Local isostacy versus regional
regional…
Flexural topography versus dynamic topography:
…the large-scale convective flow involving both upwelling
and downwelling deforms the Earth's surface creating
"d
"dynamic
i ttopography".
h " D
Dynamic
i ttopography
h iis b
bestt seen
by removing the isostatic contribution from the observed
topography
Subsidence analysis
Accommodation
EUSTACY
SUBSIDENCE / UPLIFT
Posamentier, 198
Eustasy
Relative Sea Level
(Accommodation Space)
Water Depth
Water Bottom
Eusstasy
Sea Surface
Sediment
Center of the Earth
The term eustasy refers to global sea level independent of local factors; namely the
position of the sea surface with reference to a fixed datum including the center
of the
Posamentier
et al., 1988
earth or a satellite in fixed orbit around the earth
T+E=S+W
T: Tectonic subsidence
E=rate of Eustatic sea level rise
S: sedimentation rate
W: water depth
Geohistory analysis
(i.e. Backstripping)
• A quantitative analysis of subsidence rates
through time requires the following
corrections:
– decompaction of stratigraphic units to their
correct thickness at the time of interest;
– corrections for the variations in depositional
water depth through time
– corrections for absolute fluctuations of sea
level (eustacy).
Corrections that need to be made
when
h d
doing
i geohistory
hi t
analysis
l i
• (1) compaction;
• (2) variations in depositional water depth
through time;
• (3) absolute fluctuations of sea level
((eustasy)
y) relative to the p
present sea-level
datum.
In isostatic equilibrium (i.e. local
compensation)
• The summed masses of any column of the earth
above an equipotential surface in the astenosphere
must equal that of all other colums:
-if two locations are compared the sum for all the
layers of the individual mass differences must be
zero; i.e.
An equipotential surface in the astenosphere exists because it has a low enough
viscosity to flow
i
 Δ( h)  0
i
0
i
 Δh  Δ elevation
i
0
(differences in thicknesses of layers in a column produce differences in elevation)
0-i: levels of different densities; : difference between colums; : density; h: thickness of each level
Airy backstripping
(i e local isostatic compensation)
(i.e.
•
•
Considering two colums of the
crust and upper mantle that
are in isotatic equilibrium and
balancing the pressure at the
base:
w g Wdi + si g Si* + c g T =
Yi w g + c g T + x m g
Decompacted sed thick
Mean crustal thickness
Tectonic subsidence
Water depth
Sea-level loading
sediment loading
Decompaction of stratigraphic units
• In order to decompact we need to know the
variation of porosity with depth:
  e
0
-cy
Where is the porosity at any depth y,  is the surface porosity and c is the
coefficient that is dependent on lithology and describes the rate at which the
exponential decrease in porosity takes place with depth (governs slope)
Simple model for decompaction
The porosity of the
sediments is given by
the ratio of the volume of
water (VW) to the total
volume (Vt).
Assuming that the cylinder
is of uniform cross
sectional area:  hw / ht,
i.e. hw =  ht
ht hw + hg
So if hg is the height of the
sediment grains then:
hg = ht – hw
i.e. hg = ht (1- 
• During compaction and de-compaction
de compaction
hg is constant and as ht changes so will 
hg = Si (1- 
hg = Si* (1- 
Si = compacted
p
sediment thickness
Si* = decompacted sediment thickness
Si*= Si(1- 
Decompaction exercise
• Assuming that the
equivalent height of
the grains is the same
before and after
compaction then:
Si (1  i )
Si* 
(1  i*)
i.e. solve for Si*
Decrease in porosity with depth for
diff
different
lilithologies
h l i
Decompaction excercise
• Consider a 100m thick shale horizon that
is now at a depth of 3km. The porosity of
shale is (?; use the porosity curve) at 3km
and (?; use the porosity curve) at the
surface.
surface
• What is the decompacted thickness of the
unit?
Solution
• The porosity of shale is 0.18
0 18 at depth 3km
and 0.7 at the surface.
• What is the decompacted thickness of the
unit?
Solution
Following the equation:
Si (1  i )
Si* 
(1  i*))
Si*= 100 x ((1-0.18)/(1-0.70)=273m
)(
)
Backstripping requires an
estimate of density as well as
thickness
• Vt = Vw + Vg (volumes)
• mt = mw + mg (masses)
• The decompacted total average density is:
Average density of decompacted layer
Average grain density
If we substitute for Vg and divide by Vt :
Backstripping multiple layers
• When doing backstripping we need to unload a
de-compact layers and, therefore, we need to
know their thicknesses as well as an estimate of
their densities ((s)
s)
• When decompacting multiple layers we need to
restore all the stratigraphic units for each time
step- de-compacting the younger unit and
compacting the older ones.
• The tectonic subsidence is calculated from the
sediment thickness and the average
g density
y of
the entire sedimentary sequence at a particular
time.
Backstripping multiple layers
After correcting for water depth and sea level change the Tectonic
subsidence (Y) is calculated from the sediment thickness and the
average of the entire sedimentary sequence at a particular time.
Backstripping multiple layers
• The total thickness,
thickness S*
S , is easily obtained
by summing all the individual thicknesses
i.e. the mass of the total thickness = the sum of the masses of
all individual stratigraphic units
Where n is the total number of stratigraphic units
(
(e.g.
Formations)
F
ti
) in
i a sequence att a certain
t i time
ti
The final tectonic subsidence (Y) will be:
Eustasy
Sediment loading
assuming isostatic
compensation
Tectonic subsidence signature
• Stretching and flexure of the lithosphere
are the most important mechanisms of
subsidence and they produce very
different signals:
Tectonic subsidence signature
• Stretching produces:
– Rapid synrift subsidence followed by an
exponential decreasing postrift subsidence
(concave-up phase) due to thermal relaxation;
the duration of the susbidence is 10->10
10 102My;
subsidence rates are in the order of
<0.2mm/yr to <0.05mm/yr.
Tectonic subsidence signature
• Flexure produces:
– Accelerating subsidence through time
(convex-up
(convex
up phase); the duration of
subsidence is 20-40My; subsidence rates are
in the order of 0.2-0.5mm/yr
y
Tectonic subsidence signature
• Cratonic basins:
– Are characterized by long periods (>102My) of
slow susbidence
susbidence, characterized by regional
unconformities; subsidence rates are in the
order of 0.01-0.04mm/yr
y
Tectonic subsidence signature
• Strike
Strike-slip
slip basins:
– Are characterized by short subsidence
duration (ca
(ca. 10My) and very high susbidence
rates (>0.5mm/yr).
Subsidence for different tectonic settings
After Xie and Heller (2009)
After Xie and Heller (2009)
Tectonic subsidence signature:
excercise
i
Tectonic subsidence signature:
excercise
i
St ik Sli b
Strike-Slip
basins
i
late
early
synrift
Foreland basins
Rift basins
postrift
Cratonic basins
Which kind of basin are we looking at?
3.5 3.0 2.5 2.0 1.5 1..0 0.5
kkm
Subsidence
28
20
Rup. Ch. Early
Olig
Olig.
12
Mid. Late
Miocene
Literature
• Chapter 9; in Basin Analysis
Analysis, Principle and
Application, Allen and Allen Eds., 2005.
• Extra material on backstripping is from T
T.
Watts (Oxford University); see
photocopies.
photocopies