Problem Tiga Titik.ppt

TEKNIK GEOLOGI FT-UGM

(Three point problem)

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TEKNIK GEOLOGI FT-UGM

Elev. 3400 ft A Elev. 2400 ft C N B

Elev. 2700 ft 1000 ft

Map showing the location and elevation of three points.

The elevation of the unconformity (or other outcrops) is known at three locations (A, B, and C). We want to find the strike and dip of the unconformity 2

TEKNIK GEOLOGI FT-UGM

Elev. 3400 ft A

Elev. 2400 ft C N

B Elev. 2700 ft 1000 ft

Map showing the location of the line of strike from data in previous slide

The standard approach is graphical solution. The elevation of B is between the elevation at A and C, so a contour passing through B (i.e. the 2700 ft contour). Dividing AC into proportional part according to the elevation differential. 3

TEKNIK GEOLOGI FT-UGM

A Find the dip

C B 1000 ft

Map

Map and cross-section showing true dip from data in previous slide 4

TEKNIK GEOLOGI FT-UGM

Sometimes it is easy to find drafting triangles and a ruler than it is to find the protector First, draw line segments AA’ and CC’ perpendiculars to the line of strike. Second, draw right triangle BDC’ by drawing a vertical line (parallel to the north arrow) through B and a horizontal line segment (perpendicular to the north arrow) through C’. Then measure the distances BD, DC’, AA’, and CC’ and find a calculator. The azimuth of strike ( θ strike) is

 DC '   BD  

 strike  arctan 

A

D ’

and the angle of dip (θ dip) is: B

h h   hA  hA '    arctan  C C '   AA'   CC ' 

 dip  arctan 

C B’ C A’ ’

See next slide

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TEKNIK GEOLOGI FT-UGM

D’ C’

A

N B’

C A’

B 1000 ft

Map showing location of auxiliary lines to calculate strike and dip from arctangents

Graphical solutions take great care. How would you like to have to find the answer to 50 different three point problems ? 6

TEKNIK GEOLOGI FT-UGM

(north) Y

(400, 1200, 3400)

(2200, 900, 2400)

A

C (1000, 200, 2700)

B X (east) The same- three point problem in Cartesian form

Computational Solution

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TEKNIK GEOLOGI FT-UGM

Computational solution The data are in the Cartesian form. We can calculate the xy-location of B and C by using the sine and cosine functions, and thereby have the xyz – location of all three points

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TEKNIK GEOLOGI FT-UGM

(north) Y

A

C

B

X (east) Contours of z on the three-point location

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TEKNIK GEOLOGI FT-UGM

Elevation A 3400

C North 2700

B 1200

2400

900 200

East 400

1000

2200

Three-dimensional context of the representation shown in previous slide

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TEKNIK GEOLOGI FT-UGM

A

y x2, y2 x1, y1

yo

Slope = m

The two-dimensional two-point problem: equation of the straight line in slope- intercept from (A) and in linear – coefficients form (B)

x

B

y x2, y2

yo = - c/b x1, y1

Slope = - a/b

x xo = - c/a 11