2307501 Basin analysis
The physical state of the lithosphere
Banded iron formation, Karijini National Park, Western Australia (image credit Graeme Churchard)
Sukonmeth Jitmahantakul
WEEK 2
Course schedule / 2016
Week
Date
1
9 Aug
2
16 Aug
The physical state of the lithosphere
3
23 Aug
Basin due to lithospheric stretching
4
30 Aug
Analogue modelling of rift basin
5
6 Sep
Basin due to flexure
6
13 Sep
Basins associated with strike-slip deformation
7
20 Sep
Basin development in Thailand
8
27 Sep
9
4 Oct
Effects of mantle dynamics
10
11 Oct
The sediment routing system
11
18 Oct
Basin stratigraphy
12
25 Oct
Subsidence history
13
1 Nov
Thermal history
14
8 Nov
Building blocks of the petroleum play
15
15 Nov
Clastic and unconventional plays
16
22 Nov
Presentation 10% Report 20%
17
29 Nov
Final exam 40%
2307501 Basin analysis
Topic / exam
Introduction to sedimentary basins
Foundations
Mechanics
Mid-term exam 30%
Sedimentary basin-fill
Application
Knowledge sharing
Week 2 - Outline
Basic concepts of stress
Stress measurements
Stress in the lithosphere
Strain in the lithosphere
Summary
2307501 Basin analysis
Stress & strain
Stress - force per area (Pa or kg/m.s2)
Strain - deformation of the solid due to stress
(dimensionless)
2307501 Basin analysis
Body forces & surface forces
A body force is a force that acts throughout the
volume of a body (e.g. gravity, magnetic forces).
Surface force acts on a surface bounding a volume
(e.g. lithostatic stress or weight of overburden)
Rocks increase in density with depth in the Earth
due to their compressibility, but they expand due to
heating.
From Allen and Allen (2013)
2307501 Basin analysis
Pressure & stress
In geology, use of the term pressure (p) is generally limited to media with no
or very low shear resistance (fluids), while stress (σ) is used when dealing
with media with a minimum of shear resistance (rocks).
In a buried porous sandstone layer we can talk about both pressure and
stress: it has a certain pore pressure and it is in a certain state of stress.
From Allen and Allen (2013)
2307501 Basin analysis
Sign conventions
Compressive normal forces are always
positive in geology, while tensile ones are
negative (in engineering geology the sign
convention is opposite).
Geologists like this convention because
stresses tend to be compressive in the
crust.
Both extension and contraction can result
from a stress field where all stress axes
are compressional.
Positive stress
Negative stress
From Fossen (2010)
Normal stress & shear stress
The component of stress
σn perpendicular to a
surface (such as a fault)
is the normal stress.
The part of the stress σs
parallel to a surface is
called the shear stress.
From Fossen (2010)
2307501 Basin analysis
Principal stresses & stress ellipsoid
At any point in a material, principal
axes of stress are perpendicular to
three mutually perpendicular planes
on which there are no shear
stresses.
σ1 = maximum principal axis
σ2 = intermediate principal axis
σ3 = minimum principal axis
σ2
σ3
σ1
The stress ellipsoid and its
orientation tell us everything about
the state of stress at a given point in
a rock, or in a rock volume in which
stress is homogeneous.
From Fossen (2010)
2307501 Basin analysis
Mean stress & deviatoric stress
To distinguish two very important components of stress, the isotropic and
anisotropic components.
Total stress tensor
Mean stress tensor
(isotropic component)
Deviatoric stress tensor
(anisotropic component)
where σm = mean stress (an average measure of stress)
σm = (σ1 + σ2 + σ3) / 3
2307501 Basin analysis
Mean stress & deviatoric stress
Total stress tensor
Mean stress tensor
(isotropic component)
Deviatoric stress tensor
(anisotropic component)
The deviatoric stress is generally considerably smaller than the isotropic
mean stress, but of greater significance when it comes to the formation of
geologic structures in most settings.
Isotropic stress results in dilation (inflation or deflation), only the anisotropic
component results in strain. The relationship between its principal stresses
influences what type of structures are formed.
2307501 Basin analysis
Hydrostatic stress/pressure
The stress ellipsoid is a perfect sphere, σ1 = σ2 = σ3
No shear stress “anywhere”
No off-diagonal stress in the total stress tensor.
Hydrostatic stress or hydrostatic pressure represents
an isotropic state of stress.
Total stress tensor
2307501 Basin analysis
Mean stress tensor
(isotropic component)
Stress measurements
Borehole breakouts are zones of failure
of the wall of a well that give the borehole
an irregular and typically elongated shape.
The spalling of fragments from the
wellbore occurs preferentially parallel to
the minimum horizontal stress (σh) and
orthogonal to the maximum horizontal
stress (σH).
Tunnels (eye view)
Borehole breakout (top view)
From Fossen (2010)
Stress measurements
Overcoring is a strain relaxation method where a sample (core or block) is
extracted from a rock unit, measured, and then released so that it can freely
expand.
The change in shape that occurs reflects the compressive stresses that have
been released, but also depends on the rock’s elasticity.
In general, maximum expansion occurs in the direction of σh.
From Fossen (2010)
Stress measurements
Hydraulic fracturing (hydrofracturing, “hydrofracking”) means increasing the
fluid pressure until the rock fractures.
The pressure that is just enough to keep the fracture(s) open equals σh in the
formation.
Earthquake focal mechanisms give information about the Earth’s immediate
response to stress release along new or preexisting fractures.
Geologic structures formed by active tectonic processes also give reliable
indications of certain aspects of the present day stress field.
From Fossen (2010)
Stresses in the lithosphere
Our information about the current stress field below a few (4–5) kilometers
depth is indirect, inaccurate and incomplete.
Various theoretical models (reference states of stress) exist that describe
how the state of stress changes through the crust.
Reference states of stress define idealized states of stress in the crust as if
the crust were a static planet with no tectonic processes.
Three fundamental reference states:
Lithostatic reference state
Uniaxial reference state
Constant-horizontal-stress reference state
2307501 Basin analysis
Lithostatic/hydrostatic reference state
The lithostatic reference state is
an isotropic state of stress, where
the vertical and horizontal stresses
are equal.
It is based on an idealized situation
where the rock has no shear
strength (σs = 0).
σ1 = σ2 = σ3 = ρgz
where
ρ is the density of the rock column,
g is the acceleration of gravity,
z is the height of the column (depth)
Some similar numbers: Common stress gradient, 27MPa/km; common
temperature gradient, 27 C/km; common rock density, 2.7 g/cm3.
From Fossen (2010)
2307501 Basin analysis
Uniaxial-strain reference state
The uniaxial-strain reference state is based
on the boundary condition that no elongation
(positive or negative) occurs in the horizontal
directions.
During burial, the horizontal stresses are
equal (σH = σh) and will increase as a function
of increasing burial depth or σ1v
The vertical stress will increase faster than
the horizontal stress
σv = ρgz = σ1 ; σH = σh = σ2 = σ3
σH =
v
1-v
σv =
v
1-v
ρgz
where v is Poisson’s ratio
Rocks typically have v-values in the range
0.25–0.33.
From Fossen (2010)
Uniaxial-strain reference state
In this model, the vertical stress comes from
overburden while the horizontal one is influenced
by the uniaxial-strain boundary condition.
The model fits well the effect of compaction in
sedimentary basins.
In contrast to the lithostatic model, the horizontal
stress depends on the physical properties of the
rock.
The horizontal stress is predicted to be between
1/2 and 1/3 of the vertical stress, i.e.
considerably less than what is predicted by the
lithostatic reference state.
But for a sediment that progressively becomes
more and more cemented and lithified, its elastic
property changes (v increases) and the uniaxialstrain model approaches the lithostatic one.
From Fossen (2010)
Constant-horizontal-stress reference state
The constant-horizontal-stress reference state is based on the assumption
that the average stress in the lithosphere is everywhere the same to the
depth of isostatic compensation under the thickest lithosphere (z1).
Below z1, the Earth is assumed to behave like a fluid (σH = σh = σv = σm),
where the lithostatic stress σm is generated by the overburden.
z
pl
w
pm
2307501 Basin analysis
Constant-horizontal-stress reference state
Assume that an amount z was eroded from the lithosphere, the level of
isostatic compensation moved up by the amount w.
pm . w = p l . z
After erosion, before isostatic re-equilibrium, the average horizontal stress
(σ*h) in the thinner portion of the lithosphere must be higher than that in the
thicker portion (σh).
σh . z1 = σ*h (z1 - z) + pm . w
z
pl
w
pm
2307501 Basin analysis
State of stress in the crust vs. depth
Rocks in crust that has been
tectonically inactive for tens or
hundreds of millions of years, such
as the interior of the Baltic Shield,
behave similar to fluids.
The resulting state of stress is
lithostatic (equal in all directions)
and increases with burial depth.
From Fossen (2010)
2307501 Basin analysis
State of stress in the crust vs. depth
Crust in extensional regimes
experiences true tensional stress
only within the uppermost few
100m.
At deeper levels stress is
compressional in all directions.
The horizontal stresses are less
than the vertical stress
From Fossen (2010)
2307501 Basin analysis
State of stress in the crust vs. depth
In contractional regimes horizontal
stresses are generally larger than
the vertical stress
From Fossen (2010)
2307501 Basin analysis
World Stress Map
www.world-stress-map.org
From Heidbach et al. (2008)
Strain in the lithosphere
Strain in the lithosphere commonly results from tectonic activity.
Repeated co-seismic displacement allow the strain rate to be calculated.
Tectonic displacements can be measured from satellites in space using the GPS
Synthetic aperture radar interferometry is able to make radar backscatter images
of the Earth’s surface before and after a tectonic movement.
2307501 Basin analysis
Focal mechanism solutions for earthquakes
From Allen and Allen (2013)
Map of continuous stress-strain
From Allen and Allen (2013)
Radar interferometric image
From Allen and Allen (2013)
Next..
Week
Date
1
9 Aug
Introduction to sedimentary basins
2
16 Aug
The physical state of the lithosphere
3
23 Aug
Basin due to lithospheric stretching
4
30 Aug
Analogue modelling of rift basin
5
6 Sep
Basin due to flexure
6
13 Sep
Basins associated with strike-slip deformation
7
20 Sep
Basin development in Thailand
8
27 Sep
9
4 Oct
Effects of mantle dynamics
10
11 Oct
The sediment routing system
11
18 Oct
Basin stratigraphy
12
25 Oct
Subsidence history
13
1 Nov
Thermal history
14
8 Nov
Building blocks of the petroleum play
15
15 Nov
Clastic and unconventional plays
16
22 Nov
Presentation 10% Report 20%
17
29 Nov
Final exam 40%
2307501 Basin analysis
Topic / exam
Foundations
Mechanics
Mid-term exam 30%
Sedimentary basin-fill
Application
Knowledge sharing