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What are the principles behind Area-Depth Strain Analysis?
Early structural geologists (Chamberlin, Bucher, Goguel, Laubscher, Dahlstrom) recognized that measurements of bed length and bed area could be used to provide estimates of detachment depth. However, Epard and Groshong (1993, Excess Area and Depth to Detachment, AAPG Bulletin, V. 77, No. 8.) made a significant advance when they recognized that plotting horizon excess area as a function of depth could be used to estimate both detachment depth and structural displacement parallel to the detachment. In StructureSolver, this is referred to as the Depth to Detachment Method of area-depth analysis.
Groshong and Epard (1994, The role of strain in area-constant detachment folding, Journal of Structural Geology, V. 16, No. 5) further recognized that a combination of displacements from area-depth graphs and from bed length measurements could be used to estimate how bed lengths may have changed during deformation due to layer-parallel strain within each formation. Groshong, Pashin, Chai and Schneeflock (2003, Predicting reservoir-scale faults with area balance: Application to growth stratigraphy: Journal of Structural Geology, v. 25, p1645-1658) demonstrated that displacements and strains could be also be estimated for growth strata.
The next advance in area-depth analysis was the recent work by Eichelberger, Nunns, Groshong and Hughes (2015, Predicting the dip and location of master faults beneath forced folds, Geological Society of America Annual Meeting) which extended area-depth analysis to include structures controlled by dipping faults. Referred to as the Fault Trajectory Method, this approach to area-depth analysis estimates fault dip in addition to fault depth, displacement, and layer parallel strain.
The publications quoted above show comparisons of the theoretical predictions with actual results for both numerical and synthetic structural models. In these examples, the area-depth-strain analysis reproduces the model fault locations and displacements. In those pubilcations, area-depth analyses of seismically imaged natural examples consistently give estimated fault depths and dips that match the imaged fault planes.
Area-depth analysis will yield:
- An estimate of the detachment depth.
- An estimate of the vector displacement along the detachment.
- Estimates of the vector displacements of each layer (growth as well as pre-growth).
- Estimates of the layer-parallel strain in each layer.
Area-Depth analysis can also be useful for identifying Interpretation errors:
- An area-depth point that does not fall on the linear trend shared by other horizons in the interpretation may indicate the the horizon has been mis-interpreted.
- Abnormally high or non-systematic layer-parallel strain values may also indicate line-length errors in the interpretation.
As a tool for structural balancing, area-depth analysis in StructureSolver is more flexible than many other techniques because it can be performed before the interpretation is complete. However, the Area-Depth Strain Analysis feature in StructureSolver does immediately provide full constant-area and constant line-length displacements without performing multiple measurements and calculations.
A strength of area-depth analysis is that the horizon displacements estimated from area-depth graphs only assume that area is maintained during deformation. This is in contrast to other common techniques for estimating displacement, such as balanced cross-sections, which assume constant bed length and thickness. Indeed, it appears from multiple studies that bed-length is rarely conserved in most common styles of deformation.
A fundamental assumption of the area-depth graph method to determine displacement and fault location is that area is conserved within the section plane during deformation. For example, if the cross-section being analyzed is not parallel to the principal displacement direction, then you might get inaccurate or unexpected results because this assumption may not be true.
Another common situation in which area is not conserved involves migration of shale or salt into the core of a detachment fold. In these cases, the flat detachment method may predict detachment depths that are too deep. However, if we know the approximate depth of the detachment, we can estimate the "area" of material that has migrated into the core of the fold. This can be done interactively in StructureSolver using the "Non-Zero Intercept" option.
The fault trajectory method for dipping faults is sensitive to regional dip so it is good practice to remove regional dip (for example, using the Restoration feature) to obtain reliable estimates of fault dip, depth, and displacement..
An additional assumption of the area-depth method is that each pre-growth horizon records constant displacement. If the structure has accommodated significant shear, this may not be the case. It is good practice to limit the regression fit to horizons outside of shear zones to reduce the influence of depth-dependent horizon displacements.