Structural Geology 3443 Lab 4 Dimension Calculations

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Structural Geology (3443)Lab 4 Dimension
Calculations
Department of Geology University of Texas at
Arlington
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Dimension Calculations

• It is often necessary to predict the following
• How deep a layer will be at a certain location on
  the surface
• How thick a layer is
• The area and volume of a layer
• The offset along a fault.

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Depth to a layer in a vertical hole
This problem assumes we know the attitude of a
planar layer and a location of a point on that
layer. The layer crops out at point O with an
attitude of 360, 30 A well is drilled at J, 100M
West of O. How deep do we have to drill to
encounter the layer?
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Depth to a layer in a vertical hole
Easy problem Depth JT OJ tan f
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Depth to a layer in a vertical hole
More difficult problem Direction of well not in
dip direction Layer crops out at O with an
attitude of 360, 30 Well is drilled at K, 139M at
310o from O Draw line OK Draw line through K
parallel to the strike
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Depth to a layer in a vertical hole
Draw line OJ in the dip direction perpendicular
to strike Flip up OJT and construct triangle
knowing dip (f) (not shown) Measure length of
line JT. JT KM, the well depth to layer. Trig
Depth KM JT (OK cosb)(tanf)
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Depth to a layer in a vertical hole
More Difficult Ground surface not
horizontal Layer at O 360,30 Well 104M up
slope from O Slope angle D /-30 in direction
of dip Flip up cross section and construct
triangles NOT and NOJ Measure JT, depth of well
to layer
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Depth to a layer in a vertical hole
Layer at O 360,30 Well 104M up slope from
O Slope angle D /-30 in direction of dip Trig
Solution Depth JT OJcosD Tanf /- SinD
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Depth to a layer in a vertical hole
More complicated sloping surface well not
perpendicular to strike. Layer attitude 360,
30 Bearing and distance to well 310,
100M Surface slope /- 15
Trig Solution Depth KM OK(cosD cosb tanf)
/- sinD
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Depth to a layer in an inclined hole
More complicated drill hole inclined down-dip,
horizontal surface Layer attitude 360, 30 Well
spudded 105m from pt N in direction 318 Well
drilled along line trending 300 and plunging
50 How long is the drill hole when it hits the
layer?
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Depth to a layer in an inclined hole
Step 1 make map with pt N, the strike line
through pt N, and location of well at pt O. Step
2 Draw line QOJ parallel to trend of drill
hole. Step 3 calculate apparent dip in
direction of QOJ and well d arctantanf
cosb Step 4 Flip up section along QOJ Step 5
construct lines QS OT knowing d and W Step 6
Lines QS OT intersect at J. Measure OJ, the
length of the drill hole.
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Depth to a layer in an inclined hole
Trig Method OJ OG/cosW tanW sina
tanf And, OG OQ tan d
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Depth to a layer in an inclined hole
More complicated drill hole Inclined up-dip,
horizontal surface Layer attitude 360, 30 Well
spudded 215m from pt N in direction 307 Well
drilled along line trending 120 and plunging
30 How long is the drill hole when it hits the
layer?
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Depth to a layer in an Inclined hole
Step 1 make map with pt N, the strike line
through pt N, and location of well at pt C. Step
2 Draw line QOC parallel to trend of drill
hole. Step 3 calculate apparent dip in
direction of QOC and well d arctantanf
cosb Step 4 Flip up section along QOC Step 5
construct lines QJ CE knowing d and W Step 6
Lines QJ CE intersect at E. Measure CE, the
length of the drill hole.
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Depth to a layer in an Inclined hole
Trig Method CE CJ/cosW tanW sina
tanf And, CJ CQ tan d
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Calculation of Layer Thickness
Layer thickness is the perpendicular thickness
between two parallel layer boundaries. If the
layer boundaries are not parallel, layer
thickness is defined as an average value.
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Calculation of Layer Thickness
Thickness is commonly measured using a Jacob
Staff, tape and compass traverse, or a drill hole.
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Jacob Staff
The Jacob staff is ruler 5 long or 2m. It must
be held perpendicular to the layer boundaries, so
the strike dip of the layers must be known.
Jacob staff is used at field camp so you should
learn how to use it in the strat lab.
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Traverse
The traverse method measures the distance between
layer bounradies along the surface and then
converts that measurement to thickness.
We will learn to make a traverse over spring
break.
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Traverse
The simplest traverse is on a horizontal surface
perpendicular to strike (in the dip direction).
The traverse measures distance OT in Fig 4.8. The
layer thickness (TB) is TB OT tanf
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Traverse
The next simplest traverse is on a horizontal
surface oblique to strike. The traverse measures
bearing distance of OK. Knowing the strike, can
determine a, so depth is TB OK sina sinf
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Traverse
A more complicated and more common case is when
the traverse is on a sloping surface
perpendicular to strike. Three case must be
distinguished Traverse in dip direction slope
(D) dip direction slope (D) dip (f) TB OT
sin(D - f) Traverse in dip direction slope (D)
dip (f) TB OT sin(D f)
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Traverse

• The most complicated case is when the traverse is
  on a sloping surface oblique to strike.
• OT is the traverse
• D slope of the traverse
• Dashed lines OXY are on a horizontal plane.
• angle between strike and the traverse bearing
• Trig formula

TB TB TX XB OT(cosD)(sina)(sinf)
(sinD)(cosf)
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Thickness from Drill Holes
The Simplest case is a vertical drill hole
intersecting a dipping layer. In this case, the
thickness is TB OT(cosf)
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Thickness from Drill Holes
The Usual case is an inclined drill hole
intersecting a dipping layer. ML is the inclined
drill hole MK is the trend (bearing) if the
inclined drill hole PK is the dip direction TB is
the layer thickness KL, LT TL are all distances
that must be calculated to get TB, the
thickness. D plunge of drill hole a angle
between strike trend of drill hole f dip of
layer
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Thickness from Drill Holes
Trig formula TB ML(sinD cosD cosa tana
tanf)sin(90-f) This can be simplified to TB
ML(sinD cosD sina tanf) (cosf)
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Fault Slip
Fault Slip can only be measured form the offset
of a line cut by the fault. In this case, the
line is the intersection of a dike (thick lines)
with a layer (thin lines)
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Fault Slip
The fault plane is 290, 90 The dike is 160,
40 The layer is 030, 70
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Fault Slip
The first step is to determine the apparent dip
of the dike and layer on the plane of the fault.
Remember, d arctan(tanf cosb)
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Fault Slip
The next step is to draw the fault plane showing
the dike and layer interseting the fault. The
dike and layer on the north side intersects at
different places than than the dike and layer
from the south side.
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Fault Slip
The arrow shows the displacement of the line
formed by the intersection of the two surfaces
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Area of a dipping plane
The Example is a layer with SD of 020, 40
outcropping at A The layer is bounded by faults
YN and XM Need to find the area of the layer from
the surface at XY to a depth of 200m.
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Area of a dipping plane
Step 1 find the area of the layer projected
onto the horizontal plane Flip up the triangle
showing the dip and find PK Tanf KK/PK Draw
line WZ showing the 200m depth projected onto the
horizontal.
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Area of a dipping plane
Fine the area of XYZW using the rectangle and two
triangles
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Area of a dipping plane
The area of a surface can be represented by a
vector. The length of the vector is surface area.
The direction of the vector is perpendicular to
the surface. The area of the dipping surface is
the vector AL The vector of its projection onto
the horizontal is AH
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Area of a dipping plane
We have calculated AH so AL AH/cosf