Rit (Vísindafélag Íslendinga) - 01.06.1971, Blaðsíða 20

20
GUÐMUNDUR PÁLMASON
Formulas for head wave coefficients, which depend on the pro-
perties of both media, have heen given e.g. by Zvolinsky (1958).
The formula (4.3.1) is not valid at distances close to the critical
one for total reflection. The range of applicability of the formula
has been discussed by Donato and O’Brien (1963) with the con-
clusion that it may be applied with values of L greater than about
5—6 times the predominant wavelength in the pulse.
For more than two layers it is still possible to use a formula of
the form (4.3.1) by using the concepts of virtual source and virtual
distance (Werth, 1967). This method requires computing a new shot
point and source strength in layer n-1, which is equivalent to the
actual model as viewed from layer n. The problem is thus reduced
to a two-layer case.
At large distances L?sr and the geometrical factor becomes r-2.
In order to correct for amplitude variation with distance for more
than two layers as the case is here, it will be assumed to be accurate
enough to use formula (4.3.1). The virtual source strength and
transmission coefficients between upper layers introduce a constant
attenuation which is not of importance in relative amplitude studies.
The change in r as a result of using virtual distances is relatively
small when the surface layers are thin compared to the shot-detector
distance, as is usually the case.
In the present work the geometrical spreading factor of the head
waves has for simplicity been taken as r~2. This may introduce an
error of a few decibels in reduced amplitudes at short distances com-
pared to the reduced amplitudes at larger distances. This error is of
no major significance here.
The trace amplitudes of the head waves have been reduced in the
following manner to compensate for the effects of geometrical spread-
ing, instrumental amplification and charge size.
A,.
= A0.
100
M
(4.3.2)
where
Ar = reduced amplitude
A0 = trace amplitude
M = instrumental amplification in per cent
Q = charge size in kg
Q0 = reference charge size, taken as 1 kg.