CLASS 2: ATTITUDES OF LINES AND PLANES

LAB 1: ATTITUDES OF LINES AND PLANES

Hand in complete solutions to Exercises 1.1-1.9.

Due no later than 1pm Monday, September 18

A. Graphical Solutions for determining structural attitudes:

To derive true dip from a strike and apparent dip.

1.Draw the strike line

2.Knowing the apparent dip direction (ADD), draw the true dip direction (TDD)

3.Draw the ADD as a hypotenuse between the strike and TDD

4.Draw the apparent dip angle (a ) to the ADD, from the point of intersection with strike towards the intersection of the TDD and ADD

5.Measure a depth “D” perpendicular to the ADD, from the TDD/ADD intersection point to the apparent dip plane.

6.Scale the same depth “D” perpendicular to the TDD, from the intersection of the TDD and ADD.

7. Draw in the hypotenuse in a triangle formed by “D” depth and the TDD.

8.Measure the true dip angle (d) between the hypotenuse and the TDD.

To derive a true dip from apparent dips in two different vertical planes:

1.Draw in the two apparent dips

2.Pick two equal “D” depth normal to each apparent dip direction (ADD).

3.Connect two points of equal D; thus, constructing a strike line

4.True dip direction is perpendicular to strike line.

5.At point of intersection between strike and true dip direction (TDD), draw in “D” depth along the strike line

6. Measure the true dip angle formed by the triangle formed by the intersection of the two ADDs and the TDD, to the TDD and strike intersection, and the D depth measured along the strike line.

To derive apparent dip angle from true dip and apparent dip direction:

1.Draw the true dip

2.Draw the apparent dip direction

3.Draw a strike which intersects the true dip and apparent dip direction

4.True dip angle has a “D” depth at point intersecting the strike

5.Draw the same “D” depth where the apparent dip direction intersects strike

6. Measure the apparent dip angle.

Given true dip, solve for apparent dip angle in a given direction:

1.Scale true dip angle; e.g., cot 17=3.27 in true dip direction

2.Draw a strike line

3.Draw in the apparent dip direction to intersect the strike line

4.Measure the apparent dip direction length

5.Compute the inverse cotangent to determine apparent dip angles

C. Trigonometric  Solutions:

To determine true dip from a strike and apparent dip:

                Tan d=    Tan a

                                Sin b.

To determine the true dip angle (plunge) from the apparent dip and TDD:

                Tan d=    Tan a

                                Cos f.

To determine the apparent dip angle (plunge) from the true dip:

                Tan a = (Cos f)(Tan d)

To determine the true dip direction from two apparent dip angles (plunges):

                Tan f₁ = Csc (q₁-q₂) ((Cot a₁) (Tan a₂) – Cos (q₁-q₂))

TRIGONOMETRIC SYMBOLS:

a             (alpha)    Plunge of apparent dip (apparent dip angle)

b              (beta)      Horizontal angle between the strike of a plane and the

                                trend of the apparent dip (ADD)

d              (delta)     Plunge of true dip (true dip angle)

q              (theta)    Direction (trend) of apparent dip

f              (phi)        Horizontal angle between trend of true dip (TDD) and the

                                trend of the apparent dip (ADD)

TRIGONOMETRIC FUNCTIONS:

Sine =         opposite / hypotenuse           Sin values range from 0-1

Cosine =     adjacent / hypotenuse            Cos values range from 0-1

Tangent =     opposite / adjacent               Tan values range from 0 to infinity

Cotangent =    adjacent / opposite              Cot values range from 0 to infinity

Secant =       hypotenuse / adjacent            Secant always >1

Cosecant =   hypotenuse  / opposite          Cosecant always >1

Cosine=       1/Secant

Sine=          1/Cosecant

Tan=          1/Cotangent

                                        Adjacent
                                 d

                                                           Opposite

                         Hypotenuse

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