Annual Report 2000 - WIT

k ilm
§
51
0
X 0
v 0
Depth [km]
1
2
3
v 1
v 2
NIP
0 1 2 3 4 5 6
Distance [km]
Figure 2: NIP-wavefront associated to the central zero-offset ray QSRUT'V7WXQSR , in red.
To well describe the wavefront curvature along a ray path that propagates through
the layered medium, we should consider two distinct situations: (a) the propagation
occurs inside a homogeneous layer and (b) transmission occurs across an interface.
Figure 3 depicts a ray that traverses the homogeneous Y -th layer (of velocity NZ ) being
transmitted (refracted) at the interface Y[©]\ . Let us denote by ô_^a`Z
the wavefront
radius of curvature at the initial point of the ray (that is, just below the Y -th interface).
The wavefront radius of curvature, ô¤öb`Zc5d
, just before transmission, satisfies the relationship
Z ¢ (1)
NZgf
ô-ö%`Zc5d ø±ô)^e`Z ©
‚ iE„Nm
xzy%{ uNv}|EsB~%uw
nobp i
r st%uvaw
‚ƒi
hji
xzy%{ uNv}|EsB~%uw_ €
p ilm n¥q
iPlm nobp
‚ƒilm
Figure 3: Ray propagation through layer Y .
where f §
is the traveltime of the ray inside the layer. We now consider the change
Z
in wavefront curvature due to transmission at the interface. As shown in, e.g., Hubral