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The map presents a summary example of topography and mapped units X and Y. From the information presented, can someone help me determine or estimate the actual dip along the line of section, A-A'? cross section I am somewhat uncertain regarding the steps to be taken given the information presented on this example map. What, specifically, is the difference between true dip and apparent dip in regard to A-A'?

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    $\begingroup$ @trondhansen: it's a very poorly asked homework questions that most likely is about the dip of geological or topographical features. $\endgroup$
    – Fred
    Mar 6 at 9:48
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    $\begingroup$ @trondhansen I am not doing homework and am years out of school. I am however studying for the ASBOG, which is a test on geology (earth science). I am stumped on the answer given for this question and was looking for some guidance. This question comes verbatim from an ASBOG review guide. It would be more helpful if you could explain why this is a poor question or where it should be posted. I'm all ears. $\endgroup$
    – CH-
    Mar 6 at 23:48
  • $\begingroup$ @Fred ^ I can also try to clarify anything your confused about if you're interested in answering. $\endgroup$
    – CH-
    Mar 6 at 23:49
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    $\begingroup$ This is a poorly asked question for Stack Exchange. See How do I ask a good question? in the help center. $\endgroup$ Mar 7 at 8:55
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    $\begingroup$ I also think this is a perfectly valid geological question and falls within the topic. Though perhaps a little homeworky in presentation. $\endgroup$
    – Siv
    Mar 8 at 13:49

1 Answer 1

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This is an excellent question. The answer requires that one visualize a 3-dimensional space with a dip plane, a vertical plane coincident with, and aligned along, our line of interest, and the trace that our line of interest will make on the dip plane where the vertical plane and dip plane intersect. These aspects are already projected onto a two-dimensional map. In this answer, true dip is taken as the dip measured or estimated perpendicular to the strike. Dip is always given a compass heading in the down direction of the dip. Apparent dip is any other dip measured or estimated, and similarly given a compass heading. Also note that rise and fall are somewhat synonymous terms regarding elevation change over a measured horizontal distance.

We can readily identify, on the provided geologic map, two marked geologic units, X and Y, topographic elevation contours at 400 ft and 300 ft, geologic-unit contacts or boundaries denoting the top of unit X, contact of unit X with unit Y (which is also the bottom of unit X, or the top of unit Y), and bottom of unit Y. Presumed units W above, and Z below, are unmarked. North is indicated, and a graduated 1000 ft scale is given, marked in 250 ft divisions. Also, the trace of a line of section, A - A', is shown on the map. This is our line of interest. Within the given context of the question, the dip of line A - A' that is desired is of the projection of line A - A' onto a formation contact; or equivalently for a vertical section along A - A', the apparent dip of the formations in that vertical projection. Otherwise, the true dip of line A - A' in the map plane is zero.

To make this exercise easier to do we need the following -

  • drafting straight edge
  • protractor
  • engineer's scale (to proportion our map scale for measured distance)
  • drafting pencil (2 or 2H)
  • vinyl eraser for goofs/corrections
  • a drafting brush helps keep the drafting surface clean

The explanation, herein, will use and explain measurements by hand so that the process will be clear. A piece of drafting vellum or tracing paper placed over our map is sometimes easier for sketching work and correcting errors or noting scratch calculations.

First, we have to determine the true dip and strike of these units by structure-contouring one of the contact surfaces. An obvious choice is to use the contact boundary between units X and Y. Notice that this contact crosses the 300 ft topographic elevation contour in 3 locations on our map. Consequently, the elevation of the contact is 300 ft at these locations. We can free-hand sketch a structure contour through these three points, but they are close enough to being along a straight line that we can use a straight edge to sketch-in a 300 ft contour line for the structure contour through these points. The alignment of this contour is along the strike of the contact between units X and Y. Take note of the compass alignment of this contour, and take note of the compass alignment of our line of interest, A - A'. Of particular interest is the noted angle between the compass headings of these lines.

The following were determined from the map: 1) alignment of A - A' is N 60 deg E (or S 60 deg W), and 2) alignment of 300 ft structure contour, N 75 deg E (or S 75 deg W). The angle between these lines is difference between their headings, or 15 deg. The true dip of the X - Y contact is to the northwest. In other words, the true dip heading of the X - Y contact is perpendicular to the northeast - southwest alignment of the strike. The alignment of the strike is N 75 deg E (or S 75 deg W).

To continue, we note that the contact of interest crosses the 400 ft topographic elevation contour at 4 locations, all essentially in a linear alignment parallel to the 300 ft structure contour, and somewhat to the southeast. We, therefore, use our straight edge to again sketch-in the parallel alignment of the 400 ft-elevation structure contour. The dip of this contact surface is determined by the arctan(rise/run), wherein the rise is the difference in elevation between the contours, or 100 ft, and the run is determined from the map distance measured perpendicularly between 400 and 300 ft contours, or about 400 ft. Doing the math, the dip is determined as approximately 14 deg. Note the true dip is to the northwest, or 14 deg true dip directed, or aligned at, N 15 deg W. In other words, the map direction of the true dip is perpendicular to the strike, and by using the rise/run we have determined the true dip angle is approximately 14 deg.

Second, we take note of some simple 3-dimensional aspects related to the dip and strike of our X - Y contact, and the map direction of our line of interest. We are interested in knowing the apparent dip traced by of our line of interest on the X - Y contact surface. The line of strike is a horizontal line that has no dip, and we know the rise and run used to determine the contact dip. Essentially, any line of strike (such as a tangent to a structure contour) defines a level line. But the path of our line of interest is tilted against the contact surface. The dip of line A - A' projected on the contact surface, is presented by the intersection of a vertical plane containing A - A', at the contact surface. The slope of the line of interest along the contact plane is an apparent dip, the value of which we seek.

Let's examine some details. When looking at our map, we are looking perpendicular to a horizontal-plane projection of mapped features. Our line of section, A - A', is in a vertical plane that is perpendicular to our map plane. We have to visualize how this line of section is projected onto the contact surface. Obviously, the line of section on the contact surface is defined by the intersection of the vertical plane with the contact surface.

Imagine we are facing down-dip while standing on our line of interest where it crosses the 300 ft elevation structure contour of our contact surface. This would be just to the east of where our line of interest crosses the 300 ft topographic elevation contour; we are standing on our line of interest in the very basal section of formation X. To the left, our line of interest can be imaginarily seen tracing a path that is rising gently along the surface of the X - Y contact; to the right descending gently along the contact surface. We already have mapped information on the dip and strike that is useful: the map distance between the 300 and 400 ft structure contours of the contact surface is a run of 400 ft, consequently resulting in an elevation change (rise) of 100 ft. The apparent dip of our line of interest can be determined trigonometrically from the application of this information, and the angle made by the heading of the line of interest with the X - Y contact line of strike. Let's see how.

The line of true dip on our X - Y contact is aligned down-elevation on the X - Y contact plane perpendicular to the strike. From where we stand, we can scribe an imaginary circular arc of radius 400 ft on the map plane that crosses our line of interest and the line of strike defined by the 300 ft elevation structure contour of our contact surface. The radius of the circular arc is the distance of the run used in determining the dip. The angle measured between the line of interest and the line of strike of the X - Y contact surface is 15 deg. This was determined as the difference, in degrees, of their heading alignments. The apparent vertical rise (or fall) of our line of interest along the plane of the X - Y contact will be the sine of the measured angle between the map heading of the line of interest and strike heading of the X - Y contact (sin of 15 deg) times the known vertical rise (100 ft) of the contact true dip. This gives a vertical rise (or fall) of about 26 ft. Taken along a run of 400 ft, the vertical angle is the arctan(26/400), or about 3.7 deg. Along our line of interest, therefore, the magnitude and direction of this apparent dip is 3.7 deg aligned at N 60 deg E. Our map units, therefore, projected onto the vertical plane of the A - A' line of section, would show an apparent dip of about 3.7 deg.

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  • $\begingroup$ You spent a lot of time writing out a cogent process to an answer. Hopefully, the OP will appreciate your effort and acknowledge it. $\endgroup$ Mar 13 at 10:51
  • $\begingroup$ @Thomas Perry thanks again for your help! I appreciate the thoughtful answer. $\endgroup$
    – CH-
    Mar 14 at 3:20

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