used. Thus, the same horizontal linear element
could be recorded as (022, 00) or (202, 00).
Some curvilinear structures lie in curved surfaces that are well-defined structures themselves.
For example, the slickenlines shown in Fig. 2.14b are
in the surface of a fault. For these cases the strike
and dip of the planar element that represents the
surface are recorded, along with an angle known as
the rake that can be measured on the exposure with
a protractor (Fig. 2.15c). The rake is the angle, r ,
measured in the plane of the element from the
strike direction down to the linear element. It is
recorded using three digits and can vary from 000Њ
(the linear element is parallel to the line of strike of
the planar element) to just less than 180Њ:
(2.66)
For r ϭ 090Њ the linear element is inclined
directly down the dip of the planar element. Of
course one could measure the plunge direction
and plunge of this line, but often it is simpler to
measure the strike and dip of the planar element
and the rake angle in this planar element.
Structural geologists refer to the attitude of a
structure and by that they mean the orientation in
space, relative to the local geographic coordinate
system, of the planar or linear element that
approximates (is tangential to) the structure at the
point of measurement. Thus, the attitude of a
fault at a particular location would be recorded as
the strike and dip, or the dip direction and dip. The
attitude of a slickenline on that fault would be
recorded as the plunge direction and the plunge.
These measurements are represented on maps
using symbols and numbers placed at the appropriate location. Some of the symbols used on structural maps are illustrated in Fig. 2.16, extracted
from a more extensive table of symbols in a
manual of field geology (Compton, 1962). For most
of these symbols, longer line segments are drawn
parallel to the strike direction so the azimuth can
be determined with reference to the north direction on the map. Shorter line segments indicate
the dip direction and arrows indicate the plunge
direction. Numbers set near the shorter line segments record the dip or plunge angle. The style of
the line segments is used to distinguish different
structures that are approximated as planar or
000° Յ r Ͻ 180°
linear elements. For example, note the different
symbols for joints and veins or dikes. In this way a
lot of information is conveyed in a compact form
on the map, and structures can be related to one
another in terms of their locations.
2.3.2 Stereographic projection of
structural elements
It is useful to have a graphical means to visualize
the attitudes of planar and linear structural elements. The most effective tools for this purpose
are a family of projections that create an image of
the elements on a flat piece of paper. The locations
of the structures are not recorded in this image,
but their orientations relative to the geographic
coordinate system are recorded. Here we introduce one of these projections, the so-called stereographic projection. Details concerning the use of
this projection, and other members of this family
of projections, can be found in books devoted to
the subject (Phillips, 1954; Ragan, 1985; Marshak
and Mitra, 1988). In some courses in structural
geology much of the student’s time is committed
to the manipulation of these projections by hand
and many of the geometric problems encountered
in fieldwork are described in these reference
works. Here we adopt the more analytical
approach described by Goodman and Shi (1985,
p. 56) that avoids the tedium and inaccuracy of
hand constructions. We also take advantage of the
visualization power of modern computer applications for plotting quantitative field data.
We begin by reviewing the basic concepts and
present the analytical expressions necessary to
plot stereographic projections of planar and
linear structural elements. Consider a linear
element fixed in space at the center, C, of a transparent sphere called the reference sphere (Fig. 2.17a).
Only the part of the linear element extending
from C to the point P on the sphere is shown.
Points such as P are projected onto the equatorial
plane of this sphere and the intersection of the
sphere and this plane is called the reference circle.
Points on the reference circle represent the four
compass directions (north, east, south, and west),
and the axis perpendicular to the equatorial plane
intersects the top of the sphere at the zenith, Z. In
the view shown in this figure the sphere is rotated
56
STRUCTURAL MAPPING TECHNIQUES AND TOOLS
could be recorded as (022, 00) or (202, 00).
Some curvilinear structures lie in curved surfaces that are well-defined structures themselves.
For example, the slickenlines shown in Fig. 2.14b are
in the surface of a fault. For these cases the strike
and dip of the planar element that represents the
surface are recorded, along with an angle known as
the rake that can be measured on the exposure with
a protractor (Fig. 2.15c). The rake is the angle, r ,
measured in the plane of the element from the
strike direction down to the linear element. It is
recorded using three digits and can vary from 000Њ
(the linear element is parallel to the line of strike of
the planar element) to just less than 180Њ:
(2.66)
For r ϭ 090Њ the linear element is inclined
directly down the dip of the planar element. Of
course one could measure the plunge direction
and plunge of this line, but often it is simpler to
measure the strike and dip of the planar element
and the rake angle in this planar element.
Structural geologists refer to the attitude of a
structure and by that they mean the orientation in
space, relative to the local geographic coordinate
system, of the planar or linear element that
approximates (is tangential to) the structure at the
point of measurement. Thus, the attitude of a
fault at a particular location would be recorded as
the strike and dip, or the dip direction and dip. The
attitude of a slickenline on that fault would be
recorded as the plunge direction and the plunge.
These measurements are represented on maps
using symbols and numbers placed at the appropriate location. Some of the symbols used on structural maps are illustrated in Fig. 2.16, extracted
from a more extensive table of symbols in a
manual of field geology (Compton, 1962). For most
of these symbols, longer line segments are drawn
parallel to the strike direction so the azimuth can
be determined with reference to the north direction on the map. Shorter line segments indicate
the dip direction and arrows indicate the plunge
direction. Numbers set near the shorter line segments record the dip or plunge angle. The style of
the line segments is used to distinguish different
structures that are approximated as planar or
000° Յ r Ͻ 180°
linear elements. For example, note the different
symbols for joints and veins or dikes. In this way a
lot of information is conveyed in a compact form
on the map, and structures can be related to one
another in terms of their locations.
2.3.2 Stereographic projection of
structural elements
It is useful to have a graphical means to visualize
the attitudes of planar and linear structural elements. The most effective tools for this purpose
are a family of projections that create an image of
the elements on a flat piece of paper. The locations
of the structures are not recorded in this image,
but their orientations relative to the geographic
coordinate system are recorded. Here we introduce one of these projections, the so-called stereographic projection. Details concerning the use of
this projection, and other members of this family
of projections, can be found in books devoted to
the subject (Phillips, 1954; Ragan, 1985; Marshak
and Mitra, 1988). In some courses in structural
geology much of the student’s time is committed
to the manipulation of these projections by hand
and many of the geometric problems encountered
in fieldwork are described in these reference
works. Here we adopt the more analytical
approach described by Goodman and Shi (1985,
p. 56) that avoids the tedium and inaccuracy of
hand constructions. We also take advantage of the
visualization power of modern computer applications for plotting quantitative field data.
We begin by reviewing the basic concepts and
present the analytical expressions necessary to
plot stereographic projections of planar and
linear structural elements. Consider a linear
element fixed in space at the center, C, of a transparent sphere called the reference sphere (Fig. 2.17a).
Only the part of the linear element extending
from C to the point P on the sphere is shown.
Points such as P are projected onto the equatorial
plane of this sphere and the intersection of the
sphere and this plane is called the reference circle.
Points on the reference circle represent the four
compass directions (north, east, south, and west),
and the axis perpendicular to the equatorial plane
intersects the top of the sphere at the zenith, Z. In
the view shown in this figure the sphere is rotated
56
STRUCTURAL MAPPING TECHNIQUES AND TOOLS