The geometric relationship between faults in folds have been extensively documented and modeled (e.g., Suppe, 1985). The question of when do these folds grow has recieved a bit less attention (e.g., Souter and Hager, 1997; Dolan et al., 2003). Essentially the question is whether hanging wall folds grow during earthquakes (coseismically) or in between earthquakes (interseismically). Essentially when does deformation occur along the fold (red dashed line) in the figure below?
Geodetic evidence for either case appears limited but serveral models co- and inter-seismic surface deformation near thrust faults been proposed 
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So if data are lacking it's the perfect time to understand the behavior of idealized fault and fold models and make predictions for the spatial patterns of surface deformation consisent with both co- and inter-seismic fold growth. The simple models here do this for single dipping thrust fault that ramps down to a flat detachment. A single fold bisects these two structures. Following Souter and Hager (1997) we approximate the fold as a dislocation plane exploiting the focal mechanism ambiguity Figure 5. This means that deformation associated with material passing through the kink axis is treated elastically.
The individual constributions to a surface deformation are shown in 
with blue lines representing horizontal motion and green lines representing vertical motion. The upper right panel shows the long term motions over many earthquake cycles with steps at the surface trace of both the fault and fold. The region between the fault and fold in uniformly uplifted. The upper right panel shows surface motions in response to unit slip on the fault ramp. The lower left panel shows the surface motions in response to unit slip on a small portion of the horizontal detachment. The lower right panel shows the surface motions in response to unit slip across the fold axis. Over geologic time the last three panels must sum to match the first.
The predicted surface displacements from the different classes of models are shown in: 
The 6 panels show: a) interseimsic horizontal deformation (note that the label is incorrect in this panel!), b) interseismic vertical deformation, c) coseismic horizontal deformation, d) coseismic vertical deformation, e) cumulative horizontal deformation, f) cumulative vertical deformation. Predictions from the four different kinematic models (definined in figure 3) colored as 1-green, 2-blue, 3-cyan, 4-red.
The central results may be summarized as:
1 - Multiple earthquake cycle deformation (bottom panels: e, f). The kinematically consistent fault and fold model (red line) produces distinct displacement jumps at both the locations where both the fault and fold intersect the surface rather than just at the fault trace (other 3 models). In particular for the flat detachment case considered here long-term vertical uplift is localized entirely between the surface intersection between the fault and fold and is consistent with long-term antiformal growth.
2 - Coseismic deformation (middle panels: c, d). Large and distinct differences in coseismic displacements between models 12, 3 (identical) and 4 are expressed in the hanging wall. Specifically the kinematically consistent model includes coseismic fold growth which gives rise to a displacment discontinuity (both vertical and horizontal) where the fold intersects the surface. This is a clear prediction from model 4 for which I know of no supporting geodetic observations. The Chi-Chi earthquake would be have been a good candidate earthquake to test this on but the InSAR data appear incoherent in the hanging wall :(
3 - Interseismic deformation (top panels: a, b). Horizontal interseismic deformation for all models is qualitatively similar (by geodetic standards) and differs essentially in the width of the region over which the velocity transition occurs. Absent prior data on fault geometry and "locking depths" it would be challenging to infer differences from horizontal interseismic data alone...at least with current ~5 km geodetic station spacing. In contrast, the interseismic vertical velocities are predicted to be quite different. As has been pointed out previously (Kanda and Simons, Kai's group, among others) the classic backslip (a) type modes predict bulk uplift the hanging wall. In theory this would be relatively easy to observe but thrust faults are rarely isolated enough to allow for isolated observations. In contrast, the kinematically consistent model predicts that interseismic deformation is localized not near the fault trac but instead in the hanging wall above the ramp to detchment transition.
So none of this may provide clarity! The kinetically consistent model (red lines) seems like a neat idea in the sense that long-term growth looks like Suppe (1985)-style. The bad news is that for this specific kinematic model be sensible we should observe a distinct coseismic signature in hanging wall deformation...and I'm not aware of observations consistent with this. Again, Souter and Hager (1997) pointed this out in the study of coseismic displacements from the Northridge earthquake but that event may have been too small to involve slip on both the ramp and the detachment and therefore may not have activated the fold axis coseismically. As is often the case it seems like interseismic vertical deformation may be useful in resolving this (as we have lots of intersesimic observations a few coseismic).
All figures (except figures 1, 3, and 5) are produced by the matlab scripts included here.