Geoscience Reference
In-Depth Information
velocities and thickness changed, or layers inserted or removed, and the computa-
tions repeated until the synthetic seismograms match the recorded seismograms
to the desired degree. It is not usually possible to match every detail of a seis-
mogram, but it is possible to match the arrival times and relative amplitudes of
the main phases in a refraction record section and probably to match a few of the
waveforms well. It should be stressed that this is still not an easy, quick or cheap
process, even with increasing computer power.
Figure 4.41 shows examples of velocity models that agree with the first-arrival
travel times but for which the synthetic seismograms do not match the recorded
seismograms. For the final velocity model, both travel times and seismograms
match well. The importance of synthetic seismograms in the determination of
velocity structures should be evident from this example.
To match synthetic seismograms with recorded seismograms, one must com-
pute the synthetics to include (a) the source function (explosion, earthquake,
airgun or vibrator); (b) the effects of transmission through the Earth; and (c)
the response of the detection systems (seismometers, amplifiers, filters, tape
recorders, etc.).
The most difficult and time-consuming part of the computation of synthetic
seismograms is the calculation of the effects on the seismic waveform caused
by its passage through the Earth. There are undoubtedly lateral variations in the
crust and upper mantle, but, provided that these are gradual and small compared
with the wavelength of the incident seismic signal and the horizontal scale of
the proposed or possible structure, they can often be approximated by a model in
which the structure varies only with depth. This variation of
with depth
can always be approximated by a large stack of uniform horizontal layers. Because
computation of the total response, which means including all interconversions
and reverberations of such a stack of layers, is costly, various approximations
have been developed. Some of the approximations permit inclusion of lateral
variations in the model.
α
,
β
and
ρ
←−
(
α
= 1.5 km s
−1
) and a thin seabed layer of fractured material (
α
= 2.8-3.0 km s
−1
). (a)
The recorded record section is part of a refraction line shot along the median valley
of the Mid-Atlantic Ridge at 37
◦
N; these were some of the data used for the model in
Fig. 9.22. (b) A model with a layer 3 and normal upper mantle. The large-amplitude
arrivals at 4 s are the reflections from the 6.3
/
8.2-km s
−1
interface. (c) The amplitude
and complexity of the first arrivals have been increased. There are no
large-amplitude reflections because the velocity contrast at the interfaces is much
less than in (b). (d) These seismograms match the recorded record section (a) best;
the model was obtained from model (c) by making slight changes in layer
thicknesses and velocities and by including 7.6-km s
−1
material at depth. (e)
Replacing the 7.6-km s
−1
material of model (d) with material with a normal
upper-mantle velocity of 8.1 km s
−1
dramatically changes the seismograms. The
large-amplitude arrival is the reflection from the 7.2
8.1-km s
−1
/
interface.
