Stereographic projection

From Dr Harisingh Gour Central University

1. DR. HARISINGH GOUR VISHWAVIDYALAYA SAGAR (M.P.) (A Central University ) UNDER GUIDENCE OF :- PROF P.K KATHAL & DR GAURAV K SINGH SEMINAR TOPIC : STEREOGRAPHIC PROJECTION DEPARTMENT OF APPLIED GEOLOGY POORVA PANDEY Y1 9251026 Mtech 1 st sem 1

2. CONTENT Content Page no Introduction of stereographic projection 01 -02 Idea about stereonet 03-04 Principle of stereographic projection 05 -06 construction of stereographic 07- 08 projection on stereonet How to plot a plane 09 6) How to plot a lineation 10 how to plot a pole 11 How to plot a plunge 12 Geometrical represation of planer and linear structure 13 About pi and ß diagram 14 stereographic projection of folded surface 15 12) some problems related to stereographic projection 16

3. INTRODUCTION Stereographic projection is a powerful method for solving geometric problems in structural geology. Unlike structure contouring and other map-based techniques, it preserves only the orientation of lines and planes with no ability to preserve position relationships. However, it is extremely useful, as orientation problems are very common in structural geology. Used by crystallographers as a tool for representing variations in crystal form There are several varieties of stereonet available. Wulff net - which is used for the construction of the true, or equal-angle stereographic projection . Schmidt net - which constructs an equal area projection.

4. General idea about stereonet : - FIGURE 1 FIGURE 2

5. Great circle and Pole A plane intersects the sphere in trace that is a great circle that bisects the sphere precisely . A family of planes dipping at various increments is shown in Figure , Planes project as curves that are actually perfectly circular arcs called cyclographic traces or just great circles. Lines project as points or poles. Zenith point. To image features on a sheet of paper, these traces and points are projected from a point at the summit or zenith of the sphere onto the equatorial plane. Principle of stereographic projection

6. A B C A stereonet is a lower hemisphere graph on to which a variety of geological data can be plotted . stereonet are used in many different branches of geology and can be used in a range of ways beyond those which are discussed here ,stereographic projection involves plotting 34D data (planner and linear )on to the 2D surface ,where it can be manipulated and interpreted . Imagine a sphere with lines lattitude and longitude marked on it ,A stereonet is the plane of projection of the lower half of the sphere –it is a lower hemisphere graph Imagine a plane cutting through the centre of a lower hemisphere ( figure A) ,The stereonet forms the surface of this lower hemisphere looking from above where the plane touches the edge of the lower hemisphere is an arc is projected back up on the stereonet to form a great circle ( figure B) and figure C Shows the resulting plot.

7. HOW TO PLOT A PLANE Plot a plane with strike/dip as 090/40S

8. Lineations are measured using plunge/azimuth. Examples:- slickenslide and slicken fiber,fold axis , mineral stretching lineation etc. Plotting a lineation

9. Plotting a pole The pole to a plane is an imaginary line perpendicular to the plane. A stereonet with poles is known as a Pi (π) plot. Plotting a pole to 055/20 SE. ● Mark on the strike reading 055° ● Note which way the plane is dipping, then rotate the tracing paper round until this mark is aligned with north on the stereonet. ● Find the great circle of the plane by counting along the equator from the primitive. Count in from the direction of dip as marked on the tracing paper (in this case SE) along the equator line 20°. ● Count a further 90° through the centre of the net and mark a point – this is the pole to the plane

10. Pi-plots and folds on stereonets Poles are a common way of plotting folded bedding on stereonets. The distribution of poles on the stereonet gives information on the fold’s geometry including estimates of the fold axis and the fold axial plane. In this simple example the beds all have the same strike, it is only their dip that varies round the fold.

11. Fold geometries and the stereographic projections of the folded surface

12. Problems in Stereographic projection Apparent dip of a bed is 26 degreeNE on a cliff trending N60degreeE.The same bed has an apperent dip of 19degree SW on a cliff trending N10degreeE. Find the strike and true dip of the bed.

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14. An ore body occures in the plunging trough formed by a basic dyke crossing a limestone layer. The limestone strikes N20degree E and dips 20degreeW. The dyke strikes N15degreeW and dips 65degreeW. Find the orientation and plunge of the ore body and its pitch on bothe vein and the bed .

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16. A set of homoclinal bed ids dipping 60 degree 048degree within which the foreset laminae of cross bedding dips 40 degree 084degree. If the original dip direction of foreset laminae give the direction of palaeocurrent, findout original direction of palaeocurrent.

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18. Lisle,R.J,and Leyshon,P.R (2004),Stereographic projection Technique for Geologists ad Civil Engineers.(2 nd edition) Cambridge Publication. Jain .A.K (2014) ,an Introduction to Structural Geology( 1 st edition) Geological Society of india , p.p 41-54 Marshak .S. Mitra G(1985) , Basic method of Structural Geology, prentice hall publication new jersey . p.p 87-192 . Roy ,A.K , (2009) ,Introduction to Geological Map and Structure, 3 rd edition ,the world press private limited , p.p 149-173 Fossen Haakon (2010),Structural Geology 1 st year of publication REFERENCES

19. Conclusion In engineering geology project require stable slope ,which are dependent upon the orientation of planer structure and their relation with angle and direction of slope . Invaluable tools in determining attitude of ancient paleodepositional bedding which needed to established other significant geological data . It is helpful in plotting pi and β diagram hence guessing form of fold, We find many undersurface bedding , folding, faulting etc ,which could be analysed by finding its attitude with the help of stereographic projection. We can plot many data in one place in any time and can find interrelated attitude, so it is helpful in saving time and making many structural problem easy.

20. Thank you