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If the geophones on the surface z=0 are transformed into loudspeakers, where the
seismograms denoted by
(where
)
are used as the time history of the loudspeaker's causal signal,
then Huygen's principle says that the
resulting wavefield
is a linear superposition of
weighted point sources given by:
where
.
Musgrave (1970) restates Huygen's principle as "Given a wavefront at some time t_{0},
consider every point on the wavefront as a secondary point of disturbance initiated at
t_{0}.".
Consistent with this definition,
Equation 3.13 says that the forward light cones have their tips fixed
to points on the hyperbola, and at some later listening time,
their associated wavefronts superimpose to give an expanding
semicircular wavefront, as shown by the dotted
semicircle in Figure 3.6. This wavefront is that for a downgoing wavefield
reflected from the freesurface at z=0.
Figure 3.6:
Seismic waves recorded by geophones on the z=0 plane are denoted by the dashed
hyperbola, and
emanate from "past wavefronts" that
emerge from the buried point source at *.
The geophones
can be then be turned into causal loudspeakers with the
seismic traces as time
histories of the loudspeaker's signal. These loudspeakers generate
the downgoing future wavefront denoted
by dots.

Next: Loudspeakers and Backward Light
Up: Physical Interpretation
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Gerard Schuster
19980729