7-2 3 ' e can use the program Spline to smooth Odfs too and to plot these as rose diagrams or regular histograms. If you compare the rose diagrams with the corresponding characteristic shapes you note that they are different and in particular, that the rose diagram of the OdF of ellipses is not itself an ellipse(see Fig 7.1) ODF OF ELLIPSE≠ ELLIPSE Since the surfor analysis is only sensitive to the orientation of surface, but not to its distribution in the x-y plane, the results obtained for the deformed L100C*** and L100D*** are exactly the same Again, for strain interpretation, you have to carefully observe the the following points (1 )check if the characteristic shape is symmetric, (2)derive the fabric ellipse, (3.) check (as best as you can)if the fabric ellipse was produced by deformation only, or whether other processes were involved (e. g, sedimentary deposition), (4 )try to find out whether the undeformed state was really one of random orientation of surface In the case of the oolithic limestone one may well assume that the initial orientation of surface was random. Note that this is not the same as assuming that the ooides were initially spherical. This is a great advantage of the SUrFoR method, because as a rule ooides are not spherical, but may display considerable flattening and furthermore they may be of a shape which is not at all elliptical. due to the random orientation of long axes(which we may assume if we can exclude cross bedding) the orientation of the surface becomes random too The deformed oolites shown in Fig.7.3. a to 7. 3.d have been obtained by axial compression in a triaxial apparatus44. The question was whether the strain measured from the flattened oolites would be a reliable measure of the bulk strain the axial ratios of the fabric ellipses derived from the projection functions of the deformed oolites is always higher, i. e. they always indicate less strain, than the applied shortening has produced. If z is the undeformed length of the sample, then 1/z is the cross sectional area normal to the axis (x y). If we assume volume constan deformation, xyz= XYZ (capital letters indicating the deformed lengths). the ratio Z/X (or Z/Y), which corresponds to the axial ratio b/a is given by the following relation 3 Schmid, S M, Panozzo, R, Bauer, S, 1987. Simple shear experiments on calcite rocks rheology and microfabric. J. Structural Geology, 9, 747-778 (experiments by S. Corbett, Texas A&M University, Center for Tectonophysics07 - 2 shape3. We can use the program SPLINE to smooth ODFs too and to plot these as rose diagrams or regular histograms. If you compare the rose diagrams with the corresponding characteristic shapes you note that they are different, and in particular, that the rose diagram of the ODF of ellipses is not itself an ellipse (see Fig.7.1)! ODF OF ELLIPSE ¹ ELLIPSE Since the SURFOR analysis is only sensitive to the orientation of surface, but not to its distribution in the x-y plane, the results obtained for the deformed L100C*** and L100D*** are exactly the same. Again, for strain interpretation, you have to carefully observe the the following points: (1.) check if the characteristic shape is symmetric, (2.) derive the fabric ellipse, (3.) check (as best as you can) if the fabric ellipse was produced by deformation only, or whether other processes were involved (e.g., sedimentary deposition), (4.) try to find out whether the undeformed state was really one of random orientation of surface. In the case of the oolithic limestone one may well assume that the initial orientation of surface was random. Note that this is not the same as assuming that the ooides were initially spherical. This is a great advantage of the SURFOR method, because as a rule ooides are not spherical, but may display considerable flattening, and furthermore they may be of a shape which is not at all elliptical. Due to the random orientation of long axes (which we may assume if we can exclude cross bedding) the orientation of the surface becomes random too. The deformed oolites shown in Fig.7.3.a to 7.3.d have been obtained by axial compression in a triaxial apparatus44. The question was whether the strain measured from the flattened oolites would be a reliable measure of the bulk strain. The axial ratios of the fabric ellipses derived from the projection functions of the deformed oolites is always higher, i.e., they always indicate less strain, than the applied shortening has produced. If z is the undeformed length of the sample, then 1/z is the cross sectional area normal to the axis (x·y). If we assume volume constant deformation, xyz = XYZ (capital letters indicating the deformed lengths). The ratio Z/X (or Z/Y), which corresponds to the axial ratio b/a is given by the following relation: 3 Schmid, S.M., Panozzo, R., Bauer, S., 1987. Simple shear experiments on calcite rocks: rheology and microfabric. J.Structural Geology, 9, 747-778. 4 (experiments by S. Corbett, Texas A&M University, Center for Tectonophysics)