Page 59 - Fundamentals of Physical Volcanology

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36 CHAPTER 3

140 potential vertical length, the values being about
5.3 and 10.8 km, respectively. However, if the
120 magma is richer in volatiles, and the effective
Stress intensity (MPa m 1/2 ) 80 D ρ –3 length would be about 9 km. the maximum vertical
fracture toughness increases as the dike grows to,
100
1/2
−3
say, 70 MPa m , then for ∆ρ equal to −300 kg m
m
the dike would grow to only about 3.8 km and for
−3
∆ρ equal to −150 kg m
m
60
∆ρ m = –150 kg m
2 Density traps. Even if a magma does not become
40
well do so somewhere within the crust itself. This
ρ
D
is because the density of the crust decreases as
20 ∆ρ m = –300 kg m –3 negatively buoyant at the base of the crust, it may
the surface is approached, as a result of the way
0 in which the crust itself grows. In some places,
0 2 4 6 8 10 12 14
especially in continental areas, the crust will con-
Length of dike (km)
sist mainly of sedimentary rocks, whereas in others,
Fig. 3.2 The variation of the stress intensity at the growing especially on the ocean floor, it will be formed of
tip of a dike as a function of the dike length, shown for two volcanic rocks. Sedimentary deposits are formed
values of the amount ∆ρ by which the melt in the dike is
m by the accumulation of clastic material, and subse-
less dense than the surrounding mantle rocks from which it
quently these are compacted into denser rock by
has formed.
the accumulated weight of overlying deposits.
Volcanic rocks are erupted either as fragmental
An order of magnitude for the distance to which pyroclasts or as lavas which contain gas bubbles,
a dike tip can rise after it becomes negatively buoy- and in both of these cases compaction will occur as
ant can be illustrated by setting ∆ρ in eqn 3.3 the volcanic rock layers pile up. The effect of the
m
equal to a negative value, i.e., the magma is now compaction process is to produce density profiles
denser than the host rocks, and retaining ∆P = such as shown in Fig. 3.3. Figure 3.3a deals with a
4.4 MPa. Initially, as H increases, the first term in volcano built on typical oceanic crust and Fig. 3.3b
eqn 3.3 greatly exceeds the second term and the shows an average continental interior.
stress intensity at the dike tip increases. However, as Also shown in these figures are the ranges of

dike growth continues, the second term eventually depths at which one might expect to find two mag-
increases faster than the first term and the stress mas, the denser one labeled D with a density of
intensity goes through a maximum and then 3000 kg m −3 and a less dense one labeled L with a
−3
decreases: Figure 3.2 shows two examples. With density of 2700 kg m . Both magmas are produced
∆ρ =−300 kg m −3 the dike-tip stress intensity when partial melting starts somewhere in the man-
m
reaches a maximum of 92.7 MPa m 1/2 when H has tle. Magma D has its neutral buoyancy level at the
grown to about 1995 m, and decreases to small base of the crust in both the oceanic (Fig. 3.3a) and
values as H approaches about 6 km. With ∆ρ = continental (Fig. 3.3b) environments, because it
m
−150 kg m −3 the dike-tip stress intensity reaches a is at this level that the density of the surrounding
maximum of 131 MPa m 1/2 when H has grown to rocks decreases from a value greater than the
about 4000 m, and decreases to small values as H magma density to a value smaller than the magma
approaches about 12 km. Thus if the magma has a density. Thus if local buoyancy alone were the
relatively low volatile content, so that as the dike controlling factor, this magma should always be
grows there is not a great accumulation of vapor in trapped at the base of the crust. In the continental
the dike tip, and the effective fracture toughness of case, magma L should apparently be able to pene-
1/2
the surrounding rocks increases to, say, 30 MPa m , trate all the way to the surface, being buoyant at all
then for both of these magma density differences depths in both the mantle and the crust. In the
the dike will be able to grow to most of its maximum oceanic case for magma L, however, a neutral buoy-