Page 251 - Physical Principles of Sedimentary Basin Analysis

7.12 Lithospheric extension and decompression melting 233

0 0
β = 5
20 20 β = 5
β = 4 β = 4
β = 3
40 40 β = 2 β = 3
depth [km] 60. β = 2 liquidus depth [km] 60

80 80 β = 1
β = 1 solidus
100 100

120 120
0 500 1000 1500 2000 0.00 0.05 0.10 0.15 0.20 0.25 0.30
temperature [°C] melt fraction [−]
(a) (b)
Figure 7.23. Melt generation for different stretching factors. (a) the geotherms for different stretching
factors are plotted together with the solidus. (b) the melt fraction as a function of depth for different
stretching factors. (Data from Table 7.1 are used.)

10

8
total melt thickness [km] 6

4

2 β min

0
0 2 4 6 8 10 12
β [−]
Figure 7.24. The total melt thickness is plotted as a function of the stretching factor β. (Data from
Table 7.1 are used.)

which becomes
2
T a a Aβ 1 1
2
M(β) = − (7.136)
2(T l,0 − T s,0 )(βT a − aA) β min β
when it is expressed as a function of the stretching factor. (See Note 7.9 for the details of
the derivation.) Figure 7.24 shows the total thickness of melt production as a function of the
stretching factor β, and to generate more than 3000 m with melt requires stretching factors
larger than 3. The amount of melt shown in Figure 7.24 should be handled with care, not
only because the model is very simple, but also because there are great uncertainties in