surements of them. Several examples demonstrate
that strain typically has a continuous variation
within structures, providing one constraint on the
process of formation. More detailed treatment of
practical methods of strain estimation from
deformed geological objects are given in other
textbooks of structural geology (Ramsay and
Huber, 1983). Interpretation of deformed xenoliths
in the Chindamora batholith by means of an
appealing, but ad hoc, kinematic model illustrates
a methodology aimed at constraining the mechanism of intrusion by means of strain measurements. In contrast, we showed how a simple
steady-state distribution of velocity in a rising
“diapir,” provided by the complete mechanical
model afforded by the Stokes solution, might be
used to follow the positions of particles, thus generating a detailed picture of the evolution of the
strain distribution in the body. As another bridge
between observations of geometry and strain and
detailed models of structural evolution, we considered geometric and ad hoc kinematic models of
chevron folds. We study a mechanical model for
their origin in a later chapter. The kinematic
model presented here provides a simple example
with which to illustrate the formal treatment of
strain and rotation as integrals that follow a particle moving through a temporally and possibly
spatially varying velocity field. In the rising viscous
sphere example, strain ellipses were computed by
following dense sets of particles by numerical
means. The chapter concluded with a more formal
treatment of plane deformation in two dimensions, and descriptions of deformation and strain
in three dimensions. In this discussion we point
out how to evaluate the errors expected when one
chooses to employ the infinitesimal strain in the
analysis of problems in structural geology.
5.6 CONCLUDING REMARKS
193
that strain typically has a continuous variation
within structures, providing one constraint on the
process of formation. More detailed treatment of
practical methods of strain estimation from
deformed geological objects are given in other
textbooks of structural geology (Ramsay and
Huber, 1983). Interpretation of deformed xenoliths
in the Chindamora batholith by means of an
appealing, but ad hoc, kinematic model illustrates
a methodology aimed at constraining the mechanism of intrusion by means of strain measurements. In contrast, we showed how a simple
steady-state distribution of velocity in a rising
“diapir,” provided by the complete mechanical
model afforded by the Stokes solution, might be
used to follow the positions of particles, thus generating a detailed picture of the evolution of the
strain distribution in the body. As another bridge
between observations of geometry and strain and
detailed models of structural evolution, we considered geometric and ad hoc kinematic models of
chevron folds. We study a mechanical model for
their origin in a later chapter. The kinematic
model presented here provides a simple example
with which to illustrate the formal treatment of
strain and rotation as integrals that follow a particle moving through a temporally and possibly
spatially varying velocity field. In the rising viscous
sphere example, strain ellipses were computed by
following dense sets of particles by numerical
means. The chapter concluded with a more formal
treatment of plane deformation in two dimensions, and descriptions of deformation and strain
in three dimensions. In this discussion we point
out how to evaluate the errors expected when one
chooses to employ the infinitesimal strain in the
analysis of problems in structural geology.
5.6 CONCLUDING REMARKS
193