shallow intrusion. To address questions about the
cooling of the magma in tabular intrusions, and
heating of the host rock, a number of models have
been investigated, some that consider heat flow
from a stagnant magma (Lovering, 1935, 1936;
Jaeger, 1957, 1964b; Irvine, 1970), and others that
consider the transport of heat within and from a
flowing magma (Delaney and Pollard, 1982;
Habert and De Saint-Blanquat, 2004). The context,
or general boundary conditions, for these analyses is the subject of heat transfer, and there are
many useful textbooks on this subject (Carslaw
and Jaeger, 1959; Bird et al., 1960).
12.3 A methodology for the
practice of structural geology
Newton’s axiomatic framework allowed him to pursue
a strategy in which he could construct a simplified,
idealized mathematical model of the physical system
he wanted to probe – in this case, the solar system.
Using mathematics, Newton could work out the consequences of certain actions and compare them with
measurements and empirical observations. That comparison, in turn, would suggest ways in which the
model could be adjusted and refined to achieve even
greater realism. In essence, this strategy of maintaining a right interplay between mathematical analysis
and physical experience afforded a marvellously productive way of using mathematics to explain the workings of nature. Revolutionary in Newton’s time, this
kind of approach is taken for granted in modern
research (Peterson, 1993).
The material presented in this textbook reveals
two distinct views of structural geology. On the
one hand we have described observations of structures: for example views through a microscope of
tiny spherical objects that were deformed into
ellipsoidal shapes as rocks were contorted into the
South Mountain fold (Fig. 5.4), or photographs of
exposures that show successive stages in the development of strike slip faults in granitic rock of the
Sierra Nevada (Fig. 9.37). On the other hand we
have described models of structures: for example
a plot of principal stress trajectories associated
with a pattern of dikes around the Spanish Peaks
(Fig. 6.37), or a plot of displacement vectors associated with the 1999 Hector Mine earthquake (Fig.
8.15). The outcome of a structural investigation is
judged to be successful if there is a compelling
correspondence between the views provided by
observation and modeling.
At times these different views of structural
geology seem too disparate to be reconciled. The
one is the world of boots and backpacks, rock saws
and microscopes, maps and photographs, compasses and measuring tapes. The other is the
world of vectors and tensors, material continua
and differential equations, keyboards and computers, graphs and numbers. For some practitioners of structural geology a choice is made at an
early stage in their education that closes the door
on one of these worlds in favor of the other. One
objective of this textbook is to encourage structural geologists to integrate these two worlds and
discover the benefits of both.
A methodology for the practice of structural
geology that integrates observations and modeling
is illustrated in Fig. 12.14 as a set of ten stepping
stones on a path with the suggestion that this be
traversed in a counterclockwise sense starting at
the top. Of course scientific investigations are
rarely this well organized or rationalized. Instead
of beginning with a field observation one may be
inspired to investigate a new problem while
reading a textbook on fluid mechanics or contemplating the solution to an elastic boundary value
problem displayed as velocity vectors on a computer screen. Regardless of the source of inspiration one could argue that seeking the map or
photograph or measurement in the field to confirm
that the phenomenon in question occurs naturally
in Earth’s crust is a pre-requisite to launch an investigation. Thus, we find ourselves at the top of the
diagram and suggest that this step of seeking data
in the field should benefit from the techniques of
field-based structural geology described in Chapter
2. Also, for the quantitative characterization of
structures we advocate the use of differential
geometry, some of which is described in Chapter 3.
Once launched along the path (Fig. 12.14) it is
common to step off and move directly to a stepping stone out of sequence, or even to backtrack
along the path. None-the-less this simple diagram
provides a way to organize the primary scientific
procedures employed by a structural geologist
and to understand how they might relate to one
474
MODEL DEVELOPMENT AND METHODOLOGY
cooling of the magma in tabular intrusions, and
heating of the host rock, a number of models have
been investigated, some that consider heat flow
from a stagnant magma (Lovering, 1935, 1936;
Jaeger, 1957, 1964b; Irvine, 1970), and others that
consider the transport of heat within and from a
flowing magma (Delaney and Pollard, 1982;
Habert and De Saint-Blanquat, 2004). The context,
or general boundary conditions, for these analyses is the subject of heat transfer, and there are
many useful textbooks on this subject (Carslaw
and Jaeger, 1959; Bird et al., 1960).
12.3 A methodology for the
practice of structural geology
Newton’s axiomatic framework allowed him to pursue
a strategy in which he could construct a simplified,
idealized mathematical model of the physical system
he wanted to probe – in this case, the solar system.
Using mathematics, Newton could work out the consequences of certain actions and compare them with
measurements and empirical observations. That comparison, in turn, would suggest ways in which the
model could be adjusted and refined to achieve even
greater realism. In essence, this strategy of maintaining a right interplay between mathematical analysis
and physical experience afforded a marvellously productive way of using mathematics to explain the workings of nature. Revolutionary in Newton’s time, this
kind of approach is taken for granted in modern
research (Peterson, 1993).
The material presented in this textbook reveals
two distinct views of structural geology. On the
one hand we have described observations of structures: for example views through a microscope of
tiny spherical objects that were deformed into
ellipsoidal shapes as rocks were contorted into the
South Mountain fold (Fig. 5.4), or photographs of
exposures that show successive stages in the development of strike slip faults in granitic rock of the
Sierra Nevada (Fig. 9.37). On the other hand we
have described models of structures: for example
a plot of principal stress trajectories associated
with a pattern of dikes around the Spanish Peaks
(Fig. 6.37), or a plot of displacement vectors associated with the 1999 Hector Mine earthquake (Fig.
8.15). The outcome of a structural investigation is
judged to be successful if there is a compelling
correspondence between the views provided by
observation and modeling.
At times these different views of structural
geology seem too disparate to be reconciled. The
one is the world of boots and backpacks, rock saws
and microscopes, maps and photographs, compasses and measuring tapes. The other is the
world of vectors and tensors, material continua
and differential equations, keyboards and computers, graphs and numbers. For some practitioners of structural geology a choice is made at an
early stage in their education that closes the door
on one of these worlds in favor of the other. One
objective of this textbook is to encourage structural geologists to integrate these two worlds and
discover the benefits of both.
A methodology for the practice of structural
geology that integrates observations and modeling
is illustrated in Fig. 12.14 as a set of ten stepping
stones on a path with the suggestion that this be
traversed in a counterclockwise sense starting at
the top. Of course scientific investigations are
rarely this well organized or rationalized. Instead
of beginning with a field observation one may be
inspired to investigate a new problem while
reading a textbook on fluid mechanics or contemplating the solution to an elastic boundary value
problem displayed as velocity vectors on a computer screen. Regardless of the source of inspiration one could argue that seeking the map or
photograph or measurement in the field to confirm
that the phenomenon in question occurs naturally
in Earth’s crust is a pre-requisite to launch an investigation. Thus, we find ourselves at the top of the
diagram and suggest that this step of seeking data
in the field should benefit from the techniques of
field-based structural geology described in Chapter
2. Also, for the quantitative characterization of
structures we advocate the use of differential
geometry, some of which is described in Chapter 3.
Once launched along the path (Fig. 12.14) it is
common to step off and move directly to a stepping stone out of sequence, or even to backtrack
along the path. None-the-less this simple diagram
provides a way to organize the primary scientific
procedures employed by a structural geologist
and to understand how they might relate to one
474
MODEL DEVELOPMENT AND METHODOLOGY