Analyzing
Dipmeters with Tangent Diagrams Tangent
diagrams, such as the example shown below, are special
polar coordinate graphs that provide convenient graphic solutions
for many problems of structural geology. Direction of dip is read
at the circumference, and angle of dip is read from the concentric
circles. The radius of each circle is proportional to the tangent
of the angle of dip. High dips, therefore, plot farther from the
center than low dips. The distinctive feature of this method of
display is that planes can be represented by vectors, in a manner
similar to stereonets, although tangent diagrams are more easily
applied than stereonets.
Shown below is a block diagram of a sloping plane, illustrates the basic principle of the tangent diagram. Line B1 is a horizontal line in the direction of true dip, and B2 is another horizontal line making an angle with B1. The trigonometric relations on this drawing demonstrate that the tangent of apparent dip in any direction is equal to the tangent of the true dip times the cosine of the angle between the directions of true dip and apparent dip.
The problem of finding apparent dip from true dip can be resolved
vectorially on a tangent diagram, shown at right, below:
The illustration at top left shows how the tangent diagram is used to find
true dip from two apparent dips: If
two planes intersect, they have equal apparent dips in the vertical
plane containing their line of intersection. The illustration at top
right shows how this principle is used to find the line of intersection
of two planes. The lines of intersection of planes tangent to the bedding on the same or opposite flanks of an ideal cylindrical fold are parallel to the crestal line. Dip measurements obtained at random locations on such a structure will fall on a straight line when plotted on tangent diagrams, as exemplified by the dashed line in in the middle illustration above. The line for nonplunging folds passes through the center of the plot, plunging folds to one side (bottom illustration). Cylindrical folds plot as straight lines and conical folds as curved lines (see below).


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