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Unformatted text preview: GEOS 304 – LAB 4 Spring, 2010 Name:_____________________ 3-Point Problems & Orthographic Projections Problem 1 (20 points): Determine the strike, dip, and thickness of a planar bed from the analysis of a geologic map. Visualizing: Study how the map trace of the bed interacts with topography. Visualize the topography and the bed orientation. Is the bed N-dipping or S-dipping? Approximately what angle is the bed dipping at (shallow, steep, moderate)? Determine strike and dip: Accurately determine the strike and dip of the bed. Steps: (1) Connecting two points of equal elevation along the trace of either contact provides the strike for the bed; (2) The map distance and elevation difference, measured perpendicular to the strike line to any point along the other contact, can be used to determine the dip of the bed by using the equation below. You can use either the N contact trace or the S contact trace - they will give the same result. A cross-section sketch is very useful for helping visualize the geometric relationships. You can either (1) draw the cross-section to scale and measure the dip, or (2) using trigonometry. tanθ = opposite/adjacent; tan(dip angle) = elevation difference / map distance. Determine the true thickness: Determine the true thickness of the bed. Procedure: (1) Draw a cross section (perpendicular to strike) across the bed. Include a topographic profile. (2) Mark both the N and S contacts of the bed on the topographic profile of the cross section and extend them to depth using the dip angle that you determined above. (3) Measure the perpendicular distance between the two contacts- true thickness! NOTE: Map scale is in meters (m) Problem 2 (30 points): Use the attached problem 2 map and assume that the base of a planar bed is exposed at points X, Y, and Z. Start off with a sketch from the point with the highest elevation to the point with the lowest elevation. Refer to D&R 684-691. 1) What is the strike and dip of the bed? 2) Construct a structure map of the bed and then show the full outcrop trace of the bed. 3) If the top of the bed is exposed at point W, how thick is the bed? Page 2/9 Page 3/9 Practice with Orthographic Projection On the midterm, you will be asked to use the technique of orthographic projection to determine the slip direction and magnitude across a fault of specified orientation, given the orientation(s) and separation(s) of planar features that are offset across it. This problem set is meant to prepare you for this question. If you have any questions, please contact us! Orthographic projection: 2D line drawings that are used to determine angular and spatial relationships in 3D. The drawings are difficult to visualize at first, because they convert map relationships into mixtures of maps and cross sections. Slip: Slip is the actual relative displacement across a fault. It can be determined by studying offset lines which were originally coincident prior to faulting. Slip vector: Is the direction and magnitude of slip across a fault. Separation: Separation is the distance between the two map traces of a displaced marker plane measured in a specified direction. For example, strike separation is the displacement of a planar feature, measured parallel to the strike of the fault. The magnitude and direction of separation is almost never the same as the magnitude and separation of slip! Rake: The acute angle between the horizontal (strike line) and a line in a plane, as measured in the plane. See page 701 in D&R for determining rake using a stereonet. The Goal: Use the strike separation of planar features across a fault to determine the magnitude and direction of slip across a fault (the slip vector). See D&R 714-716. As the approach is difficult to explain in text, the following is a step-by-step example on how to do this. Example question: Given a fault striking E-W and dipping 55 to the south, and displacing a planar bed and a planar vein as shown in the figure below, determine: (a) The direction (rake) and magnitude of the slip vector (b) The magnitude of the strike-slip component and the dip-slip component of the slip vector (c) What type of fault is it? Page 4/9 Step 1: Two planes intersect at a line. Determine the rake of the intersection line between (1) the bed and the fault, and (2) the vein and the fault. See page 701 in D&R for determining rake using a stereonet. In the plane of the fault, the bed rakes 30 degrees from the east and the vein rakes 50 degrees from the west. Step 2: Draw a map in the plane of the fault (assume that the plane of the paper is dipping 55 degrees to south). The challenge is to imagine what the surface of the fault looks like and the orientations and locations of the intersection lines between (1) the bed and the fault plane, and (2) the vein and the fault plane—on both sides of the fault! Plot the rakes of the vein and bed in the plane of the fault using a protractor. Step 3: Slip is the actual relative displacement across a fault of lines which were originally coincident prior to faulting. The intersection of two planes (between the bed and the vein, for
Page 5/9 example) is a line. This line appears as a point in the plane of the fault. Below, is a point on the northern face (footwall) of the fault, defined by the intersection of the bed and the vein. Step 4: Likewise, the intersection of fault and vein define a point on the south face (hanging wall) of the fault. Step 5: Before faulting, the two points were on top of each other (the intersection line between the vein and bed was continuous across the fault). Therefore, the vector between the two points is the slip vector for the fault. Its direction: Rake is 84 to 85 degrees from the east. The slip magnitude is the length of the line: 1.8 cm (measured with a ruler). Converting to m using the scale provided above, this corresponds to a slip magnitude of 25.7 m. The component of dip slip vs. strike slip can be determined by drawing a right triangle, with the slip vector as the hypotenuse, and directly measuring the lengths of the lines. Or by trigonometry. The fault is a normal fault (hanging wall moves down with respect to footwall) with a small component of left-lateral slip (the sense of slip can be determined by keeping one point on the fault fixed and looking at how the other point moved relative to the fixed point). Page 6/9 Page 7/9 Problems 3) (20 points) The plane of a normal fault strikes due north and dips 60 west. Assume that the normal fault accommodated pure dip-slip motion (the rake of the slip vector is 90 degrees in the plane of the fault). The fault displaces a bed with an attitude of N90W/30N, separating the bed 100m in a left-lateral sense along the strike of the fault. What is the total magnitude of slip? Page 8/9 4) (30 points) A fault with an attitude of N90W/60N cuts a bed and a dike: the bed has an attitude of N45W/30NE; the dike has an attitude of N50E/45NW. The magnitudes and senses of separation are shown in the figure below. What is the rake of the slip vector in the plane of the fault? What is the magnitude of slip? What type of fault is this? Page 9/9 ...
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This note was uploaded on 02/17/2010 for the course GEOS 13245 taught by Professor Kapp during the Spring '10 term at University of Arizona- Tucson.
- Spring '10