Chapter%202.%20Grain%20Texture

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Chapter 2. Grain Texture
Clastic sediment and sedimentary rocks are made
up of discrete particles.
The texture of a sediment refers to the group of
properties that describe the individual and bulk
characteristics of the particles making up a
sediment
Grain Size
Grain Shape
Grain Orientation
Porosity
Permeability
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These properties collectively make up the texture
of a sediment or sedimentary rock.
Each can be used to infer something of
The history of a sediment.
The processes that acted during transport and
deposition of a sediment.
The behavior of a sediment.
This section focuses on each of these properties,
including
Methods of determining the properties.
The terminology used to describe the properties.
The significance of the properties.
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Grain Size
I. Grain Volume (V)
a) Based on the weight of the particle
Where m is the mass of the particle. V is the
volume of the particle. rs is the density of the
material making up the particle. (r is the lower
case Greek letter rho).
1. Weigh the particle to determine m.
2. Determine or assume a density.
(density of quartz 2650kg/m3)
3. Solve for V.
Error due to error in assumed density Porous
material will have a smaller density and less
solid volume so this method will underestimate
the overall volume.
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b) Direct measurement by displacement.
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b) Direct measurement by displacement.
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b) Direct measurement by displacement.
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Accuracy depends on how accurately the displaced
volume can be measured.
Not practical for very small grains.
For porous materials this method will
underestimate the external volume of the particle.
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c) Based on dimensions of the particle.
Where d is the diameter of the particle And the
particle is a perfect sphere.
Measure the diameter of the particle and solve
for V.
Problem natural particles are rarely spheres.
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II. Linear dimensions.
a) Direct Measurement
Natural particles normally have irregular shapes
so that it is difficult to determine what linear
dimensions should be measured.
Most particles are not spheres so we normally
assume that they can be described as triaxial
ellipsoids that are described in terms of three
principle axes
dL or a-axis longest dimension.
dI or b-axis intermediate dimension.
dS or c-axis shortest dimension.
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To define the three dimensions requires a
systematic method so that results by different
workers will be consistent.
Sedimentologists normally use the Maximum Tangent
Rectangle Method.
Step 1. Determine the plane of maximum
projection for the particle.
-an imaginary plane passing through the particle
which is in contact with the largest surface area
of the particle.
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Step 2. Determine the maximum tangent rectangle
for the maximum projection area.
-a rectangle with sides having maximum tangential
contact with the perimeter of the maximum
projection area (the outline of the particle)
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Step 2. Determine the maximum tangent rectangle
for the maximum projection area.
-a rectangle with sides having maximum tangential
contact with the perimeter of the maximum
projection area (the outline of the particle)
dL is the length of the rectangle.
dI is the width of the rectangle.
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Step 3. Rotate the particle so that you view the
surface that is at right angles to the plane of
maximum projection.
dS is the longest distance through the particle
in the direction normal to the plane of maximum
projection.
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The volume of a triaxial ellipsoid is given by
p
dL x dI x dS
V
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For fine particles only dL and dI can be measured
in thin sections.
Thin sections are 30 micron (30/1000 mm) thick
slices of rock through which light can be
transmitted.
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Axes lengths measured in thin section are
apparent dimensions of the particle.
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Axes lengths measured in thin section are
apparent dimensions of the particle.
The length measured in thin section depends on
where in the particle that the plane of the thin
section passes.
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Axes lengths measured in thin section are
apparent dimensions of the particle.
The length measured in thin section depends on
where in the particle that the plane of the thin
section passes.
For a spherical particle its true diameter is
only seen in thin section when the plane of the
thin section passes through the centre of the
particle.
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The three axes lengths that are commonly measured
are often expressed as a single dimension known
as the nominal diameter of a particle (dn)
dn is the diameter of the sphere with volume (V1)
equal the volume (V2) of the particle with axes
lengths dL, dI and dS.
By the definition of nominal diameter, V1 V2
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dn can be solved by rearranging the terms
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dn can be solved by rearranging the terms
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dn can be solved by rearranging the terms
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dn can be solved by rearranging the terms
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b) Sieving
Used to determine the grain size distribution (a
bulk property of a sediment).
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Grains that are larger than the holes remain on a
screen and the smaller grains pass through,
collecting on the screen with holes just smaller
than the grains.
The grains collected on each screen are weighed
to determine the weight of sediment in a given
range of size.
The later section on grain size distributions
will explain the method more clearly.
Details of the sieving method are given in
Appendix I of the course notes.
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III. Settling Velocity
Another expression of the grain size of a
sediment is the settling velocity of the
particles.
Settling velocity (w the lower case Greek letter
omega ) the terminal velocity at which a
particles falls through a vertical column of
still water.
Possibly a particularly meaningful expression of
grain size as many sediments are deposited from
water.
When a particle is dropped into a column of fluid
it immediately accelerates to some velocity and
continues falling through the fluid at that
velocity (often termed the terminal settling
velocity).
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The speed of the terminal settling velocity of a
particle depends on properties of both the fluid
and the particle
Properties of the particle include
The size if the particle (d).
The density of the material making up the
particle (rs).
The shape of the particle.
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a) Direct measurement
Settling velocity can be measured using settling
tubes a transparent tube filled with still water.
In a very simple settling tube
A particle is allowed to fall from the top of a
column of fluid, starting at time t1.
The particle accelerates to its terminal velocity
and falls over a vertical distance, L, arriving
there at a later time, t2.
The settling velocity can be determined
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A variety of settling tubes have been devised
with different means of determining the rate at
which particles fall. Some apply to individual
particles while others use bulk samples.
Important considerations for settling tube design
include
Otherwise, settling velocity will be
underestimated.
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ii) Tube diameter the diameter of the tube must
be at least 5 times the diameter of the largest
particle that will be passed through the tube.
If the tube is too narrow the particle will be
slowed as it settles by the walls of the tube
(due to viscous resistance along the wall).
iii) In the case of tubes designed to measure
bulk samples, sample size must be small enough so
that the sample doesnt settle as a mass of
sediment rather than as discrete particles.
Large samples also cause the risk of developing
turbulence in the column of fluid which will
affect the measured settling velocity.
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b) Estimating settling velocity based on particle
dimensions.
Settling velocity can be calculated using a wide
variety of formulae that have been developed
theoretically and/or experimentally.
Stokes Law of Settling is a very simple formula
to calculate the settling velocity of a sphere of
known density, passing through a still fluid.
Stokes Law is based on a simple balance of
forces that act on a particle as it falls through
a fluid.
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FB, the buoyant force which opposes the gravity
force, acting upwards.
FD, the drag force or viscous force, the
fluids resistance to the particles passage
through the fluid also acting upwards.
Force (F) mass (m) X acceleration (A)
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FG depends on the volume and density (rs) of the
particle and is given by
FB is equal to the weight of fluid that is
displaced by the particle
FD is known experimentally to vary with the size
of the particle, the viscosity of the fluid and
the speed at which the particle is traveling
through the fluid.
Viscosity is a measure of the fluids
resistance to deformation as the particle
passes through it.
Where m (the lower case Greek letter mu) is the
fluids dynamic viscosity and U is the velocity
of the particle 3pd is proportional to the area
of the particles surface over which viscous
resistance acts.
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The net gravity force acting on a particle
falling through the fluid.
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We now have two forces acting on the falling
particle.
Acting downward, causing the particle to settle.
Acting upward, retarding the settling of the
particle.
What is the relationship between these two forces
at the terminal settling velocity?
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Stokes Law is based on this balance of forces.
Such that
The settling velocity can be determined by
solving for U, the velocity of the particle, so
that U w. Therefore
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Rearranging the terms
Stokes Law of Settling
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Example
A spherical quartz particle with a diameter of
0.1 mm falling through still, distilled water at
20C
rs 2650kg/m3
r 998.2kg/m3
d 0.0001m
m 1.005 10-3 Ns/m2
g 9.806 m/s2
Under these conditions (i.e., with the values
listed above) Stokes Law reduces to
For a 0.0001 m particle w 8.954 10-3 m/s or
9 mm/s
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Stokes Law has several limitations
i) It applies well only to perfect spheres (in
deriving Stokes Law the volume of spheres was
used).
The drag force (3pdmw) is derived experimentally
only for spheres.
Non-spherical particles will experience a
different distribution of viscous drag.
ii) It applies only to still water.
Settling through turbulent waters will alter the
rate at which a particle settles upward-directed
turbulence will decrease w whereas
downward-directed turbulence will increase w.
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iii) It applies to particles 0.1 mm or finer.
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iii) It applies to particles 0.1 mm or finer.
Coarser particles, with larger settling
velocities, experience different forms of drag
forces.
Stokes Law overestimates the settling velocity
of quartz density particles larger than 0.1 mm.
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When settling velocity is low (dlt0.1mm) flow
around the particle as it falls smoothly follows
the form of the sphere.
Drag forces (FD) are only due to the viscosity of
the fluid.
Pressure forces acting on the sphere vary.
Negative pressure in the lee retards the passage
of the particle, adding a new resisting force.
Stokes Law neglects resistance due to pressure.
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iv) Settling velocity is temperature dependant
because fluid viscosity and density vary with
temperature.
0 1.792 10-3 999.9 5
100 2.84 10-4 958.4 30
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Grain size is sometimes described as a linear
dimension based on Stokes Law
Stokes Diameter (dS) the diameter of a sphere
with a Stokes settling velocity equal to that of
the particle.
Set d dS and solve for dS.
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IV. Grade Scales
Grade scales define limits to a range of grain
sizes for a given class (grade) of grain size.
Sets most boundaries to vary by a factor of 2.
They provide a basis for a terminology that
describes grain size.
e.g., medium sand falls between 0.25 and 0.5 mm.
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Sedmentologists often express grain size in units
call Phi Units (f the lower case Greek letter
phi).
Phi units assign whole numbers to the boundaries
between size classes.
To make Phi dimensionless it was later defined as
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Phi is the negative of the power to which 2 is
raised such that it equals the dimension in
millimetres.
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Note that when grain size is plotted as phi units
grain size becomes smaller towards the right.
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V. Describing Grain Size Distributions
a) Grain Size Data
Data on grain size distributions are normally
collected by sieving.
1. Grain Size Class (f) 2. Weight (grams) 3. Weight () 4. Cumulative Weight ()
-0.5 0.40 1.3 1.3
0 1.42 4.6 5.9
0.5 2.76 8.9 14.8
1.0 4.92 15.9 30.7
1.5 5.96 19.3 50.0
2.0 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3.0 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4.0 0.40 1.3 100
Total 30.92 100
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1. Grain size class the size of holes on which
the weighed sediment was trapped in a stack of
sieves.
2. Weight (grams) the weight, in grams, of
sediment trapped on the sieve denoted by the
grain size class.
1. Grain Size Class (f) 2. Weight (grams) 3. Weight () 4. Cumulative Weight ()
-0.5 0.40 1.3 1.3
0 1.42 4.6 5.9
0.5 2.76 8.9 14.8
1.0 4.92 15.9 30.7
1.5 5.96 19.3 50
2.0 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3.0 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4.0 0.40 1.3 100
Total 30.92 100
3. Weight () the weight of sediment trapped
expressed as a percentage of the weight of the
total sample.
4. Cumulative Weight () the sum of the weights
expressed as a percentage (column 3).
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Each value in column 4 is the percentage of the
sample that is coarser than the screen on which
the sediment was trapped.
1. Grain Size Class (f) 2. Weight (grams) 3. Weight () 4. Cumulative Weight ()
-0.5 0.40 1.3 1.3
0 1.42 4.6 5.9
0.5 2.76 8.9 14.8
1.0 4.92 15.9 30.7
1.5 5.96 19.3 50
2.0 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3.0 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4.0 0.40 1.3 100
Total 30.92 100
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Each value in column 4 is the percentage of the
sample that is coarser than the screen on which
the sediment was trapped.
1. Grain Size Class (f) 2. Weight (grams) 3. Weight () 4. Cumulative Weight ()
-0.5 0.40 1.3 1.3
0 1.42 4.6 5.9
0.5 2.76 8.9 14.8
1.0 4.92 15.9 30.7
1.5 5.96 19.3 50
2.0 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3.0 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4.0 0.40 1.3 100
Total 30.92 100
30.7 of the total sample is coarser than 1.0 f.
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Each value in column 4 is the percentage of the
sample that is coarser than the screen on which
the sediment was trapped.
1. Grain Size Class (f) 2. Weight (grams) 3. Weight () 4. Cumulative Weight ()
-0.5 0.40 1.3 1.3
0 1.42 4.6 5.9
0.5 2.76 8.9 14.8
1.0 4.92 15.9 30.7
1.5 5.96 19.3 50
2.0 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3.0 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4.0 0.40 1.3 100
Total 30.92 100
30.7 of the total sample is coarser than 1.0 f.
85.2 of the total sample is coarser than 2.5 f.
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b) Displaying Grain Size Data
Readily shows the relative amount of sediment in
each size class.
Each bar width equals the class interval (0.5 f
intervals in this case).
Bars extend from the maximum size to the minimum
size for each size class.
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ii) Frequency Curves
A smooth curve that joins the midpoints of each
bar on the histogram.
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iii) Cumulative Frequency Curves
A smooth curve that represents the size
distribution of the sample.
Several curves for different samples can be
plotted together on one diagram for comparison of
the samples.
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Sedimentologists commonly plot cumulative
frequency curves on a probability scale for the
cumulative frequency.
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Plots of samples which are made up of normally
distributed subpopulations plot as a series of
straight line segments, each segment representing
a normally distributed subpopulation.
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Plots of samples which are made up of normally
distributed subpopulations plot as a series of
straight line segments, each segment representing
a normally distributed subpopulation.
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A benefit of cumulative frequency plots is that
percentiles can be taken direction from the graph.
fn is the grain size that is finer than n of the
total sample.
fn is referred to as the nth percentile of the
sample.
0.86f is that grain size that is finer than 20
of the sample.
Conversely, 0.86f is coarser than 80 of the
sample.
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c) Describing Grain Size Distributions.
Folk and Ward (1957) introduced the Graphic
Method to estimate the various statistical
parameters describing a grain size distribution
using only percentiles taken from cumulative
frequency curves.
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i) Median (Md)
The midpoint of the distribution the 50th
percentile.
50 of the sample is finer than the median and
50 of the sample is coarser than the median.
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ii) Mean (M)
The arithmetic average of the distribution.
If the distribution is purely symmetrical M Md.
The Udden-Wentworth Scale is used to define terms
to describe the sediment based on the mean size.
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Example calculation of the Mean
1. Determine f16, f50and f84
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Example calculation of the Mean
1. Determine f16, f50and f84
f16 -0.59f
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Example calculation of the Mean
1. Determine f16, f50and f84
f16 -0.59f
f50 0.35f
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Example calculation of the Mean
1. Determine f16, f50and f84
f16 -0.59f
f50 0.35f
f84 1.27f
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Example calculation of the Mean
1. Determine f16, f50and f84
f16 -0.59f
f50 0.35f
f84 1.27f
0.34f
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iii) Standard Deviation (s lower case Greek
letter sigma)
Also referred to as the sorting coefficient or
dispersion coefficient of a sediment.
The units of sorting are phi units.
A measure of how much variation in grain size is
present within a sample.
E.g., M 0.34f and s 0.75f
68 of the sample falls in the range from -0.41
to 1.09f.
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Sedimentologists use a specific terminology to
describe the sorting of a sediment
Very well sorted 0 lt s lt 0.35f
Well sorted 0.35 lt s lt 0.50f
Moderately well sorted 0.5 lt s lt 0.71f
Moderately sorted 0.71 lt s lt 1.00f
Poorly sorted 1.00 lt s lt 2.00f
Very poorly sorted 2.00 lt s lt 4.00f
Extremely poorly sorted s gt 4.00f
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Examples of sorting
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iv) Skewness (Sk)
A measure of the symmetry of the distribution.
Values range from 1.0 to 1.0.
Perfectly symmetrical.
Md M
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Sk gt 0
The distribution has more fine particles than a
symmetrical distribution would have.
The distribution is said to be fine tailed.
M is finer than Md
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Sk lt 0
The distribution has more coarse particles than a
symmetrical distribution would have.
The distribution is said to be coarse tailed.
M is coarser than Md
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Terminology
Sk gt 0.3 strongly fine skewed
0.1 lt Sk lt 0.3 fine skewed
-0.1 lt Sk lt 0.1 near symmetrical
-0.3 lt Sk lt -0.1 coarse skewed
Sk lt -0.3 strongly coarse skewed
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v) Kurtosis (K)
A measure of the peakedness of the distribution
(related to sorting).
K 1 normal (Mesokurtic)
K lt 1 flat peaked (Platykurtic)
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VI. Implications of Grain Size
Grain size is a fundamental property of any
granular material.
It influences other fundamental properties.
Historically it was hoped that ancient
depositional environments could be determined on
the basis of grain size and grain size
distributions.
When drilling wells (oil, gas, water) the most
abundant samples are small pieces of rock called
drill chips.
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Anatomy of a Rotary Drilling Rig
Drill bit Boron alloy buttons /- diamond grit.
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Anatomy of a Rotary Drilling Rig
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Mud is pumped through the drill string to the
bit as the mud rises to the surface it carries
drill chips along with it.
Drill Chips
1 to 5 millimetre diameter pieces of rock.
Collected and bagged as the mud brings the chips
to the surface.
1 sample bag represents 3 metres of drilled rock.
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One attempt to distinguish depositional
environments on the basis of grain size
distribution focused on beach versus river sands.
Samples were collected from rivers and beaches
(both lake and ocean beaches) and Skewness was
plotted against Sorting Coefficient.
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Beaches tend to have sands that are better sorted
and with more common coarse tail skewness than
river sands.
This reflects the difference in processes that
act in rivers and beaches.
Rivers transport a wide range of grain sizes
large particles move in contact with the bed and
large volumes of fine particles are carried in
suspension in the current.
Their deposits tend to be relatively poorly
sorted and rich in fine particles (ve or fine
tailed skewness).
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Beaches experience repeated swash and backwash of
waves running up the beach face.
The repeated action of the currents washes fine
sand from the beach (improving its sorting) and
leaving larger grains behind (causing coarse tail
skewness).
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The difference in processes acting on beaches and
in rivers results in distinct differences in
their grain size distributions.
Other attempts to apply this method had limited
results.
The problem is that grain size distribution can
be inherited from the source material that makes
up the sediment.
If a beach forms on ancient river sediments then
the beach deposits will inherit characteristics
of river deposits.
If a river erodes through ancient beach deposits
then its sediment will bear the characteristics
of beach sediments.
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In rivers it has been found that, overall,
sorting of a sediment improves with the distance
of transport.
The longer the distance of transport the greater
the opportunity to remove fine material (in
suspension) and to leave coarser material behind,
reducing the range of grain sizes present
(improving the sorting and decreasing the sorting
coefficient).
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Why measure Grain Size?
1. It is a fundamental property of any granular
material.
2. It influences a variety of other properties.
3. It gives clues to the history of a sediment
(more details later in the course).
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Grain Shape
An individual property (rather than a bulk
property) that is as fundamental as grain size.
Shape can be described in a variety of ways
Roundness a description of how angular the edges
of a particle are.
Sphericity how closely a particles shape
resembles a sphere.
Form the overall appearance of a particle.
Surface texture scratches, pits, grooves, etc.
on a particles surface.
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I. Roundness
Several methods of description some more
practical than others.
a) Wadells Roundness (RW)
Time consuming and very impractical but results
are reliable.
RW the ratio of the average radius of curvature
of the corners on the surface of a grain to the
radius of curvature of the largest circle that
can be inscribed within the projection of the
particle.
RW approaches 1 for a perfectly round particle.
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b) Dobson and Fork Roundness (RF)
RF the ratio of the radius of curvature of a
particles sharpest corner (r) to the radius of
curvature of the largest circle that can be
inscribed on the projection of the particle (R).
c) Powers visual comparison chart.
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The most commonly used method of determining
roundness.
Defines terms for describing roundness.
e.g., 0.25 lt RW lt0.35 is termed sub-angular.
Also gives a shape parameter (r) which is a
logarithmic transformation of RW so that the
boundaries between roundness classes are whole
numbers.
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II. Sphericity
A measure of how closely a particle resembles a
sphere.
Usually denoted by Y, the capital Greek letter
psi.
A measure of sphericity is useful to determine
whether or not Stokes Law of settling is
applicable (e.g., how much a particle differs
from a sphere).
Sphericity determines the use of a sediment
(e.g., high sphericity sediment is not
particularly good for making concrete).
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a) Wadells Sphericity (Y)
Y the ratio of the diameter of a sphere with the
same volume as the particle to the volume
diameter of a sphere that will circumscribe the
particle.
There are a couple of methods of determining Y.
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i) Based on volume measurement.
Step 1. Measure the volume of the particle by
displacement in water in a graduated cylinder.
This determines VS.
Step 2. Measure the long axis of the particle
(dL) as this will be the diameter of the largest
circumscribing sphere.
By this procedure
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ii) Approximate VS by assuming that the particle
is a triaxial ellipsoid.
By either method, as Y approaches 1 the particle
approaches a sphere in overall shape (i.e., for a
perfect sphere Y 1).
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b) Sneed and Folk (YP) or Maximum Projection
Sphericity
YP the ratio of the maximum projection area of a
sphere with volume equal to the particle to the
maximum projection area of the particle.
Sneed and Folk argued that it was the projection
area of a particle that experienced the viscous
drag of moving fluid, therefore it was more
important than the volume of the particle.
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c) Corey Shape Factor (SF)
Not really a measure of sphericity but similar to
YP.
Used in a variety formulae used to calculate
sediment transport rates.
d) Riley Sphericity (YR)
Used when only a two dimensional view is
available on thin sections.
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III. Form
Provides a consistent terminology for describing
the overall form of particles.
Based on various ratios of dL, dI and dS
Assigns specific shape terms based on ratios of
dI/dL and dS/dI.
Independent of sphericity although equant
particles are highly spherical.
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b) Sneed and Folk Form Index
Defines 10 shape classes.
Shows sphericity for each class.
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IV. Implications of particle shape
a) Controls on particle shape.
i) Lithology
For particles that are rock fragments aspects of
the lithology of the source rock can influence
shape.
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ii) Hardness
Particularly hard clasts (e.g., granite,
quartz-cemented sandstone, etc.) change in shape
during transport less readily than softer
lithologies.
Softer lithologies (e.g., limestone) change shape
much more readily.
Unconsolidated material (e.g., cohesive mud)
changes shape almost immediately when it is
transported.
b) Changes in Shape by Transport
Transport of particles by water, wind or flowing
glaciers has the potential to cause changes to
their shape over time.
During transport particles interact with each
other and with the surface over which they move.
Shape is modified by grinding, chipping and
crushing that takes place due to this interaction.
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The following figure reports data derived from
long distance transport of blocks cut initially
as cubes within a circular flume.
Changes in roundness and sphericity for cubes of
chert (a very hard rock type) and softer
limestone.
Roundness increases for limestone much more
quickly with transport than the harder chert,
especially during the early phase of transport.
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The rate of increase in roundness is greatest
during early transport for both rock types.
As rounding takes place it becomes increasingly
more difficult to change the shape to further
improve roundness.
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With an initially angular particle it is
relatively easy to increase roundness by breaking
off the sharp corners.
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As the particle becomes rounder, larger and
larger masses of material must be removed to
cause a comparable increase in roundness.
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Sphericity changes shape only very slowly because
the particles began as relatively equant shaped
cubes (i.e., with high sphericity to begin with).
Relatively large masses of material must be
removed to significantly change the sphericity of
a particle.
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Gravel size material changes shape relatively
rapidly with transport in comparison to sand size
material.
Shape change in sand can be inferred from rates
of change of weight of particles with transport
changes in shape require changes in mass.
For quartz grains in the size range 2 mm to 0.05
mm, that are transported in water, the weight
loss is lt0.1 per 1000 km of transport (the rate
is doubled for feldspars).
For quartz grains finer than 0.05 mm that are
transported in water there is virtually no change
in weight with transport.
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Why so little change in very fine sand?
Breakage takes place during collisions (between
grains and a solid substrate) and depends on the
amount of momentum that is exchanged during
collisions.
Momentum mass velocity
Very fine sand, silt and clay particles have very
small mass so that they have little momentum.
During collisions there is little momentum
exchanged and, therefore, little breakage which
is required to change the mass and shape of the
grains.
Momentum is further reduced when transport is in
water because the buoyant force reduces its
effective weight.
Most of the particles momentum is used in
pushing the water as the particle moves, losing
momentum due to the viscosity of the water.
112
When transport is in water there is little
momentum to cause breakage and change in shape.
Finally, well see later that particles finer
than 0.05 mm are transported in suspension
(floating in the water column), further reducing
the chances of shape-changing collisions.
Transport by wind is more effective in changing
the shape of fine grains.
Air has low density (little buoyant force) and
very low viscosity so that there is more momentum
exchanged during collisions.
Rate of weight loss is 100 to 1000 times that
when transport is in water.
Eolian desert sands tend to have relatively high
sphericity.
113
Shape Sorting by Transport
The roundness and sphericity of particles
influence the ease with flowing water can move
the particle.
To cause an angular cube to roll the fluid force
acting on it must overcome the weight of the cube
and pivot it 45 before its centre of mass passes
over the pivot point.
Once the centre of mass passes over the pivot
point the weight of the particle aids in the
motion.
114
A rounder, octagonal particle need only be
pivoted over 20 before its center of mass
passes over the pivot point and the weight
contributes to the motion.
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Shape sorting involves the selective removal of
particles due to their shape.
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b) Depositional environments and particle shape
Roundness and sphericity may be useful in helping
determine ancient environments or processes
associated with deposition.
Glacial till that is transported within glacial
ice is typically angular in shape.
Angularity reflects a lack of transport by water
prior to deposition.
Eolian (windblown) sands commonly have a higher
sphericity than water transported sand.
118
In rivers changes in roundness and sphericity
with transport are well documented.
119
It has been found that, in general, river gravels
are relatively compact whereas beach gravels tend
to be more platy or disc-shaped.
120
As for grain size distribution, it is the
processes in the two environments that differ and
lead to the characteristic shapes.
In rivers, gravel rolls along the bottom so that
more equant or spherical shapes are most commonly
transported.
On beach faces the swash and backwash may play
two rolls in enhancing the enrichment by
disc-shaped particles
121
ii) The swash and backwash may lead to back and
forth motion of the particle on the beach face.
This leads to abrasion of one side and if the
waves cause it to flip over abrasion takes place
on the other side, ultimately leading to a
disc-shaped clast.
Problem lithology plays an important roll in
determining shape.
e.g., a river with a well-bedded limestone source
of gravel will have predominantly platy gravel.
122
Furthermore, like grain size distribution, shape
may be inherited from the source material of the
particles.
A river that erodes through ancient beach gravel
will have clasts that are platy in form.
http//www.sandcollectors.org
123
Porosity and Permeabilty
Both are important properties that are related to
fluids in sediment and sedimentary rocks.
Fluids can include water, hydrocarbons, spilled
contaminants.
Most aquifers are in sediment or sedimentary
rocks.
Virtually all hydrocarbons are contained in
sedimentary rocks.
Porosity the volume of void space (available to
contain fluid or air) in a sediment or
sedimentary rock.
Permeability related to how easily a fluid will
pass through any granular material.
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I. Porosity (P)
The proportion of any material that is void
space, expressed as a percentage of the total
volume of material.
In practice, porosity is commonly based on
measurement of the total grain volume of a
granular material
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Porosity varies from 0 to 70 in natural
sediments but exceeds 70 for freshly deposited
mud.
Several factors control porosity.
a) Packing Density
Packing density the arrangement of the particles
in the deposit.
The more densely packed the particles the lower
the porosity.
e.g., perfect spheres of uniform size.
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Porosity varies from 0 to 70 in natural
sediments but exceeds 70 for freshly deposited
mud.
Several factors control porosity.
a) Packing Density
Packing density the arrangement of the particles
in the deposit.
The more densely packed the particles the lower
the porosity.
e.g., perfect spheres of uniform size.
Porosity can vary from 48 to 26.
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Shape has an important effect on packing.
128
In general, the greater the angularity of the
particles the more open the framework (more open
fabric) and the greater the possible porosity.
b) Grain Size
On its own, grain size has no influence on
porosity!
Consider a cube of sediment of perfect spheres
with cubic packing.
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Length of a side of the cube d n dn
Volume of the cube (VT)
Total number of grains n n n n3
Total volume of grains (VG)
130
d (grain size) does not affect the porosity so
that porosity is independent of grains size.
No matter how large or small the spherical grains
in cubic packing have a porosity is 48.
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There are some indirect relationships between
size and porosity.
i) Large grains have higher settling velocities
than small grains.
When grains settle through a fluid the large
grains will impact the substrate with larger
momentum, possibly jostling the grains into
tighter packing (therefore with lower porosity).
ii) A shape effect.
Unconsolidated sands tend to decrease in porosity
with increasing grain size.
Consolidated sands tend to increase in porosity
with increasing grain size.
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Generally, unconsolidated sands undergo little
burial and less compaction than consolidated
sands.
Fine sand has slightly higher porosity.
Fine sand tends to be more angular than coarse
sand.
Therefore fine sand will support a more open
framework (higher porosity) than better rounded,
more spherical, coarse sand.
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Fine sand is angular, with sharp edges, and the
edges will break under the load pressure and
become more compacted (more tightly packed with
lower porosity).
Coarse sand is better rounded and less prone to
breakage under load therefore the porosity is
higher than that of fine sand.
134
c) Sorting
In general, the better sorted the sediment the
greater the porosity.
In well sorted sands fine grains are not
available to fill the pore spaces.
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Overall porosity decreases with increasing
sorting coefficient (poorer sorting).
For clay-free sands the reduction in porosity
with increasing sorting coefficient is greater
for coarse sand than for fine sand.
The difference is unlikely if clay was also
available to fill the pores.
136
For clay-free sands the silt and fine sand
particles are available to fill the pore space
between large grains and reduce porosity.
137
Because clay is absent less relatively fine
material is not available to fill the pores of
fine sand.
Therefore the pores of fine sand will be less
well-filled (and have porosity higher).
138
d) Post burial changes in porosity.
Includes processes that reduce and increase
porosity.
Porosity that develops at the time of deposition
is termed primary porosity.
Porosity that develops after deposition is termed
secondary porosity.
50 reduction in porosity with burial to 6 km
depth due to a variety of processes.
139
i) Compaction
Particles are forced into closer packing by the
weight of overlying deposits, reducing porosity.
May include breakage of grains.
Freshly deposited mud may have 70 porosity but
burial under a kilometre of sediment reduces
porosity to 5 or 10.
140
ii) Cementation
Precipitation of new minerals from pore waters
causes cementation of the grains and acts to fill
the pore spaces, reducing porosity.
Most common cements are calcite and quartz.
Heres a movie of cementation at Paul Hellers
web site.
141
iii) Clay formation
Clays may form by the chemical alteration of
pre-existing minerals after burial.
Feldspars are particularly common clay-forming
minerals.
Clay minerals are very fine-grained and may
accumulate in the pore spaces, reducing porosity.
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iv) Solution
If pore waters are undersaturated with respect to
the minerals making up a sediment then some
volume of mineral material is lost to solution.
Calcite, that makes up limestone, is relatively
soluble and void spaces that are produced by
solution range from the size of individual grains
to caverns.
Quartz is relatively soluble when pore waters
have a low Ph.
Solution of grains reduces VG, increasing
porosity.
Solution is the most effective means of creating
secondary porosity.
v) Pressure solution
The solubility of mineral grains increases under
an applied stress (such as burial load) and the
process of solution under stress is termed
Pressure Solution.
The solution takes place at the grain contacts
where the applied stress is greatest.
143
Pressure solution results in a reduction in
porosity in two different ways
1. It shortens the pore spaces as the grains are
dissolved.
2. Insoluble material within the grains
accumulates in the pore spaces as the grains are
dissolve.
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v) Fracturing
Fracturing of existing rocks creates a small
increase in porosity.
Fracturing is particularly important in producing
porosity in rocks with low primary porosity.
145
Why is porosity important?
Especially because it allows us to make
estimations of the amount of fluid that can be
contained in a rock (water, oil, spilled
contaminants, etc.).
Example from oil and gas exploration
146
Why is porosity important?
Especially because it allows us to make
estimations of the amount of fluid that can be
contained in a rock (water, oil, spilled
contaminants, etc.).
Example from oil and gas exploration
147
Why is porosity important?
Especially because it allows us to make
estimations of the amount of fluid that can be
contained in a rock (water, oil, spilled
contaminants, etc.).
Example from oil and gas exploration
148
Why is porosity important?
Especially because it allows us to make
estimations of the amount of fluid that can be
contained in a rock (water, oil, spilled
contaminants, etc.).
Example from oil and gas exploration
149
Why is porosity important?
Especially because it allows us to make
estimations of the amount of fluid that can be
contained in a rock (water, oil, spilled
contaminants, etc.).
Example from oil and gas exploration
How much oil is contained in the discovered unit?
In this case, assume that the pore spaces of the
sediment in the oil-bearing unit are full of oil.
Therefore, the total volume of oil is the total
volume of pore space (VP) in the oil-bearing unit.
150
Therefore
151
II. Permeability (Hydraulic Conductivity k)
Stated qualitatively permeability is a measure
of how easily a fluid will flow through any
granular material.
More precisely, permeability (k) is an
empirically-derived parameter in DArcys Law, a
Law that predicts the discharge of fluid through
a granular material.
152
DArcys Law
Another way to express DArcys Law is as the
flow rate as the apparent velocity (V) of the
fluid through the material where
Thus, DArcys Law can be expressed as
153
So, the apparent velocity of a fluid flowing
through a granular material depends on several
factors
Dp this is the driving force behind the flow of
fluid through granular materials.
The greater the change in pressure the greater
the rate of flow.
(try blowing pop out of a straw!)
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The higher the viscosity the more difficult it is
for the pressure to push the fluid through the
small pathways within the material.
(try sucking molasses through a straw!)
(try drinking a milkshake through a 1 metre long
straw!)
This is a viscous effect resistance to
deformation is cumulative along the length of the
tube the longer the tube (or pathway) the
greater the total resistance.
155
Those are all properties that are independent of
the granular material.
There are also controls on permeability that are
exerted by the granular material and are
accounted for in the term (k) for permeability
k is proportional to all sediment properties that
influence the flow of fluid through any granular
material (note that the dimensions of k are cm2).
Two major factors
1. The diameter of the pathways through which
the fluid moves.
2. The tortuosity of the pathways (how complex
they are).
156
1. The diameter of the pathways.
Narrow pathway the region where the velocity is
low is a relatively large proportion of the total
cross-sectional area and average velocity is low.
Large pathway the region where the velocity is
low is proportionally small and the average
velocity is greater.
Its easier to push fluid through a large Pathway
than a small one.
157
2. The tortuosity of the pathways.
Tortuosity is a measure of how much a pathway
deviates from a straight line.
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2. The tortuosity of the pathways.
Tortuosity is a measure of how much a pathway
deviates from a straight line.
The greater the tortuosity the lower the
permeability because viscous resistance is
cumulative along the length of the pathway.
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Pathway diameter and tortuosity are controlled by
the properties of the sediment and determine the
sediments permeability.
The units of permeability are Darcies (d)
1 darcy is the permeability that allows a fluid
with 1 centipoise viscosity to flow at a rate of
1 cm/s under a pressure gradient of 1 atm/cm.
161
a) Sediment controls on permeability
i) Packing density
Smaller pathways reduce porosity and the size of
the pathways so the more tightly packed the
sediment the lower the permeability.
162
ii) Porosity
In general, permeability increases with primary
porosity.
The larger and more abundant the pore spaces the
greater the permeability.
Pore spaces must be well connected to enhance
permeability.
163
Shale, chalk and vuggy rocks (rocks with large
solution holes) may have very high porosity but
the pores are not well linked.
The discontinuous pathways result in low
permeability.
Fractures can greatly enhance permeability but do
not increase porosity significantly.
164
iii) Grain Size
Unlike porosity, permeability increases with
grain size.
The larger the grain size the larger the pore
area.
For spherical grains in cubic packing
Pore area 0.74d2
165
A ten-fold increase in grain size yields a
hundred-fold increase in permeability.
iv) Sorting
The better sorted a sediment is the greater its
permeability.
166
v) Post-burial processes
Like porosity, permeability is changed following
burial of a sediment.
Cementation Clay formation Compaction Pressure
solution
All act to reduce permeability
167
b) Directional permeability
Permeability is not necessarily isotropic (equal
in all directions)
168
Variation in grain size and geological structure
can create directional permeability.
169
Fabric (preferred orientation of the grains in a
sediment) can cause directional permeability.
The direction along the long axes of grains will
have larger pathways and therefore greater
permeability than the direction that is parallel
to the long axes.
170
Grain Orientation
Fabric the group of properties that are related
to the spatial arrangement of the particles
(including packing and orientation).
The term is commonly used to refer to orientation
only.
Why is it important?
1. It can affect other properties.
e.g., permeability, how it breaks (building
stone).
2. It can have genetic significance.
The problem with grain size and shape was that
they may be inherited from their source rock.
171
Particle orientation is achieved at the time of
deposition in response to processes that acted in
the environmental setting.
It remains fixed unless
It becomes compacted (the change is trivial for
sands).
It is structurally deformed (normally such
deformation is obvious).
It is bioturbated (reworking by organisms that
may or may not leave a visible structure).
172
a) How grain orientation is measured.
i) Gravel-size material.
Measured in terms of the a-axis (dL), the b-axis
(dI) and the plane of maximum projection (the a-b
plane).
Strike will be the trend of the a-axis or the
b-axis.
Dip is measured from the plane of bedding (not
the horizontal plane if the beds are tilted).
In tilted rocks measure the dip with respect to
the horizontal and correct for regional dip of
bedding.
The particle will dip along the a- or b-axes.
173
The dip of a particle is termed imbrication.
The direction is the imbrication direction and
the dip angle is the angle of imbrication.
On average, the a-axis is either parallel to or
perpendicular to the direction of imbrication.
Particles that are deposited from water normally
dip into the current imbrication direction is at
180 to the flow of the depositing current.
174
ii) Sand-size material
Can be determined with a microscope from thin
sections cut from oriented specimens.
Before removing the specimen from the outcrop it
should be marked to show
175
ii) Sand-size material
Can be determined with a microscope from thin
sections cut for oriented specimens.
Before removing the specimen from the outcrop it
should be marked to show
1. The direction to magnetic north.
176
ii) Sand-size material
Can be determined with a microscope from thin
sections cut for oriented specimens.
Before removing the specimen from the outcrop it
should be marked to show
1. The direction to magnetic north.
2. The top direction in outcrop.
177
In the lab, three thin sections must be cut
The thin sections allow the identification of the
average a-axis orientation, whether the a- or
b-axes are imbricate and the direction of
imbrication.
178
b) Types of Grain Frabric
i) Isotropic fabric
No preferred alignment of the particles.
179
ii) Anisotropic fabric
Complex fabrics also develop with a mix of
a(t)b(i) and a(p)a(i) that may appear isotropic.
180
A problem with measuring grain orientation in
thin section
181
a) Displaying directional data.
Directional data come in a variety of forms
including the examples listed below
Particle a-axis orientation
Imbrication direction
Cross-bed dip direction
Symmetrical ripple crest orientation
Orientation of fossils
Sedimentologists normally display such data on
circular histograms called rose diagrams.
182
The distribution appears to be very different
than normal.
Actually, the distributions are very similar and
effectively normal but this cannot be recognized
on such histograms because 0 and 360 are equal
but shown to be at extreme ends of the scale.
183
Sedimentologists normally display directional
data on a rose diagram
184
Florence Nightingales Polar-Area Diagrams or
coxcombs
Mortality figures during the Crimean War (1854 -
56)
185
30 class intervals
186
30 class intervals
187
30 class intervals
188
30 class intervals
189
30 class intervals
190
30 class intervals
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Rose diagrams better display the distribution of
directional data than regular histograms because
they give a sense of the spatial significance of
the data.
199
There are two common ways of showing the
frequency (number of observations) scale on a
rose diagram
Length Proportional Scale
Area Proportional Scale
Length of scale is proportional to the square
root of the number of observations segment area
is proportional to the number of observations.
Length of scale is proportional to the number of
observations
200
Length Proportional Scale
Area Proportional Scale
201
Length Proportional Scale
Area Proportional Scale
202
Length Proportional Scale
Area Proportional Scale
203
Length Proportional Scale
Area Proportional Scale
204
Length Proportional Scale
Area Proportional Scale
205
Length Proportional Scale
Area Proportional Scale
1
1
2
2
3
3
4
4
5
5
206
In a graphical representation of the data the eye
sees the area of the segments.
With a length proportional scale the sense that
is given is that an increase in number of
observations from 1 to 5 is 25 times rather than
5 times.
The area proportional scale shows an increase in
area that is truly proportional to the increase
in the number of observations.
Length proportional scales overly emphasizes
class intervals with large numbers of
observations.
207
Types of Rose Diagrams
Unimodal with one prominent mode (predominant
direction).
Bimodal with two modes.
Bipolar with 2 modes at 180 to each other.
Polymodal with three or more modes.
208
Always make sure that you know what kind of data
is being presented in a given rose diagram.
Some data are unidirectional (point only in one
direction e.g., the dip direction of a planar
surface such as cross-bedding).
On a rose diagram for such data each observation
will have one unique direction.
Some data are bidirectional (a trend with two
directions at 180 to each other e.g., the
alignment of a particle long axis.).
The rose diagrams will plot as what appears to be
perfectly symmetrical bipolar distributions
whereas the data are actually unimodal.
209
Rose diagrams for common anisotropic fabrics are
shown below (note that all of the roses are shown
as bidirectional data and are not really bipolar).
210
b) Statistical Treatment of Directional Data
Directional data cannot be treated with scalar
arithmetic calculations for statistical measures
because directional data are circular (vary from
0 to 360) and not infinitely continuous.
E.g., what is the average of the three
directional measurements?
Treated arithmetically
Clearly wrong!
211
Directional data must be treated as vectors.
Every vector has two parts direction and
magnitude.
Think of a vector as an arrow pointing in some
direction (q the lower case Greek letter theta)
and the arrow has a length (R) which is its
magnitude (the longer the arrow the greater the
magnitude).
Every directional measurement is a unit vector a
vector with a magnitude equal to 1.
The average direction can be determined by lining
the unit vectors up end to end and joining the
beginning and the end.
The three directional measurements are
represented as
212
The average vector is termed the resultant
vector ( ).
It points in the average direction of the data.
It has a specific direction and a magnitude
In this case
213
The magnitude of the resultant vector depends on
the amount of variation in the directions of the
directional observations.
214
Statistics for directional data can be calculated
for both grouped and ungrouped data.
215
The following outlines the steps to calculate the
direction and magnitude of the resultant vector
Step 1. Calculate the direction of the resultant
vector.
Where N is the total number of observations ni
is the magnitude of the ith vector (1 for each
observaton) qi is the ith observation.
Where NC is the number of classes ni is the
number of observations the ith class qi is the
direction of the midpoint of the ith class.
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Step 2. Calculate the magnitude (R) of the
resultant vector.
Remember that R is some proportion of the sum of
the magnitudes of all of unit vectors in the data
set. Its value depends on the total number of
observations in the data set and the amount of
dispersion.
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Step 3. Calculate the probability that the
directional data are uniformly distributed (p).
220
184 187 191 196 198 201 204 205 205
207 208 210 212 214 216 222 224
Raw data
Grouped data
Class interval Midpoint Frequency
180-189 184.5 2
190-199 194.5 3
200-209 204.5 6
210-219 214.5 4
220-229 224.5 2
Note 10 classes. Total (N) 17
221
184 187 191 196 198 201 204 205 205
207 208 210 212 214 216 222 224
Raw data
Treatment of ungrouped data
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Grouped data
Class interval Midpoint Frequency
180-189 184.5 2
190-199 194.5 3
200-209 204.5 6
210-219 214.5 4
220-229 224.5 2
Note 10 classes. Total (N) 17
Treatment of grouped data
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Ungrouped data results
Slight error in the Grouped Data method because
the actual observations are not used.
228
c) The Significance of Particle Orientation.
ii) Some data suggest that with increasing flow
strength the angle of imbrication increases.
These results are not verified in other
experiments.
229
Requires a more powerful current for a given
grain size than a(t)b(i) fabric.
The rose to the right can be interpreted as a
mixture of grains that rolled on the bed (modes
perpendicular to inferred flow direction) and
grains that were deposited from suspension (modes
parallel to the inferred flow direction).
230
vi) Variation in imbrication direction.
River sands display imbrication that varies in
angle but not in direction always dipping into
the depositing current.
231
Sands that were deposited in a shallow marine
environment display imbrication directions that
vary cyclically back and forth indicating
reversing currents.
This reflects the prevalence of oscillating
currents produced by waves in the shallow marine
environment.