390
With an average sediment density of Ps = 2.15 g/em 3 ,
a sediment thiekness twice the initial water depth ean
develop (amplificationfactor 2); with Ps = 2.55 g/em 3
the amplification faetor is ab out 3. The sediment density below the sediment-water interface, in partieular
that of fine-grained sediments, increases significantly
with their thickness. Thus, the amplification factor
grows during subsidence and basin filling (cf. Fig.
11.10).
In our example of a water-filled basin (based on Eq. 8.7)
we obtained hw ,., 3.5 km. Using the density values mentioned above and listed in Fig. 8.1, Eq. (8.10) yields
h, ,., 8.7 km. This signifies that a sediment-filled segment
of this model basin will subside 2.5 times more than a
purelywater-filled segment, due to isostatie response ofthe
crust. In comparison with an air-filled depression below
sea level, the amplification factor for a corresponding
sediment-filled basin becomes even greater (in our example
approximately 1.46x2.5 ,., 3.6.
Isostatic uplift in response to denudation is treated in
Seet. 9.6.1.
Thermal Uplift and Subsidence
If a column of the lithosphere is heated above the
temperature of the surrounding rocks, its mass remains unchanged, but its volume inereases and may
eause uplift at the land surface or sea bottom.
Upwelling hot mantle material, for example at oceanic spreading centers, generates oceanie ridges
which later, due to cooling of the oeeanic erust and
thiekening of the underlying mantle lithosphere, subside considerably with age by several km. Sirnilarly,
upwelling hot mantle material below a thinning eontinental crust will first tend to raise the surface of the
thinned crust, if this thermal expansion is not exceeded by the effeets of isostasy.Later cooling will
eause subsidence which is referred to as thermal subsidenee, St. Thermal subsidence and uplift are also
affected by the 3D geometry of the system and controlled by the coefficient of thermal expansion (or
eontraction), a=3.4xlO- 5 /oC, and the thermal diffusivity ofthe lithosphere, k=8xlO- 7 m 2 /s.
If, for example, the temperature of a 50 km high rock colurnn is raised or lowered uniformly by 300°C, its height
will increase or decrease due to thermal expansion or contraction by ~0.5 km. This is, of course, an unrealistic exampIe, whieh only demonstrates the order of magnitude of
such thermal effects. In nature we observe a thermal gradient from the base of the mantle lithosphere (l350°C, Fig.
8.2) to the land surface or sea water (slightly above O°C).
With changing lithosphere thickness, this gradient and thus
the temperatures at different depths vary, but the combined
effect of this process causes approximately the same
amount of expansion or contraction as that calculated for a
rock colurnn which is subjected to the same change in
mean temperature as the lithosphere.
Chapter 8 Subsidence
As a result of mantle upwelling, a steep temperature
gradient is established. Later, this gradient is slowly
reduced by heat loss to the atmosphere, until the original gradient will be restored (Fig. 8.2b and c). This
process is described by the thermal diffusivity of the
lithosphere. Cooling of an abnormally heated lithosphere takes tens of million years. Thermal subsidence is therefore a long-term, slowly decaying process.
The mathematieal treatment of thermal expansion and contraction of the lithosphere is beyond the purpose of this text
(see, e.g., Royden et a1. 1980; Watts and Thorne 1984;
Sawyer 1988), but the following basin modeling does include thermal effects.
8.1.2 Flexural Response of the Crust to Loading
It is a well-known fact from geological observation
that the lithosphere adjacent to local or regional loads
(water, ice, sediment accumulation, isolated
seamounts on top of oceanic crust) reacts by
downwarping (Fig. 8.1 d). Similarly, unloading (lake
dessication, icemelting, rock denudation) leads to
some uplift of neighboring areas. The best studied
examples are continental ice caps, which cause not
only isostatic compensation below the ice, but also
some subsidenee in areas adjacent to the ice load.
Later, after ice melting, these regions begin to rise
again in conjunetion with the formerly ice-loaded
crust. This phenomenon rnay affect a zone 50 to 300
km wide adjacent to the loaded and unloaded crust.
Several authors have made an attempt to simulate the flexural response ofthe crust to a given load (e.g., Watts et a1.
1982; Watts and Thome 1984). They treat the lithosphere
either as an elastic or visco-elastic plate underlain by the
viscous mantle. In the ease of pure elastie behavior, the
mechanics of lithospheric flexure can be compared with the
bending of sheets or beams having a certain flexural rigidity. This flexural rigidity, D, in turn is a funetion of the
elastic constants of the rock material, i.e., Young's modulus, E, and Poisson's ratio, a, as weH as thickness, he, ofthe
elastic lithosphere.
(8.11)
Equation (8.11) clearly shows that the elastic thickness, h e'
is the most important faetor controlling the rigidity or flexural strength of the lithosphere.
Karner et a1. (1983) have derived from observations in
nature that the rigidity, D, of the lithosphere may vary by
four orders of magnitude. It is primarily a function of the
plate age at the time of loading. Young oceanie crust at or
near a mid-oceanic ridge has the lowest rigidity, while old
continental crust, for example, below the fill of foreland
basins or Precambrian shields under an ice load, shows
very high values. The base of the elastic plates is defined
by the depth of the 450°C isotherm (cf. Fig. 8.15). Thus,
With an average sediment density of Ps = 2.15 g/em 3 ,
a sediment thiekness twice the initial water depth ean
develop (amplificationfactor 2); with Ps = 2.55 g/em 3
the amplification faetor is ab out 3. The sediment density below the sediment-water interface, in partieular
that of fine-grained sediments, increases significantly
with their thickness. Thus, the amplification factor
grows during subsidence and basin filling (cf. Fig.
11.10).
In our example of a water-filled basin (based on Eq. 8.7)
we obtained hw ,., 3.5 km. Using the density values mentioned above and listed in Fig. 8.1, Eq. (8.10) yields
h, ,., 8.7 km. This signifies that a sediment-filled segment
of this model basin will subside 2.5 times more than a
purelywater-filled segment, due to isostatie response ofthe
crust. In comparison with an air-filled depression below
sea level, the amplification factor for a corresponding
sediment-filled basin becomes even greater (in our example
approximately 1.46x2.5 ,., 3.6.
Isostatic uplift in response to denudation is treated in
Seet. 9.6.1.
Thermal Uplift and Subsidence
If a column of the lithosphere is heated above the
temperature of the surrounding rocks, its mass remains unchanged, but its volume inereases and may
eause uplift at the land surface or sea bottom.
Upwelling hot mantle material, for example at oceanic spreading centers, generates oceanie ridges
which later, due to cooling of the oeeanic erust and
thiekening of the underlying mantle lithosphere, subside considerably with age by several km. Sirnilarly,
upwelling hot mantle material below a thinning eontinental crust will first tend to raise the surface of the
thinned crust, if this thermal expansion is not exceeded by the effeets of isostasy.Later cooling will
eause subsidence which is referred to as thermal subsidenee, St. Thermal subsidence and uplift are also
affected by the 3D geometry of the system and controlled by the coefficient of thermal expansion (or
eontraction), a=3.4xlO- 5 /oC, and the thermal diffusivity ofthe lithosphere, k=8xlO- 7 m 2 /s.
If, for example, the temperature of a 50 km high rock colurnn is raised or lowered uniformly by 300°C, its height
will increase or decrease due to thermal expansion or contraction by ~0.5 km. This is, of course, an unrealistic exampIe, whieh only demonstrates the order of magnitude of
such thermal effects. In nature we observe a thermal gradient from the base of the mantle lithosphere (l350°C, Fig.
8.2) to the land surface or sea water (slightly above O°C).
With changing lithosphere thickness, this gradient and thus
the temperatures at different depths vary, but the combined
effect of this process causes approximately the same
amount of expansion or contraction as that calculated for a
rock colurnn which is subjected to the same change in
mean temperature as the lithosphere.
Chapter 8 Subsidence
As a result of mantle upwelling, a steep temperature
gradient is established. Later, this gradient is slowly
reduced by heat loss to the atmosphere, until the original gradient will be restored (Fig. 8.2b and c). This
process is described by the thermal diffusivity of the
lithosphere. Cooling of an abnormally heated lithosphere takes tens of million years. Thermal subsidence is therefore a long-term, slowly decaying process.
The mathematieal treatment of thermal expansion and contraction of the lithosphere is beyond the purpose of this text
(see, e.g., Royden et a1. 1980; Watts and Thorne 1984;
Sawyer 1988), but the following basin modeling does include thermal effects.
8.1.2 Flexural Response of the Crust to Loading
It is a well-known fact from geological observation
that the lithosphere adjacent to local or regional loads
(water, ice, sediment accumulation, isolated
seamounts on top of oceanic crust) reacts by
downwarping (Fig. 8.1 d). Similarly, unloading (lake
dessication, icemelting, rock denudation) leads to
some uplift of neighboring areas. The best studied
examples are continental ice caps, which cause not
only isostatic compensation below the ice, but also
some subsidenee in areas adjacent to the ice load.
Later, after ice melting, these regions begin to rise
again in conjunetion with the formerly ice-loaded
crust. This phenomenon rnay affect a zone 50 to 300
km wide adjacent to the loaded and unloaded crust.
Several authors have made an attempt to simulate the flexural response ofthe crust to a given load (e.g., Watts et a1.
1982; Watts and Thome 1984). They treat the lithosphere
either as an elastic or visco-elastic plate underlain by the
viscous mantle. In the ease of pure elastie behavior, the
mechanics of lithospheric flexure can be compared with the
bending of sheets or beams having a certain flexural rigidity. This flexural rigidity, D, in turn is a funetion of the
elastic constants of the rock material, i.e., Young's modulus, E, and Poisson's ratio, a, as weH as thickness, he, ofthe
elastic lithosphere.
(8.11)
Equation (8.11) clearly shows that the elastic thickness, h e'
is the most important faetor controlling the rigidity or flexural strength of the lithosphere.
Karner et a1. (1983) have derived from observations in
nature that the rigidity, D, of the lithosphere may vary by
four orders of magnitude. It is primarily a function of the
plate age at the time of loading. Young oceanie crust at or
near a mid-oceanic ridge has the lowest rigidity, while old
continental crust, for example, below the fill of foreland
basins or Precambrian shields under an ice load, shows
very high values. The base of the elastic plates is defined
by the depth of the 450°C isotherm (cf. Fig. 8.15). Thus,