Thanks to Dazhi and Shoufa for your clarifying comments.

Shoufa Lin wrote:

> Hi Manuel and others,
>
>> The reference frame X1, X2, X3 of these models is fixed in such a way 
>> that X1 is parallel to the shear zone strike. As we rotate the entire 
>> structure (shear zone, shear direction and reference frame, as Shoufa 
>> Lin proposes), the angle phi between the boundary-parallel simple 
>> shear (gamma) and x1 remains constant, but the new direction x1 has 
>> no meaning in the new situation. It is only an axis included in the 
>> shear plane but with no significance in the strain geometry. On the 
>> other hand, the angle between the rotated gamma (which is, actually, 
>> the "real" shear direction) and the actual observed shear plane 
>> direction should be considered as the real obliquity of the shear zon
>
>
> I think the key here is to fully understand what the angle phi really 
> is in our papers (Lin et al. 1998, Jiang and Williams 1998). It is 
> really the angle between the boundary-parallel simple shear direction 
> and one of the principal stretching axes of the pure shear component. 
> For convenience in presentation, this axis is shown as horizontal in 
> the papers, and in this case only, the angle phi is equal to the angle 
> between the strike of the shear zone and the shear direction. This may 
> not be explicit in Lin et al., but is clear is Jiang and Williams 
> (1998, p. 1106, paragraph 3). With this original definition of angle 
> phi (as the angle between the boundary-parallel simple shear direction 
> and one of the principal stretching axes of the pure shear component), 
> the angle does not change in value with rotation of the shear zone in 
> the way you mentioned. It should be emphasized that, it is the 
> obliquity between the boundary-parallel simple shear direction and the 
> principal stretching axes of the pure shear component that leads to 
> triclinic kinematics and geometry. Because this obliquity is generally 
> present, we believe that the kinematics of shear zones are general 
> triclinic. Even if the direction of simple shear is horizontal, the 
> kinematics can still be triclinic if the principal stretching axes are 
> oblique to the shear direction. A potential example is that of Czeck, 
> & Hudleston (2003).
>
>> In a general case, this angle is not equal to phi in the predicted 
>> vertical shear zone before rotation. This doesn't mean that obliquity 
>> of the shear zone has changed due to passive rotation, and gives 
>> place to a paradox: the obliquity of the natural shear zone, which 
>> has been deduced from a theoretical model, differs from the obliquity 
>> of the theoretical model that I've used to deduce the obliquity of 
>> the natural shear zone. 
>
>
> With the above understanding of the angle Phi, there is no real 
> paradox, as far as I can see.
>
> Shoufa Lin
>
> Jiang, D., and Williams, P.F., 1998, High-strain zones: A unified 
> model: Journal of Structural Geology, v. 20, p. 1105-1120.
>
> Lin, S., Jiang, D., & Williams, P.F. 1998. Transpression (or 
> transtension) zones of triclinic symmetry: natural example and 
> theoretical modelling. In: Holdsworth, R.E., Strachan, R.A. & Dewey, 
> J.F. (eds) 1998. Continental transpressional and transtensional 
> tectonics. Geological Society, London, Special Publications, No. 135, 
> p. 41-57. see 
> http://www.science.uwaterloo.ca/earth/faculty/lin/lin%20paper.pdf for 
> a copy of the paper.
>
> Czeck, D. & Hudleston, P.J. 2003. Testing models for obliquely 
> plunging lineations in transpression: a natural example and 
> theoretical discussion. Journal of Structural Geology, 25, 959-982.
>
>
>
> Manuel Diaz Azpiroz wrote:
>
>> Hi Shoufa Lin and others. With respect to inclined (i.e., 
>> non-vertical) transpressional shear zones, Shoufa Lin pointed out  
>> that "In the model of Lin et al. (1998), as well as that of Jiang and 
>> Williams (1998), the shear zones don’t need to be vertical. Although 
>> the zones are shown as vertical for convenience of presentation in 
>> the papers, geometry predicted for non-vertical shear zones can be 
>> obtained by rotating the diagrams like Fig. 9 of Lin et al. (1998), 
>> as is explicitly pointed out in the figure caption to this diagram. 
>> This was what Lin et al. did when they applied the modeling results 
>> to the Roper Lake shear zone (their Fig. 11). The Alpine fault in New 
>> Zealand is interpreted by Jiang et al. (2001) as another example of 
>> triclinic non-vertical transpression zone." This is true. 
>> Nevertheless, some questions about obliquity remain uncertain.
>>
>> Comparison between strain geometry of natural shear zones and strain 
>> geometry predicted for theoretical models, by rotating the latter 
>> from a vertical position to a new orientation that fits the geometry 
>> of the former seems reasonable. The reference frame X1, X2, X3 of 
>> these models is fixed in such a way that X1 is parallel to the shear 
>> zone strike. As we rotate the entire structure (shear zone, shear 
>> direction and reference frame, as Shoufa Lin proposes), the angle phi 
>> between the boundary-parallel simple shear (gamma) and x1 remains 
>> constant, but the new direction x1 has no meaning in the new 
>> situation. It is only an axis included in the shear plane but with no 
>> significance in the strain geometry. On the other hand, the angle 
>> between the rotated gamma (which is, actually, the "real" shear 
>> direction) and the actual observed shear plane direction should be 
>> considered as the real obliquity of the shear zone (it is important 
>> to keep in mind that shear zone didn' t developed in a vertical 
>> position and zone was later passively rotated to the current 
>> orientation, but deformation took place in the observed inclined 
>> position), as it is monstrated in figure 10 of Jiang et al (2001). In 
>> a general case, this angle is not equal to phi in the predicted 
>> vertical shear zone before rotation. This doesn't mean that obliquity 
>> of the shear zone has changed due to passive rotation, and gives 
>> place to a paradox: the obliquity of the natural shear zone, which 
>> has been deduced from a theoretical model, differs from the obliquity 
>> of the theoretical model that I've used to deduce the obliquity of 
>> the natural shear zone. Moreover, we must suppose that the "new" real 
>> obliquity of the inclined shear zone would lead to a different strain 
>> geometry than the strain geometry of the natural shear zone, and 
>> then, do you think it would possible to calculate this strain 
>> geometry directly from the inclined position of the shear zone if the 
>> shear direction is unknown?
>>
>> Thank you and happy new year,
>>
>> Manuel
>>
>>
>>
>> Manuel Díaz Azpiroz
>> Dpto. Ciencias Ambientales
>> Universidad Pablo de Olavide
>> Crtra. Utrera, km 1
>> 41013 Sevilla
>> [log in to unmask]
>>
>
>