8.1 General Mechanisms
response of an elastic crust to a surface load (Fig.
8.lc and d).
A more eomprehensive treatment of this topie is given,
e.g., by Jarvis (1984), Suppe (1985), Allen and Allen
(1990), eloos (1993), Slingerland et al. (1994), and found
in several textbooks of geophysies and general geology.
Initial Subsidence (Without Thermal Effects)
Water-Filled Basins
In simplified cases, subsidence, Si' due to local isostatic compensation, neglecting any thermal effects,
can be calculated with the following assumptions:
- The densities of the different layers remain constant and the thicknesses of the layers (except that of
sea water) are known or will be given as variables.
- Mantle lithosphere and mantle asthenosphere are
combined into the thickness ~ with the density Pma
(= 3.33 g/cm 3 ).
- Prior to subsidence, the surface of the crust is at
sea level and covered neither by water nor sediment.
For these conditions, one can simplify Eq. (8.2) to
(8.4)
and Eq. (8.3) to
where Si = Äh w (fixed sea level)
(8.5)
After equating (8.4) and (8.5), one obtains
(8.6)
Inserting the density values listed above and in Fig.
8.1 (e.g., Pw = 1.03 g/cm 3 for sea water), we obtain
If under these simplified eonditions the ernstal thiekness h c
is redueed, for example, by 15 km (around half of its normal thiekness), the top of the ernst subsides from sea level
to a depth of 3.5 km and ereates spaee for a water body of
the same depth. Similarly, the water depth of a basin ean
inerease by I km, if the thiekness of the mantle is inereased
by 4.34 km at the expense ofthe ernst.
A more general expression for the initial subsidence
of a basin fi1led with water up to the (fixed) sea level,
derived from Eqs. (8.2) and (8.3), is
389
Si = (Pe -Pa)he +(Pm -Pa)h m (l_.!..)
P w -Pa
ß
(8.7)
ß is the stretching factor, which describes the amount
of stretching of a certain segment of the lithosphere.
For z = original thickness and b = original width
(Fig. 8.2), the new width after extension is increased
to bß and the thickness reduced to zlß. This formula,
however, still does not take into account any sediment load or thermal effects which are usually associated with crustal thinning and the formation of a
topographic low.
Inserting the values from the previous example (ß=2,
Pm=Pa=3.33 g/em 3 , hc=30 km, and hm=100 km) into Eq. 8.7,
the resultis Si "" 3.5 km. With Pm=3.4 g/em 3 , Pa=3.3 g/em 3
(Fig. 8.l), and the other parameters from this example remaining unehanged, the initial isostatie subsidenee for the
water-filled basin is Si "" 5.5 km.
These examples demonstrate that the results of such
calculations strongly depend on the density values
assumed for the mantle lithosphere and mantle
asthenosphere, as well as on the thickness of the
crust and lithosphere prior to stretching. Some authors have pointed out that stretching of a crust thinner than 18 km will generate uplift, whereas stretching of thicker crust causes subsidence. However, this
boundary condition varies considerably with the densities and thicknesses of the crust and mantle lithosphere (Jarvis 1984).
Sediment-Filled Basins
The sediment load of a partially or entirely fi1led basin causes additional subsidence due to isostatic compensation. This effect can be easily calculated if the
former water-filled basin (water depth, h w ) is completely filled with sediments up to sea level (sediment thickness, h s ) and the average density of sediments is known (e.g. Ps = 2.4 g/cm 3 ). Then the elevation above the isostatic compensation depth remains
the same as before, and from Eq. (8.3) we can assume:
(8.8)
SimilarIy, the mass above the compensation level
does not change (Eq. 8.2); hence we obtain
Pshs - P~w + Pa Äha = 0 .
Equating (8.8) and (8.9) gives
h = (Pw - Pa) h
s (Ps - Pa) w
(8.9)
(8.10)
where h s is the maximum sediment thickness up to
sea level.
response of an elastic crust to a surface load (Fig.
8.lc and d).
A more eomprehensive treatment of this topie is given,
e.g., by Jarvis (1984), Suppe (1985), Allen and Allen
(1990), eloos (1993), Slingerland et al. (1994), and found
in several textbooks of geophysies and general geology.
Initial Subsidence (Without Thermal Effects)
Water-Filled Basins
In simplified cases, subsidence, Si' due to local isostatic compensation, neglecting any thermal effects,
can be calculated with the following assumptions:
- The densities of the different layers remain constant and the thicknesses of the layers (except that of
sea water) are known or will be given as variables.
- Mantle lithosphere and mantle asthenosphere are
combined into the thickness ~ with the density Pma
(= 3.33 g/cm 3 ).
- Prior to subsidence, the surface of the crust is at
sea level and covered neither by water nor sediment.
For these conditions, one can simplify Eq. (8.2) to
(8.4)
and Eq. (8.3) to
where Si = Äh w (fixed sea level)
(8.5)
After equating (8.4) and (8.5), one obtains
(8.6)
Inserting the density values listed above and in Fig.
8.1 (e.g., Pw = 1.03 g/cm 3 for sea water), we obtain
If under these simplified eonditions the ernstal thiekness h c
is redueed, for example, by 15 km (around half of its normal thiekness), the top of the ernst subsides from sea level
to a depth of 3.5 km and ereates spaee for a water body of
the same depth. Similarly, the water depth of a basin ean
inerease by I km, if the thiekness of the mantle is inereased
by 4.34 km at the expense ofthe ernst.
A more general expression for the initial subsidence
of a basin fi1led with water up to the (fixed) sea level,
derived from Eqs. (8.2) and (8.3), is
389
Si = (Pe -Pa)he +(Pm -Pa)h m (l_.!..)
P w -Pa
ß
(8.7)
ß is the stretching factor, which describes the amount
of stretching of a certain segment of the lithosphere.
For z = original thickness and b = original width
(Fig. 8.2), the new width after extension is increased
to bß and the thickness reduced to zlß. This formula,
however, still does not take into account any sediment load or thermal effects which are usually associated with crustal thinning and the formation of a
topographic low.
Inserting the values from the previous example (ß=2,
Pm=Pa=3.33 g/em 3 , hc=30 km, and hm=100 km) into Eq. 8.7,
the resultis Si "" 3.5 km. With Pm=3.4 g/em 3 , Pa=3.3 g/em 3
(Fig. 8.l), and the other parameters from this example remaining unehanged, the initial isostatie subsidenee for the
water-filled basin is Si "" 5.5 km.
These examples demonstrate that the results of such
calculations strongly depend on the density values
assumed for the mantle lithosphere and mantle
asthenosphere, as well as on the thickness of the
crust and lithosphere prior to stretching. Some authors have pointed out that stretching of a crust thinner than 18 km will generate uplift, whereas stretching of thicker crust causes subsidence. However, this
boundary condition varies considerably with the densities and thicknesses of the crust and mantle lithosphere (Jarvis 1984).
Sediment-Filled Basins
The sediment load of a partially or entirely fi1led basin causes additional subsidence due to isostatic compensation. This effect can be easily calculated if the
former water-filled basin (water depth, h w ) is completely filled with sediments up to sea level (sediment thickness, h s ) and the average density of sediments is known (e.g. Ps = 2.4 g/cm 3 ). Then the elevation above the isostatic compensation depth remains
the same as before, and from Eq. (8.3) we can assume:
(8.8)
SimilarIy, the mass above the compensation level
does not change (Eq. 8.2); hence we obtain
Pshs - P~w + Pa Äha = 0 .
Equating (8.8) and (8.9) gives
h = (Pw - Pa) h
s (Ps - Pa) w
(8.9)
(8.10)
where h s is the maximum sediment thickness up to
sea level.