Rit (Vísindafélag Íslendinga) - 01.06.1971, Page 118
118
GUÐMUNDUR PÁLMASON
Anderson et al., 1968). It is of interest to look at the possible effect
of temperature on the velocity in layer 3 in particular.
At pressures which are sufficiently high to eliminate the effect of
porosity, presumably over 1-2 khars, the velocity is a function of
pressure and temperature, for a constant composition.
V = V(p,T)
dv=d7)T'di>+
dV
dz
rm
\8p/T dz
(w)P
dp r /8V\
• dT = V . «D
(
dT
dp + V • aT • dT
(11.9.1)
8T/p dz
= V-«»
dp
dz
+ V-
where «p = pressure coefficient of velocity
aT = temperature coefficient of velocity
g = geothermal gradient.
«t- g
(11.9.2)
According to Birch (1958) a typical value of aT for gahhro is
— 5 X 10“5 °Cr1. From gradient measurements in drillholes in Ice-
land one may expect a maximum variation of about 200°C at the 2—3
boundary. For a constant depth this gives a variation of Vp of about
0.065 km/sec or 1 per cent. This variation is too small to be detected
by field measurements.
Looking furthermore at a possible variation within layer 3 of the
P-wave velocity as a result of variations in pressure and tempera-
ture one obtains from eqn. (11.9.2), assuming the pressure to be the
lithostatic pressure
dV„ _
dz - V.. • («i» • Q ■ go + aT • g)
where q = density
go = acceleration of gravity.
Using a probable value of 4 X 10“G bam1 for ap and 2.9 g/cm3 for
Q, one obtains with two different values of the gradient g the follow-
ing results for dVp/dz in layer 3.
a) g = 50°C/km, gives —= — 8.9 X 10“3 sec“x
dz
b) g = 100°C/km, gives—= — 25.1 X 10“:! sec-1
For a layer thickness of 5 km this corresponds to a velocity decrease
of 0.04 and 0.13 km/sec, respectively, from the top to the bottom of
the layer.