I
n an insightful article about research in
geology in the early twentieth century M. King
Hubbert refers to Sir William Thomson (Lord
Kelvin) as the “Patron Saint” of geologists, including himself, who espouse a quantitative agenda,
and he cites this quotation from Thomson as their
“guiding credo” (Hubbert, 1974). Thomson is not
advocating numeration purely for the sake of collecting numbers; rather this is a call to measure
relevant physical quantities and express them as
numbers. Thomson was a physicist, not a geologist, but Hubbert recognized the importance of
quantification in the geological sciences and was
a leader among geologists of his generation in this
regard (Hubbert, 1972). In part, Hubbert was reacting to the popularity of descriptive taxonomy for
geologists of the twentieth century, structural
geologists being no exception: an introductory
textbook published in 1987 provides a glossary of
terms with over 350 entries that beginning students might be expected to master (Dennis, 1987).
In a playful reaction to the plethora of terms for
intrusive forms at mid-century Charles Hunt comments on the feeder to the Trachyte Mesa laccolith: “Because the form has certain resemblances to
the woody structure of the cane cactus the name
cactolith might be used and defined as a quasi-horizontal chonolith composed of anastomosing ductoliths whose distal ends curl like a harpolith, thin
like a sphenolith, or bulge discordantly like an
akmolith or ethmolith” (Hunt, 1953).
Here we introduce some of the concepts and
the tools necessary to practice structural geology
in a manner that Hubbert would have understood
and Thomson would have appreciated. We begin
this chapter by defining the basic physical quantities used to describe and measure Earth structures, and agree on their units of measure. This
leads to a discussion of the continuum, the mathematical idealization that forms the basis for
most of our thinking about the spatial and temporal variations of the relevant physical quantities. These so-called field quantities are defined at
every point in the continuum and are inferred to
be measurable in the rock mass. Next we consider
physical dimensions and explain how dimensional analysis is used to check the consistency of
equations and to construct graphs of physical
quantities. Dimensional analysis provides the
tools to understand the scaling of structural phenomena, and to set up scaled laboratory experiments to model the development of structures.
4.1 Physical quantities and
the continuum
4.1.1 Fundamental and derived quantities
Structural geology is concerned with deformation
of rock and this is largely a physical process,
although chemical processes can play important
roles. Most of the physical quantities we use in
this textbook can be described in terms of four
fundamental quantities for mechanical systems,
namely length, mass, time, and temperature.
Associated with each fundamental quantity are
actual objects (e.g. a cylinder of platinum–iridium
alloy residing at Sèvres, France, and assigned a
mass of one kilogram), or devices with prescribed
procedures (e.g. a device to measure the duration
of 9 192 631 770 periods of radiation corresponding to transitions of the cesium-133 atom and
assigned a time of one second; Mechtly, 1973).
These are used as standards to define the quantities, and copies of the standards are used for
everyday measurement. For example, one would
compare an unknown mass to a copy of the standard kilogram using a balance. For structural
geologists most measurements are made using
classical physical principles that predate relativity, quantum mechanics, and the physics of
atomic and sub-atomic particles. As two modern
physicists point out:
Observations are formulated in the language of classical physics because that is the language used to record
measurements with macroscopic instruments. That
statement does not imply that the measuring instruments follow classical physics instead of quantum
physics, a wrong opinion some writers ascribe incorrectly to Bohr. Instead our statement implies that the
special nature, in particular the larger size, of measuring instruments allows the description of their behavior in classical terms (Feshbach and Weisskopf, 1988).
Such measurements determine a numerical value
for the physical quantity.
It is not the measured number itself that is
useful, but rather that number in combination
4.1 PHYSICAL QUANTITIES AND THE CONTINUUM
121
n an insightful article about research in
geology in the early twentieth century M. King
Hubbert refers to Sir William Thomson (Lord
Kelvin) as the “Patron Saint” of geologists, including himself, who espouse a quantitative agenda,
and he cites this quotation from Thomson as their
“guiding credo” (Hubbert, 1974). Thomson is not
advocating numeration purely for the sake of collecting numbers; rather this is a call to measure
relevant physical quantities and express them as
numbers. Thomson was a physicist, not a geologist, but Hubbert recognized the importance of
quantification in the geological sciences and was
a leader among geologists of his generation in this
regard (Hubbert, 1972). In part, Hubbert was reacting to the popularity of descriptive taxonomy for
geologists of the twentieth century, structural
geologists being no exception: an introductory
textbook published in 1987 provides a glossary of
terms with over 350 entries that beginning students might be expected to master (Dennis, 1987).
In a playful reaction to the plethora of terms for
intrusive forms at mid-century Charles Hunt comments on the feeder to the Trachyte Mesa laccolith: “Because the form has certain resemblances to
the woody structure of the cane cactus the name
cactolith might be used and defined as a quasi-horizontal chonolith composed of anastomosing ductoliths whose distal ends curl like a harpolith, thin
like a sphenolith, or bulge discordantly like an
akmolith or ethmolith” (Hunt, 1953).
Here we introduce some of the concepts and
the tools necessary to practice structural geology
in a manner that Hubbert would have understood
and Thomson would have appreciated. We begin
this chapter by defining the basic physical quantities used to describe and measure Earth structures, and agree on their units of measure. This
leads to a discussion of the continuum, the mathematical idealization that forms the basis for
most of our thinking about the spatial and temporal variations of the relevant physical quantities. These so-called field quantities are defined at
every point in the continuum and are inferred to
be measurable in the rock mass. Next we consider
physical dimensions and explain how dimensional analysis is used to check the consistency of
equations and to construct graphs of physical
quantities. Dimensional analysis provides the
tools to understand the scaling of structural phenomena, and to set up scaled laboratory experiments to model the development of structures.
4.1 Physical quantities and
the continuum
4.1.1 Fundamental and derived quantities
Structural geology is concerned with deformation
of rock and this is largely a physical process,
although chemical processes can play important
roles. Most of the physical quantities we use in
this textbook can be described in terms of four
fundamental quantities for mechanical systems,
namely length, mass, time, and temperature.
Associated with each fundamental quantity are
actual objects (e.g. a cylinder of platinum–iridium
alloy residing at Sèvres, France, and assigned a
mass of one kilogram), or devices with prescribed
procedures (e.g. a device to measure the duration
of 9 192 631 770 periods of radiation corresponding to transitions of the cesium-133 atom and
assigned a time of one second; Mechtly, 1973).
These are used as standards to define the quantities, and copies of the standards are used for
everyday measurement. For example, one would
compare an unknown mass to a copy of the standard kilogram using a balance. For structural
geologists most measurements are made using
classical physical principles that predate relativity, quantum mechanics, and the physics of
atomic and sub-atomic particles. As two modern
physicists point out:
Observations are formulated in the language of classical physics because that is the language used to record
measurements with macroscopic instruments. That
statement does not imply that the measuring instruments follow classical physics instead of quantum
physics, a wrong opinion some writers ascribe incorrectly to Bohr. Instead our statement implies that the
special nature, in particular the larger size, of measuring instruments allows the description of their behavior in classical terms (Feshbach and Weisskopf, 1988).
Such measurements determine a numerical value
for the physical quantity.
It is not the measured number itself that is
useful, but rather that number in combination
4.1 PHYSICAL QUANTITIES AND THE CONTINUUM
121