Dear colleagues and friends,
You may have noticed my recent Comment in JSG entitled:
Comment on “Reference frame, angular momentum, and porphyroblast
rotation” by Dazhi Jiang and Paul F. Williams. Journal of Structural
Geology 27, 943-1138. (in press)
Jiang and William's "Reply", which was both constructive and
instructive, prompts me to place some additional comments regarding
three issues for those interseted in the subject.
Cheers,
Domingo
1.
In my comment, I questioned Dazhi Jiang and Paul Williams's approach of
treating the matrix as a homogenous fluid or "continuous medium". In my
opinion, this ignores the effect of matrix heterogeneity and resulting
partitioning of deformation at the scale of porphyroblasts. J & W
reject this criticism and reaffirm that rocks may be safely modelled as
continuous media as long as the scale of observation is much larger
than individual matrix grains. They write:
"As pointed out in Jiang (2001), a garnet porphyroblast typically
occupies a volume that would contain w1000 matrix grains, making it
justifiable to use the matrix vorticity to represent the angular
velocity of a spherical garnet. "
In other words, J & W regard grain-scale processes (microcracking,
dissolution, solution transfer, reprecipitation) as irrelevant to the
development of structures at larger-scales. The viscosity and vorticity
of the matrix can, according to them, be assumed to be the average of
the viscosities and vorticities of the constituent mineral grains. In
my opinion, this viewpoint overlooks the role of small-scale
instabilities in the formation of macroscopic patterns. A wide variety
of natural phenomena studied in physics, chemistry, biology etc.
exhibit small-scale heterogeneity being amplified into regular
macroscopic patterns. To mention a recent title on the subject is:
"Evolution of Spontaneous Structures in Dissipative Continuous Systems"
by F.H. Busse and S.C. Muller (editors). Lecture Notes in Physics
series. Springer, Berlin, 1998, 583 pp.). I would argue that similar
laws apply to the partitioning of deformation in metamorphic rocks.
Deformation-induced differentiation in microlithons, foliation septae,
shear bands etc. leads to regular patterns ("microfabrics") which are
intimately related to the development of porphyroblast inclusion
trails. Aporphyroblast can approach the size of a single microlithon
and still show the same basic inclusion trail geometries as larger
porphyroblasts in the same rock. Although we know that "lack of
porphyroblast rotation" results from a particular pattern of
deformation partitioning, we do not fully understand the origin of
these patterns in physical terms. A physical theory with true
explanatory power must be based on the grain-scale physical processes
rather than on uncertain analogies and extrapolations.
2.
Figure 4 in my original "Comment" I showed 3 large garnets with
spirals defined by a continuously curving single foliation. These
microstructures were argued to be inconsistent with "non-rotation"
models by Jiang and Williams (2004). Apart from argueing why this is
not true in my opinon, I also showed that internal truncation surfaces
and lines interconnecting inflexion points in Fig. 4 exhibit a certain
degree of vertical and horizontal preferred orientation. I argued that
this supports a similar origin as more "truncational" spiral showing
more pronounced preferred vertcial and horizontal orientations,such as
described by Hayward (1992), for example. Jiang & Williams replied:
"We lack the imagination to agree with Aerden’s interpretation of his
fig. 4b–d in terms of straight-line segments and fail to see the
‘subtle, yet distinctly orthogonal patterns’ (fig. 4b–d)." Further, we
find it far-fetched to claim that the orthogonal patterns are either
parallel or perpendicular to the earth’s surface (fig. 4f). Some as
interpreted are close, but the initial choice of straight-line segments
is completely subjective."
Here I point out that correct identification of inflexion points and
truncation surfaces involves little interpretation and that no
"imagination" is required to agree with geometries that are factual. To
demonstrate the "objectiveness" of these drawings I have constructed a
dip-isogon map for one of the spirals (Fig. 4b), which is attached as a
PDF file. I drew the dip-isogons conveniently by rotating the line
drawing of inclusion trails 10° increments on the computer screen and
each time tracing the tangent points of inclusion-trail lines with the
horizontal computer-screen raster lines. One can notice the close
correspondence of the isogon pattern and the originally identified
truncations and inflexion points. These features are not subjective but
real, and the same counts for their orientation indicated relative to
the Earth's surface.
