological datum horizon. In the initial restoration step, the internal and external forces of the model generated by the boundary conditions are calculated using the prescribed elastic constitutive laws and a Lagrangian finite element algorithm. When balanced by the inertial and dampening forces, the total force balance provokes movements of the model nodes. This leads to deformations of each element, where the internal and external forces are again updated using the constitutive relationship. The algorithm iterates this process until it achieves steady state (ie a minimum global strain energy), yielding a fully 3D restoration vector field.The elastic constitutive laws employed in the restorations are simple approximations of the naturally complex deformation processes that govern the growth of geological structures. To evaluate the effectiveness of these restorations, we apply the method to restore a series of forward models and natural examples. We restore forward models developed using the discrete element method, which are governed by complex macroscopic deformation styles, and natural examples where 3D deformation paths are constrained by growth strata. We find that by partitioning restoration models into fault-bounded regions, by incorporating flexural slip surfaces, and by summing small increments of deformation that …

We define the subsurface geometry, kinematics, and seismotectonics of the Coalinga anticline in the San Joaquin basin, central California. Using seismic reflection data and quantitative fault‐related folding techniques, we present a model of the Coalinga anticline that demonstrates that the structure is composed of a stack of imbricated structural wedges, related to two major fault ramps at depth, the deepest of which ruptured during the 1983 Coalinga (Mw = 6.5) earthquake. Because of the lack of basinward deformation and the observed fold shapes, these ramps are interpreted to sole to a common upper detachment, which acts as a back thrust, forming a structural wedge. This back‐thrust system generates the surface expression of the Coalinga anticline and extends to the surface as the Waltham Canyon fault and a series of related east dipping thrusts. This structural analysis helps reconcile the longstanding conflict between the southwest dipping preferred nodal plane of the 1983 main shock and the western vergence of the surface anticline. Furthermore, the seismic reflection data and our model suggest that two potentially seismogenic ramps and a major back thrust underlie the fold, rather than the single fault which has been inferred in previous studies. Using a relocated earthquake catalog, we document the three‐dimensional distribution of earthquakes over a 22 year period relative to both the main fault which ruptured in the 1983 event and within the structural wedge. This analysis indicates that the majority of moment release following the 1983 event occurred within the wedge itself, compatible with a model of wedge emplacement.

Sequential, three-dimensional restorations of geologic structures provide important constraints on their kinematic evolution, helping to validate structural interpretations and to define the temporal evolution of prospective hydrocarbon traps. We apply and evaluate two new 3D restoration approaches implemented in Gocad, using a series of contractional detachment and fault-propagation folds in the Caspian Sea, Los Angeles basin, CA, and Niger Delta. The first of these restoration approaches is based on a new parametric method applied to tetrahedral volumes, in which conservation of volume and strain minimization constraints govern the restoration kinematics. The second approach employs variable inclined shear, with restoration kinematics specified by the user, to restore geologic surfaces. Using both methods we demonstrate how sequential restorations can be guided by patterns of syntectonic (growth) strata. These restorations define the relative components of kink-band migration and limb rotation involved in the folding. On the folds that we studied, detachment folding occurred predominantly by limb rotation, whereas fault-propagation folding reflects both kink-band migration and limb rotation. These derived fold kinematics, in turn, distinguish the fault-related folding theories, such as constant-thickness, or trishear fault-propagation folding that are most appropriate for modeling the structures. To summarize, these restoration methods are qualified to guide structural interpretations, and to derive the timing and history of trap formation, for structures in both passive margin and orogenic fold-and-thrust belts.

We present a new implementation of critical taper wedge mechanics to model the three-dimensional geometry of the compressive toe of the deepwater Niger Delta. Contractional deformation in the Niger Delta is driven by gravitational collapse of shelf sediments in the hinterland, creating a 600 km long fold-and-thrust belt that is similar, in many respects, to its counterparts in accretionary margins. In the Niger Delta, contractional deformation is accommodated on folds and thrust faults that sole into a regional detachment in the Akata Formation, an overpressured marine shale sequence. This detachment is imaged in regional seismic reflection profiles to be dipping toward the shelf, while the bathymetric slope is away from the shelf, consistent with a critical taper wedge model. As in the tectonic settings, an influx of sediments into the Delta causes the wedge to internally deform by Coulomb failure in order to maintain a constant taper angle.We use these observations to create a three-dimensional model of the Niger delta fold-and-thrust belt using critical taper wedge mechanics. Regional 2-D seismic reflection profiles, detailed bathymetric data, and maps of the main detachment are used to define the regional geometry of the wedge. We supplement this dataset with deep-water well pressure information and fault maps to investigate spatial variations in the internal and basal strength of the wedge, including the distribution of fluid overpressures. Moreover, we find that topographic variations in the regional detachment directly influence the bathymetric slope of the toe of the Niger delta, in excellent agreement with the theory.

[1] Thermal models have been constructed to demonstrate how regional crustal deformation and subsequent asthenospheric upwelling associated with the migration of the Mendocino triple junction affect the thermal regime of the northern California Coast Ranges. Ephemeral crustal thickening caused by the migration of the triple junction, coupled with the thermal effects of inflow of asthenosphere into the slab window, produces a heat flow signature that is consistent with the observed surface heat flow in the region. In addition the thermal models provide evidence that slab window temperatures are lower than previously assumed following the passage of the triple junction.