Geology Reference
In-Depth Information
detail (see, for example, Yonkee & Weil ' s 2010 study of
strain in the Wyoming salient). In the Appalachians,
Alleghanian-age deformation caused a two-tier thrust
system. The lower thrust sheet is composed of Cambro-
Ordovician carbonate rocks and fl ysch while the upper
thrust sheet comprises Silurian to Pennsylvanian silici-
clastic rocks (Gray & Stamatakos 1997). The lower
sheet is deformed primarily by layer-parallel shorten-
ing and large-scale thrust faulting while the upper
thrust sheet has undergone a sequence of deformation
that includes fi rst layer-parallel shortening and top to
the foreland layer-parallel shear, then fl exural slip/
fl exural fl ow folding and fi nally fold modifi cation and
late-stage thrust faulting. The Wyoming salient
(Yonkee & Weil 2010) was also dominated by early
layer-parallel shear, but then suffered from a sequence
of tangential extension and layer-parallel shear. In
both salients, layer-parallel shortening caused by a
horizontal shortening axis has the potential to steepen
the paleomagnetic inclination while fold modifi cation
in the Appalachians caused by axial planar cleavage or
tightening of folds by homogeneous strain could also
potentially rotate the remanence into the cleavage
plane (Cioppa & Kodama 2003b). The effects of fl exu-
ral slip/fl ow (i.e. layer-parallel shear) are considered in
detail in the following section.
directions. Based on Ramsay (1967), the amount of
simple shear parallel to the fold's bedding planes was
equal in magnitude to the limb dip in radians. Kodama
considered the effects of fl exural slip/fl ow strain on the
magnetization for two different grain-scale strain
mechanisms: if the magnetization rotated as a passive
line or if it rotated as if it were carried by rigid, actively
rotating magnetic particles. For the passive line rota-
tion he used the equations of March (1932) to deter-
mine the orientation and magnitude of the strain
ellipse that would be created in each limb due to fl exu-
ral fl ow strain (continuously distributed through the
bedding) and used Wettstein ' s equation (Ramsay &
Huber 1983) to calculate how much each paleomag-
netic direction would be rotated toward the long axis
of the strain ellipse (Fig. 7.4). For rigid particle rotation
he considered that each paleomagnetic direction of the
Fisher distribution was the resultant of individually
magnetized particles that rotated like ball bearings in
bedding-parallel simple shear using the equations of
Jeffery (1923). Both equi-dimensional and prolate
magnetic particles were modeled. After the magnetiza-
tions were rotated by either passive line marker or rigid
particle strain, the deformed Fisher distributions were
stepwise unfolded to determine at what stage of partial
unfolding the best clustering of magnetic directions
occurred. The signifi cance of the clustering was
checked using the statistical test of McFadden & Jones
(1981) .
Simple consideration of the effects of rigid particle
rotation due to fl exural fl ow/slip bedding - parallel
simple shear shows that the sense of particle rotation
is opposite to that of the rigid body rotation of the fold's
limbs (Fig. 7.5). In a sense, the grain-scale strain
'undoes' the effects of rigid body rotation of the fold's
limbs, and will always lead to the rotation of a pre-
folding magnetization to appear to be syn-folding. The
numerical modeling supports this intuitive under-
standing and shows that rigid particle rotation under
the effects of fl exural fl ow/slip strain will always lead
to the best clustering of paleomagnetic directions at
about 50% unfolding, no matter what the inclination
of the initial paleomagnetic direction is. This result
assumes that the magnitude of simple shear strain is
equal to the limb dip in radians.
If the magnetization rotates as a passive line marker
due to fl exural fl ow/slip strain, the results are entirely
different. This is because during passive line marker
strain the magnetization cannot rotate through the
shear plane, i.e. the bedding plane in a fl exural fl ow
REMANENCE ROTATION AND
INTERNAL DEFORMATION OF
ROCKS DURING FOLDING
In a theoretical approach, van der Pluijm (1987) con-
sidered the effects of rigid particle and homogeneous
bulk strain during folding when rocks are deformed by
fl exural fl ow/slip strain. He showed that a pre-folding
magnetization could be rotated at the grain scale to
appear to be syn-folding. In his consideration of the
effects of internal strain on the paleomagnetic fold test,
Facer (1983) did not explicitly show that a syn-folding
magnetization could result from folding strain, but did
point out that fl exural slip/fl ow strain and shear paral-
lel to a fold's axial plane would have essentially the
same effects on a rock's magnetization.
Using numerical modeling, Kodama (1988) consid-
ered in detail the effects of fl exural slip/fl ow strain and
tangential-longitudinal strain during folding on a
rock's paleomagnetic remanence. For fl exural slip/fl ow
deformation, he considered a fold with 45° limb dips
and an initial Fisher distribution of paleomagnetic
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