N
ature, or what we might call natural
reality, can appear to our senses as a very
complicated system when we view geological structures in outcrop. Francis Crick (1988)
also faced a complicated system when viewing the
constituents of living cells. He suggests in his
book What Mad Pursuit that one should first characterize all the parts of the system and then
understand their geometric relationships. This is
what we attempt to do as structural geologists
when mapping structures in the field. In Chapters
2 and 3 some of the useful tools for mapping were
described and the principles of differential geometry were introduced to provide the fundamental
basis for characterization of structures. Unlike the
cell in a test tube, many parts of typical geological
structures are inaccessible because of limited
exposure, and usually there are limited data on
the temporal development of structures. Crick
then suggests one must study the system as a
whole to understand how it behaves when various
parts are perturbed. This step is possible when the
system is a cell in a test tube, but generally it is
impossible when the system is a rock mass larger
than a cubic meter. Consequently, we turn to
laboratory and mathematical models of geologic
structures to carry out this step in Crick’s prescription for scientific inquiry. Models are constructed with specific features and attributes of
the rock mass, and the model system is studied to
understand how it works.
This chapter focuses on the development of
mathematical models of geologic structures. In
particular we consider the idealization of observed
structures and the selection of general boundary
conditions for model development. At the end of
this chapter we present a methodology for the
practice of structural geology that summarizes the
underlying concepts that have been described and
utilized throughout this book.
12.1 Idealization of field
observations
We begin this chapter by describing how G. K.
Gilbert (1877) idealized the laccolithic intrusions
in the Henry Mountains of southeastern Utah (Fig.
7.8). The frontispiece for this chapter is an oblique
aerial photograph of the eastern flank of Mt.
Hillers showing laccolithic intrusions at Black
Mesa and Trachyte Mesa. Gilbert was one of the
masters of scientific methodology in the practice
of geology, and we have much to learn from studying the way he worked. We give an example of the
procedure of idealization, recognizing that this
will not provide one with all the knowledge
required to implement the procedure. Indeed, to
perfect this procedure requires considerable experience mapping structures in the field, and intimate familiarity with continuum mechanics.
Nevertheless, we introduce the procedure now in
a specific, and perhaps narrowly focused, manner
using the example of Gilbert’s discovery of laccolites (now called laccoliths) and his research into
the origins of the Henry Mountains (Fig. 1.16). It is
assumed that the reader is familiar with the introduction to Gilbert’s research provided in Chapter
1 and with his conceptual model for laccoliths
(Fig. 1.17).
12.1.1 G. K. Gilbert’s field observations
in the Henry Mountains
Gilbert arrived on the western edge of the Henry
Mountains in mid August of 1875 by horseback.
Intrigued by the range of mountains he saw to the
east, Gilbert wondered if they might be a good
place to consider the question of whether volcanic
mountains were just piles of lava flows or perhaps
the result of doming by injection of magma at
depth. On August 18, 1875, Gilbert observed the
sedimentary rocks circling the base of Mt. Ellsworth and dipping away from the summit (Fig.
12.1). The next day he speculated that Mt. Hillers
must be capped with trachyte (igneous rock) and
again observed the sedimentary units dipping
steeply around the base of the mountain in contrast to their nearly horizontal aspect further
from the mountain.
On August 21st Gilbert approached the base of
Mt. Hillers and recorded in words and a sketch
(Fig. 12.2) the scene that he observed:
Camp 38 is on the SE base of Hillers. We have found
several minute springs in skirting the mountain and
this one barely suffices us. It cannot be depended on as
permanent . . . The rock which rises toward Hillers
from the south is the B cliff (Ferron Sandstone). It is
12.1 IDEALIZATION OF FIELD OBSERVATIONS
457
ature, or what we might call natural
reality, can appear to our senses as a very
complicated system when we view geological structures in outcrop. Francis Crick (1988)
also faced a complicated system when viewing the
constituents of living cells. He suggests in his
book What Mad Pursuit that one should first characterize all the parts of the system and then
understand their geometric relationships. This is
what we attempt to do as structural geologists
when mapping structures in the field. In Chapters
2 and 3 some of the useful tools for mapping were
described and the principles of differential geometry were introduced to provide the fundamental
basis for characterization of structures. Unlike the
cell in a test tube, many parts of typical geological
structures are inaccessible because of limited
exposure, and usually there are limited data on
the temporal development of structures. Crick
then suggests one must study the system as a
whole to understand how it behaves when various
parts are perturbed. This step is possible when the
system is a cell in a test tube, but generally it is
impossible when the system is a rock mass larger
than a cubic meter. Consequently, we turn to
laboratory and mathematical models of geologic
structures to carry out this step in Crick’s prescription for scientific inquiry. Models are constructed with specific features and attributes of
the rock mass, and the model system is studied to
understand how it works.
This chapter focuses on the development of
mathematical models of geologic structures. In
particular we consider the idealization of observed
structures and the selection of general boundary
conditions for model development. At the end of
this chapter we present a methodology for the
practice of structural geology that summarizes the
underlying concepts that have been described and
utilized throughout this book.
12.1 Idealization of field
observations
We begin this chapter by describing how G. K.
Gilbert (1877) idealized the laccolithic intrusions
in the Henry Mountains of southeastern Utah (Fig.
7.8). The frontispiece for this chapter is an oblique
aerial photograph of the eastern flank of Mt.
Hillers showing laccolithic intrusions at Black
Mesa and Trachyte Mesa. Gilbert was one of the
masters of scientific methodology in the practice
of geology, and we have much to learn from studying the way he worked. We give an example of the
procedure of idealization, recognizing that this
will not provide one with all the knowledge
required to implement the procedure. Indeed, to
perfect this procedure requires considerable experience mapping structures in the field, and intimate familiarity with continuum mechanics.
Nevertheless, we introduce the procedure now in
a specific, and perhaps narrowly focused, manner
using the example of Gilbert’s discovery of laccolites (now called laccoliths) and his research into
the origins of the Henry Mountains (Fig. 1.16). It is
assumed that the reader is familiar with the introduction to Gilbert’s research provided in Chapter
1 and with his conceptual model for laccoliths
(Fig. 1.17).
12.1.1 G. K. Gilbert’s field observations
in the Henry Mountains
Gilbert arrived on the western edge of the Henry
Mountains in mid August of 1875 by horseback.
Intrigued by the range of mountains he saw to the
east, Gilbert wondered if they might be a good
place to consider the question of whether volcanic
mountains were just piles of lava flows or perhaps
the result of doming by injection of magma at
depth. On August 18, 1875, Gilbert observed the
sedimentary rocks circling the base of Mt. Ellsworth and dipping away from the summit (Fig.
12.1). The next day he speculated that Mt. Hillers
must be capped with trachyte (igneous rock) and
again observed the sedimentary units dipping
steeply around the base of the mountain in contrast to their nearly horizontal aspect further
from the mountain.
On August 21st Gilbert approached the base of
Mt. Hillers and recorded in words and a sketch
(Fig. 12.2) the scene that he observed:
Camp 38 is on the SE base of Hillers. We have found
several minute springs in skirting the mountain and
this one barely suffices us. It cannot be depended on as
permanent . . . The rock which rises toward Hillers
from the south is the B cliff (Ferron Sandstone). It is
12.1 IDEALIZATION OF FIELD OBSERVATIONS
457