Annual Report 2000 - WIT

Z
c
b
J
Z
`
Z
.- #0/RQTS 9
Z
det
# 9
D
V
Z
U
U
D
D
111
index, the weight function for common shot reads:
¨! "$#%"$'&(#%&)
+
+*
det .- #0/
,
.- 1/32)4$576809;:=A@B:=C0>ADFE (1)
det
where is the density, is the velocity, is the inclination angle, G is the KMAH
index. The subscript " denotes the source point, & denotes the receiver, denotes the J I H
depth point under consideration (image HKJ point), denotes the ray segment sourceimage
point ILJ and denotes the ray segment receiver-image point.
For a point source, using three near by rays we approximately write detMN.- #0/PO
as
a function of quantities that can be computed with KRT. The expression reads:
.U
# E (2)
.U
DWV S 9YX
S where is the distance vector between J 9Y[YD point J 9^\_D and , 9;[]\_D # Z
9^\_D # ` Z
9Y[YD #a
9;[]\WD Z
and take values from 1 to 3 and indicate the ray under J 9;[^D consideration, is c the
intersection of the ray with a given wavefront and is the slowness vector at the
source point (see Figure 1). The expression for Z 1/PO
is similar.
# detM7.-
9YX
S
Figure 1: S 9Y[d\_D Distance vector ,
and
Z
9Y[d\_D slowness difference .
9;[^D E where, and
b 9^\WD 9;[]\WD
take values from 1 to 3 and indicate
the ray under consideration.
is the intersection of the ray
9Y[YD
with a given wavefront and is the
Z
slowness vector at the source point.
M
(1)
p (1) p (31) p (3)
p (21)
x (21) x (31)
p (2)
M
(2)
M (3)
WAVEFRONT ORIENTED RAY TRACING
In the WORT technique, a wavefront (which is defined by the endpoints of rays) is
propagated stepwise through the model, and ray quantities are interpolated to a discrete
grid. To describe the WORT technique, we compare it with the classical 3D
WFC method by Vinje et al. (1996a, 1996b). In both methods the ray field is decomposed
into elementary cells (a cell is the region between three adjacent rays and two