Rit (Vísindafélag Íslendinga) - 01.06.1971, Side 15
CRUSTAL STRUCTURE OF ICELAND
15
that the P-wave velocity in layer 3 is in most cases close to a con-
stant value of 6.5 km/sec. Exceptions to this do occur, but are not
believed to be common. It was therefore decided, in order to extract
the maximum amount of information on depth to layer 3, to assume
the P-wave velocity in this layer to be constant and equal to 6.5
km/sec. Under these circumstances the delay time method (Gardner,
1939; Willmore and Bancroft, 1960) is well suited to depth calcula-
tion, where the depth varies smoothly. This method is used in the
present work to calculate depths to layer 3. For the shallower boun-
daries the depths are obtained from the formulas for horizontal
interfaces.
The basic principle of the delay time method is as follows: The
time taken for a head wave to travel from the shot to the detector can
be expressed as follows, assmning smoothly varying stratification.
T„
X
'v„
, /yh, •cosai„\ /\Phj • cosain\
+,+, v, /+ A
x
X
= ^ + T.>s + Tdr = —■ +T,it
V„
(4.1.1)
where T„ = travel time of wave [
layer n
X = shot-detector distance
Vi = velocity in layer i
h. = thickness of layer i
cosa,,, = (1 —(Vi/V,,)2)1^
s, r indicate values at shot and receiver ends respectively
T„a = delay time at shot end
Trtj. = delay time at receiver end
T,tt ~ total delay time
__ m I rrl __m
(1 t (1 (1 j, n -r r
* n
This can be written:
where the two delay times are related to the structure over the re-
fractor as follows:
Trt =i
Trt =|
Vhj -cosai„\ (4.1.2)
+ v' h
'\"hi • cosaln\ •éí h (4.1.3)