Structural Geology
How to locate the projection of a directed line with a stereonet
1. Mark the compass direction of the bearing of the line on the outside border. 2. Rotate the overlay until the point marked coincides with the N-S or E-W axis 3. Measure inward from the edge the number of degrees of the plunge of the line 4. This point is the projection of the directed line Note: A directed line may represent an apparent dip, an intersection of two planes, or the bearing and plunge of a line.
How to plot a plane on a stereonet
1. Mark the strike of the plane on the overlay at the outside border. 2. Rotate the overlay until the mark coincides with the N-S axis. 3. Count inward from the edge at the E-W axis the amount of dip. 4. Trace the great circle. 5. This is the plot of the plane. A horizontal plane is represented by a circle that describes the outside edge of the stereonet A vertical plane is a line straight through the center of the stereonet in whatever orientation the strike is Any dipping beds are arcs represented by the great circles which have been rotated to the direction of strike
How to determine apparent dip of a plane in any direction with a stereonet
1. Plot the plane 2. Rotate the overlay back to north 3. At the outside edge of the stereonet mark the compass direction in which you wish to know the apparent dip 4. Draw a line through the center of the stereonet to this point. 5. Rotate the overlay until this point falls on the E-W or N-S axis. 6. Count inward from the edge to this point to determine the apparent dip
How to determine which direction(s) on a plane an apparent dip of a given value will be found
1. Plot the plane 2. Rotate the overlay until the number of degrees between the arc representing the plane and the E-W axis equals the apparent dip value. Mark the point. 3. Draw a line from the center of the stereonet to the edge through this point. 4. Rotate the overlay back to north 5. Read the orientation of the line drawn. This is one apparent dip direction. Repeat to find the other apparent dip direction. Note: A given value of apparent dip will be located on a plane in two apparent dip directions
How to determine the bearing and plunge of the line of intersection between two planes
1. Plot the planes on the stereonet. 2. Draw a line from the center of the stereonet to the edge through the intersection of the two planes. 3. Rotate the overlay until the intersection lies on the E-W or N-S axis. 4. Count the degrees from the edge to the point of intersection to determine the plunge of the line 5. Rotate the overlay back to north and determine the bearing by reading off the orientation from the edge of the stereonet.
How to determine the true strike and dip of a plane from two apparent dips
1. Plot the projection of both apparent dips as directed lines. 2. Rotate the overlay until both apparent dips lie on the same grate circle 3. Trace the great circle - this is the plot of the structural plane 4. Count inward from the E-W axis to obtain the dip. 5. Rotate the overlay back to north and read the strike orientation at the outside edge.
Inclination
A general term for the vertical angle between the horizontal and a plane or line, measured downward
Fold Line
A hinge line along which a vertical cross section may be constructed and then flattened out to a horizontal or map view
Directed Line
A line described by its bearing and plunge
Pole
A line perpendicular to a plane, and represented as a point on a stereographic projection
Stereonet
A representation of angular relationships between planes and line. In structural geology, a stereonet is synonymous with Wulff net, an equal angle stereographic projection
Depth Determination: Case 2, Graphic Method
A shale is overlain by a water-bearing sandstone (structural map + topographic map provided). Both formations strike N70°E and dip 22°SE. If a well is drilled at point X (shown in the sandstone outcrop boundaries), at what depth would the shale be encountered? 1. On the map draw the strike through point X. 2. Draw a line perpendicular to strike from X to the contact between the bottom of the sandstone and the top of the shale. The length of this line is the traverse distance m. Measure m at the scale of the map. 3. Prepare a cross section along the dip direction (=traverse direction). Draw m to scale. Even though the ground is sloped, m is drawn and measured as a horizontal distance. 4. Measure the elevation difference between X and the lower sandstone contact and draw it to scale 5. Draw in the dip angle line from the lower elevation marking the top of the shale bed/traverse line in the cross section. This line is the contact between the bottom of the sandstone and the top of the shale. 6. Measure the vertical distance from X down to the sandstone-shale contact. This is the depth.
Stereonet basics
A stereonet represents the lower half of a sphere. All projections of lines and planes intersect the lower hemisphere. Planes are always represented as lines or arcs and lines are shown as points.
Preferred Graphic Method of Dip Determination
Cross Section Method Graphic solutions for dip are always drawn AT THE SCALE OF THE MAP Three points on a plane are given A = 130 ft B = 130 ft C = 90 ft Draw a cross section to obtain the dip of the plane represented by the three points 1. Points A and B are at the same elevation. A line connecting these two points is the strike. Draw the strike. 2. From the strike draw a perpendicular line through the low point (C). This is the dip direction and a fold line. 3. Draw a line parallel to the strike through the low point (C). 4. Find the difference in elevation between the low and high points: 130-90 = 40 ft 5. Along the parallel line in C, measure 40 ft from point C using the scale of the map. This is point X. 6. Draw a line connecting point X with the intersection of the strike and dip direction lines (between A and B). 7. Measure the angle formed between the dip direction and the bed. This is the dip.
Apparent Dip/True Dip Problems
Deal with determining the relationship between apparent dip, true dip, and strike. α = apparent dip 𝛿 = dip β = angle between strike and apparent dip direction Trigonomic methods or steronet methods are best for these problems.
Bed thickness: Case 2, Graphic Method
Determine the true thickness of a sandstone bed shown in map view. The sandstone has an attitude of N70°E, 22°SE Draw a vertical cross section along the dip direction. 1. Draw a line in the dip direction connecting either side of the sandstone layer. 2. Read elevations of the contours at both ends of the traverse (1040 ft and 1340 ft) and draw elevation difference (v) to scale. (no vertical exaggeration) 3. Measure distance of the traverse. This is I. 4. Should have a right triangle with the hypotenuse showing the slope of the ground surface. 5. Measure dip angle (22°) and draw in the sandstone bed dipping in the correct direction from each of the two outcrop points on the slope. 6. Draw a line perpendicular to the bounding edges of the sandstone bed. This line is the thickness (t) and its value can be measured directly from the scaled drawing.
Depth Determination Problems
Determining the vertical depth to a particular strata Depth problems vary based on two things: Is the ground horizontal or sloping? And is the distance from the outcrop measured perpendicular to strike or at some other angle?
Fold Line Concept
Dip direction is perpendicular to strike in the horizontal plane, and true dip can only be measured in the vertical plane that includes the dip direction. These relationships may be visualized by drawing the strike and dip direction on a sheet of paper, then folding the paper along the dip direction line (a fold line) Keeping the part of the paper with the strike line horizontal, the dip can be measured downward from the dip direction line and drawn in the vertical plane created by folding the paper. The fold line also may be created in any apparent dip direction to view the dipping plane in that direction
Bed thickness: Case 1, Mathematical Method
Ground surface is horizontal and outcrop width is measured perpendicular to strike. t = w*sin(𝛿) w = outcrop width on the ground surface measured perpendicular to strike 𝛿 = dip angle
Depth Determination: Case 1, Mathematical Method
Ground surface is horizontal and the ditance on the ground surface from outcrop to location X where depth determination is desired (m) is measured perpendicular to strike along dip direction. d = m*tan(𝛿) 1. Draw the strike, dip direction, and traverse direction in map view. This dip direction and traverse direction from the outcrop to point X coincide. 2. Next draw a cross section view along the traverse direction (=dip direction) and draw the dip angle. The depth (d) is the vertical distance measured from the ground surface to the dipping bed.
Accuracy
How close a measurement conforms with a standard or accepted value Relates to the quality of the result Precision has no meaning unless accuracy is also obtained. For example, if the wrong magnetic declination is set on your Brunton, you may obtain strike values that are very consistent throughout the outcrop with one another and therefore could be considered precise; however they would be inaccurate
Outcrop Pattern Problems
In outcrop pattern problems, one generates on a map the intersection of a bedding surface with the topographic surface. The strike and dip of the bed must be known and be constant, and the assumption is made that the bed is a plane. Not required on the test, but important to understand to interpret information given. Case 1: Beds are horizontal: the outcrop pattern follows the topographic contours on the map because the unit is located everywhere at the same elevation. Outcrop width depends on the thickness of the bed and the steepness of topography. Case 2: Beds are vertical: the beds cut across the topographic contours in a straight line trending in the direction of strike. The outcrop width is the same everywhere regardless of topography Case 3: Beds are inclined: outcrop pattern must be generated by the graphic method.
Strike and Dip Determination.
Many structural geology problems begin with the determination of strike and dip from information presented either on a map or from field notes. Strike and dip of beds may be determined using one or a combination of the following two methods: 1. Graphic or construction 2. Mathematical relationships Usually called a three point problem: involves determining the strike and dip from three points at different elevations on the same structural plane Locations of the points on the map and a map scale must be provided
Graphic Method for generating Outcrop Patterns
On a topographic map, point Z is the top of a sandstone bed. The strike is N70°W, dip 10°S. Plot the outcrop pattern. 1. In the direction of strike, draw a line (A-A') across the map the margins through point Z. 2. Draw a line (B-B') in the dip direction perpendicular to the line A-A'. This is a fold line which will help to visualize the dip direction. 3. At the intersection of A-A' with B-B', measure the dip angle and draw a line C-C'. The dip angle is between B-B' and C-C'. If you fold the paper along the fold line B-B' the dip should look correct visually. 4. From the intersection of A-A' with B-B' , draw a scale along the strike line A-A' equal to the scale of the map and at the same interval as the contour interval. The intersection of A-A' with B-B' has the elevation of point Z. The scale in the direction away from the map represents elevations below point Z; toward the map are elevations above point Z. 5. From the scale marks drawn in step 4, draw lines perpendicular to A-A' that intersect the dip line C-C'. 6. Where each of the elevation lines drawn in step 5 intersects C-C', draw lines parallel to strike that project across the entire map. 7. Where the lines drawn in step 6 intersect their respective contours make a dot. Each dot is where the bed and the topography intersect at the surface. 8. Connect the dots as you draw them - make sure that a contour line is not crossed until the elevation line corresponding to that same contour is intersected.
Apparent Dip Problem, Stereonet Methods
Only way to solve an apparent dip problem given 2 apparent dips but no strike and dip. See other cards re: how to __ with stereonet
Right Triangle Triogonometry
SOHCAHTOA sin α = a/c = opposite side/hypotenuse cos α = b/c = adjacent side/hypotenuse tan α = a/b = opposite side/adjacent side
Convention for Representing the Bearing/Plunge of a Line
Similar to convention 3 for planes. 13°, S51°W would represent a line plunging 13° in the S51°W direction Bearing and plunge of a line cannot be expressed as a strike and dip, because the strike and dip define a plane, and the bearing and plunge represent only a line in the plane Bearing is always noted in the direction of downward plunge
Bed Thickness Problems
Stratigraphic thickness (t) of a geologic unit is the distance between the top and bottom of the unit measured perpendicular to the bounding surfaces. Thickness problems vary based on two things: Is the ground horizontal or sloping? And can an outcrop width be measured perpendicular to strike along the dip direction? In the book they only address those conditions perpendicular to strike along dip direction.
Four Conventions for Representing Attitudes of Planes
Strike N25°W, 15°S 1. N25°W, 15°S : Strike is 25° west of north, dip is 15° to the south. Typical US Convention 2. 155°, 15° : Azimuth is 155° - measured clockwise from north to the direction you would need to face to have the dip down to the right. 3. 15°, S65°W : Inclination is 15°, dip direction has a bearing of 65° west of south (strike is N25°W) 4. 15°, 245° : Dip is 15°, dip direction has a bearing of 245° measured clockwise from north (strike is N25°W)
β
The angle between strike and the apparent dip direction
Slope angle (σ)
The angle from the horizontal down to the slope
Rake (Pitch)
The angle measured in a specified plane, between a line and the horizontal.
Strike
The bearing of a horizontal line in an inclined plane
Trend
The bearing of the vertical plane containing a line
Apparent Dip Direction
The bearing of the vertical plane containing the apparent dip angle
Precision
The degree of agreement or consistency of repeated measurements Related to the quality of the process by which those measurements are obtained. Usually illustrated by the number of decimal places the calculation is carried
Bearing
The horizontal angle between a line and a specified coordinate direction, usually north or south
Apparent Dip (α)
The inclination of a plane measured in a direction NOT perpendicular to the strike
Dip (𝛿)
The inclination of the line of greatest slope of an inclined plane, measured perpendicular to strike
Attitude
The orientation in space
Thickness (t)
The perpendicular distance between the top and bottom of a geologic unit
Projection
The process by which points on one surface are transferred to another surface, such that in each view (map or cross section) the points correspond
Plunge
The vertical angle between a line and horizontal
Depth (d)
The vertical distance from the ground surface downward to a feature of interest
Outcrop Width (w)
The width of an outcrop, as measured on a map view, perpendicular to strike
Strike and Dip Determination Example: General Case, Simplified Graphic Projection (pg 2-5)
Three points A , B, C lie on a structural plane at elevations of 80, 10, and 25 feet respectively. Determine the strike of the bed using the simplified graphic projection method. 1. Draw a line between the high point (A) and the low point (B) This line is an apparent dip direction. 2. From the low point (B) draw a line perpendicular to the line drawn in step 1, away from the mid point (C) 3. Place a scale along the vertical line drawn in step 2. Start at the low point (B) with the elevation of the high point (A) and scale down to the elevation of the low point (B). Use the horizontal scale of the map! 4. Draw a line from the high point (A) to the mark representing the elevation of the low point on the scale line draw in step 3. The line represented the bed in the subsurface along the apparent dip direction. The angle between the fold line drawn in step 1 and the line drawn in step 4 is the apparent dip angle (α) 5. From a mark representing the elevation of the mid point along the vertical scale (=25 ft), draw a line parallel to the fold line until it intersects the bed in the subsurface. 6. The intersection of the line drawn in step 5 with the bed (the line drawn in step 4) is a point on the bed at the elevation of the midpoint. Draw a line from this intersection perpendicular to the fold line. The point on the fold line where this line intersects (X) represents the same elevation as the midpoint in the map view. A line connecting the midpoints on the surface (X to C) will be the strike.
Strike and Dip Determination Example: Special Case, Simplified Graphic Projection (pg 2-7)
Three points on a plane are given, but two of the points are at the same elevation. Find the strike of the bed. A = 175 ft B = 175 ft C = 143 ft 1. Draw a line between the two points at the same elevation (points A and B). The direction of the line is the strike.
Mathematical Method of Dip Determination
To determine the dip mathematically the following equation is used: tan(𝛿) = rise/run The rise is the vertical elevation change usually measured from the strike elevation to the low point elevation. The run is the horizontal or map distance over which the rise occurs.
Apparent Dip Problem, Trigonomic method
tan(α) = tan(𝛿)*sin(β) Requires two of these values to be provided or deduced - does not work if two apparent dips are given but strike and dip are not. A limestone strikes N20°E and dips 85°SE. What is the apparent dip of the limestone along the cross-section line oriented N45°E? 𝛿 is given. β = the difference between N20°E and N45°E = 25°. Apparent dip is unknown. Apply the equation.
