Geology Reference
In-Depth Information
Location and Attitude
2.1
Introduction
This chapter covers the basic building blocks required to construct 3-D models of
geological structures. Included here are methods for locating points in three dimen-
sions on a map or in a well, for determining the attitude of a plane and the orientation
of a line, and for representing planes with structure contours. Both graphical and
analytical solutions for finding and displaying lines and planes are presented. Many of
the analytical techniques are based on vector geometry, a topic treated separately in
Chap. 12. The graphical techniques utilize stereograms and tangent diagrams.
2.2
Location
The locations of data points recorded on maps and well logs must be converted to a single,
internally consistent coordinate system in order to be used in the interpretive calcula-
tions given in this topic. The positions of points in three dimensions will be described in
terms of a right-handed Cartesian coordinate system with +
x
= east, +
y
=north, and
+
z
= up. Dimensions will be given in feet and kilofeet or meters and kilometers, depend-
ing on the units of the original source of the data. Parts of a foot will be expressed as a
decimal fraction. Unit conversions are a common source of error which are largely avoided
by retaining the original units of the map or well log. The relationships between locations
on a topographic map or well log and the
xyz
coordinate system are given next.
2.2.1
Map Coordinate Systems, Scale, Accuracy
The true locations of points on or in the earth are given in the spherical coordinate
system of latitude, longitude, and the position along an earth radius. Maps are con-
verted from the spherical coordinate system to a plane Cartesian coordinate system by
projection. Some distortion of lengths or angles or both is inherent in every projection
technique, the amount of which depends on the type of projection and the scale of the
map (Greenhood 1964; Robinson and Sale 1969; Bolstad 2002) but is not significant at
the scale of normal field mapping.
In many regions, maps are based on the transverse Mercator or polar stereographic
projections and contain a superimposed rectangular grid called the Universal Trans-
verse Mercator (UTM) or the Universal Stereographic Projection (USP) grid (Robinson
