I am glad that Riccardo Caputo and I agree that fault-slip inversions primarily give evidence of the incremental strain, not the stress.  In many ways, this is the most important issue.  We also agree on the statistical nature of the results and the averaging over finite volumes that is implicit in the technique.

In my 2009 paper (and others) the use of hexagonal blocks is a MODEL.  It is not meant to  provide a realistic picture of real fault zones, but simply to provide a way of accounting for the displacements that must occur on the surfaces bounding any rigid block.  Such models, and the statistical averaging they employ, are common and useful in deriving equations that describe the behavior of large systems.

Caputo misrepresents my conclusions in his quote from p. 1121 of my 2009 paper.  I did NOT say or imply that that the model does not describe real crustal deformation.  I specifically stated that the available evidence provides only permissive, but not conclusive, evidence of relative microrotations because either the evidence available is not complete enough to permit an independent test, or that it is of insufficient resolution to be more definitive.  I think in general that the case for relative rotations of fault blocks having a significant effect on fault-slip data is pretty strong.

It seems to me that the statement that the principal stress axes differ from the principal strain rate axes by "an angular uncertainty of several degrees (at the best)" has no basis in observation, because there is no way to obtain an independent observation of the orientation of the stress axes to compare with the incremental-strain (or strain-rate) axes obtained from fault-slip inversions.  The statement simply represents, in effect, an assertion that the mechanical properties of the cataclastically deforming brittle crust are effectively isotropic, and that relative rotation is insignificant.  Maybe the mechanical properties are, or are close to, isotropic; or maybe they are strongly anisotropic.  But I have not seen any study that provides clear evidence for the appropriate constitutive equation one way or the other, and I agree with Caputo that this is an area that really needs research.  Given what we can observe about fracture systems and the preferred orientations of fractures, however, (and essentially all rock bodies in the crust are highly fractured), and given the effect that we know such fracture systems have on brittle deformation, I would bet on some degree of anisotropy.  Regardless of who turns out to be more correct on this issue, my point is that we should interpret the inversions to be exactly what they reflect about the deforming system, i.e. the incremental strain, rather than confuse the issue with questionable and possibly incorrect assumptions, just to be able to talk about the stress.  This is all the more true when the strain interpretation leads to greater understanding of the deforming system, as I have illustrated previously.

The possibility of mismatch between the principal incremental strain axes and the principal stress axes arises not only from the possibility of relative rotation of the fault blocks, but also from the possibility of anisotropic mechanical properties, even if the relative rotation is zero.  Stress and incremental-strain axes are not in general parallel for the deformation of an anisotropic material.

The question of boundary conditions is not just a modeling issue.  If the deformation in a fault zone in the crust occurs in response, for example, to the oblique convergence of two crustal blocks, then the geometry of the deformation is constrained by the displacements on the boundaries of the fault zone, and the stress will take on whatever orientations and values are consistent with the imposed strain geometry, and they may even be highly variable in space and time (see John Dewey's March 13 posting).  In such a case, the stress is 'caused by' the strain, not vice versa.  To identify stress as always being the 'causative' factor is not consistent with the mechanics of deforming systems and can lead to confusion.

Riccardo Caputo and I do also agree that this discussion has been stimulating and fun.  Thanks from me as well.

Best regards,

Robert Twiss