9.6 Steady State and Dynamic Denudation Systems
Ci = 0.20 is assumed for the following discussion.
Equation 9.6 signifies that isostatic uplift in response
to unloading (aD t ) causes the mean elevation, H, to
decrease by aH more slowly than the rate at which
material is being removed. From equation 9.6 follows
aDt = aHiC i , and for Ci = 0.20 it is
aD t = 5 x aH (m).
(9.8)
This means, for example, that 5 x 1000 = 5000 m of rock
have to be eroded to reduce the mean elevation of a region
by 1000 m. This is solely the effect of Airy isostasy without
any additional flexural component or tectonic or thermal
process generating syn-erosional uplift. The simple model
of Fig. 9.17a shows the effect of isostatic rebound in several time steps. During each step, a rock column half as
thick as the previous elevation ofthe landscape is removed,
but at the same time rebound of the ernst generates uplift
compensating for 80% of the eroded rock column. Lowering of the landscape therefore proceeds much slower than
denudation.
An integral solution for the decay of the landscape
due to mechanical denudation is (Pazzaglia and
Brandon 1996):
(9.9)
where Ho is the initial mean elevation, H is the elevation after time t, and K.J is the constant for mechanical denudation (equation 9.2).
The time necessary, to get a 63% reduction of an initiallandscape is commonly defined as a characteristic
response time, t c ' of the dynamic system (e.g.
Pazzaglia and Brandon 1996):
(Ma).
(9.10)
A more general definition of the response time is t c =
lIe = 0.37 (e = 2.718). It is the time taken to reduce
the disequilibrium to 0.37 times the initial disequilibrium of a system (Fig. 9.18b; e.g. Kooi and Beaumont 1996). The introduction of this term is useful,
because it may take a very long time to achieve full
equilibrium conditions.
Inserting the values discussed above (Ci = 0.20, Kd
= 0.07 Ma"), the average response time of denudation is t c :::::: 70 Ma. Other denudation constants lead
to shorter and longer time values. For the rapid erosional decay of a young volcanic structure in Papua
New Guinea, for example, a response time of 1.4 Ma
was determined (Pazzaglia and Brandon 1996). Other
authors have found higher response times of up to
150 to 330 Ma, e.g. for a Paleozoic fold belt in Australia (see Harrison 1994). This problem is further
discussed in Section 9.6.3
449
9.6.2 Uplift and Denudation
General Concepts
In studies· on the interplay between tectonic uplift
and denudation, one has to distinguish the following
terms (Fig. 9.l7b; England and Molnar 1990):
- Surface uplijt is the displacement of the land surface with respect to the geoid or mean sea level.
- Rock uplijt is the displacement of rocks with respect to the geoid.
- Exhumation (= erosion, denudation) is the removal
of rocks with respect to the initial land surface. Exhumation of formerly buried rocks can also be
brought about by tectonic movements, e.g. gravity
tectonics, a case which is not considered here.
These terms should be only used for large areas
where mean values can be determined. In this case it
is (Fig. 9.l7b)
Surface uplift (aH)
= rock uplift (RU) - exhumation (E), or:
Rock uplift (RU)
= tectonic uplift (TU) + isostatic rebound (IR)
= surface uplift (aH) + exhumation (E)
The amount of exhumation can be determined by using
several methods. In favorable cases the present-day porosity of shales or the vitrinite reflectancy of fossilized plant
rernains (cf. Fig. 14.4) allow an estimate ofthe thickness of
formerly overlying rocks removed by erosion (Sect. 13.2).
Specific mineral associations formed under certain temperatures and pressures (thermobarometry) indicate the thickness of rocks eroded, but they do not provide information
about the time period involved. However, thermochronological methods (e.g. 40 ArP9 Ar and apatite fission-track
analyses) yield both the amount of exhumation as well as
the time needed for this process. These methods are described in modern textbooks of petrology and isotope geology (see, e.g. Gallagher et al. 1998 for abriefreview).
To find out the uplift and denudation history of a
region, a backstacking method has been proposed
(Fig. 9.l7c, based on Brown 1991). After having determined exhumation, E, of rock sampies from the
present land surface for a certain time period, uplift
by isostatic rebound, IR, is calculated by using equation 9.7. Then tectonic uplift is TU = E - IR - aH,
where aH = Hp - H i , i.e. is the difference in elevation
between the present and the initial land surface. If
there was a change in sea level, aSL, or base level
we get aH = Hp - H i ± aSL.
Tectonic uplift TU is difficult to evaluate when exhumation
E and surface uplift aH are uncertain. Because the amount
of E is normally greater than that of aH, for example in
orogenie belts, an error in the determination of E may
Ci = 0.20 is assumed for the following discussion.
Equation 9.6 signifies that isostatic uplift in response
to unloading (aD t ) causes the mean elevation, H, to
decrease by aH more slowly than the rate at which
material is being removed. From equation 9.6 follows
aDt = aHiC i , and for Ci = 0.20 it is
aD t = 5 x aH (m).
(9.8)
This means, for example, that 5 x 1000 = 5000 m of rock
have to be eroded to reduce the mean elevation of a region
by 1000 m. This is solely the effect of Airy isostasy without
any additional flexural component or tectonic or thermal
process generating syn-erosional uplift. The simple model
of Fig. 9.17a shows the effect of isostatic rebound in several time steps. During each step, a rock column half as
thick as the previous elevation ofthe landscape is removed,
but at the same time rebound of the ernst generates uplift
compensating for 80% of the eroded rock column. Lowering of the landscape therefore proceeds much slower than
denudation.
An integral solution for the decay of the landscape
due to mechanical denudation is (Pazzaglia and
Brandon 1996):
(9.9)
where Ho is the initial mean elevation, H is the elevation after time t, and K.J is the constant for mechanical denudation (equation 9.2).
The time necessary, to get a 63% reduction of an initiallandscape is commonly defined as a characteristic
response time, t c ' of the dynamic system (e.g.
Pazzaglia and Brandon 1996):
(Ma).
(9.10)
A more general definition of the response time is t c =
lIe = 0.37 (e = 2.718). It is the time taken to reduce
the disequilibrium to 0.37 times the initial disequilibrium of a system (Fig. 9.18b; e.g. Kooi and Beaumont 1996). The introduction of this term is useful,
because it may take a very long time to achieve full
equilibrium conditions.
Inserting the values discussed above (Ci = 0.20, Kd
= 0.07 Ma"), the average response time of denudation is t c :::::: 70 Ma. Other denudation constants lead
to shorter and longer time values. For the rapid erosional decay of a young volcanic structure in Papua
New Guinea, for example, a response time of 1.4 Ma
was determined (Pazzaglia and Brandon 1996). Other
authors have found higher response times of up to
150 to 330 Ma, e.g. for a Paleozoic fold belt in Australia (see Harrison 1994). This problem is further
discussed in Section 9.6.3
449
9.6.2 Uplift and Denudation
General Concepts
In studies· on the interplay between tectonic uplift
and denudation, one has to distinguish the following
terms (Fig. 9.l7b; England and Molnar 1990):
- Surface uplijt is the displacement of the land surface with respect to the geoid or mean sea level.
- Rock uplijt is the displacement of rocks with respect to the geoid.
- Exhumation (= erosion, denudation) is the removal
of rocks with respect to the initial land surface. Exhumation of formerly buried rocks can also be
brought about by tectonic movements, e.g. gravity
tectonics, a case which is not considered here.
These terms should be only used for large areas
where mean values can be determined. In this case it
is (Fig. 9.l7b)
Surface uplift (aH)
= rock uplift (RU) - exhumation (E), or:
Rock uplift (RU)
= tectonic uplift (TU) + isostatic rebound (IR)
= surface uplift (aH) + exhumation (E)
The amount of exhumation can be determined by using
several methods. In favorable cases the present-day porosity of shales or the vitrinite reflectancy of fossilized plant
rernains (cf. Fig. 14.4) allow an estimate ofthe thickness of
formerly overlying rocks removed by erosion (Sect. 13.2).
Specific mineral associations formed under certain temperatures and pressures (thermobarometry) indicate the thickness of rocks eroded, but they do not provide information
about the time period involved. However, thermochronological methods (e.g. 40 ArP9 Ar and apatite fission-track
analyses) yield both the amount of exhumation as well as
the time needed for this process. These methods are described in modern textbooks of petrology and isotope geology (see, e.g. Gallagher et al. 1998 for abriefreview).
To find out the uplift and denudation history of a
region, a backstacking method has been proposed
(Fig. 9.l7c, based on Brown 1991). After having determined exhumation, E, of rock sampies from the
present land surface for a certain time period, uplift
by isostatic rebound, IR, is calculated by using equation 9.7. Then tectonic uplift is TU = E - IR - aH,
where aH = Hp - H i , i.e. is the difference in elevation
between the present and the initial land surface. If
there was a change in sea level, aSL, or base level
we get aH = Hp - H i ± aSL.
Tectonic uplift TU is difficult to evaluate when exhumation
E and surface uplift aH are uncertain. Because the amount
of E is normally greater than that of aH, for example in
orogenie belts, an error in the determination of E may