Geoscience Reference
In-Depth Information
Equation 8.9 - Initial probabilistic-based GP solution
()
−
17
.
VV V
log(
)
VV
log
V
TV V
VV V
V
=
()
+
26 1
26
1
6
6
6
log
ij
2
1
2
(
)
)
)
−
14
.
++
()
+
()
(
2
−
12
.
log(
V
)
15
.
−
17
.
+
VVV
log
VVVVV
log
V
VVV
log
V VV V
+
V
1
1
1
6
2
2 8
2 6
2
1 26 22
6
6
8
+
()
2
log
V
VVV
V
+
(8.9)
VV
VV V
+
1
2
8
26
+
26 8
131
.
32
.
VV
V
+
V
V
6
2
8
+
5
6
(
)
()
(
)
117
.
2
VVVVV
loglog
+
5
2
2
2
6
8
Equation 8.10 - Simplified volume-based equation
V
2
TV
ij
=
1
−
0 008
.
−−
+
−
31 40
. †
.
+
V
(
)
5
−
297
. xp
V
−
463
V
0 78
.
V
8
6
6
V
4
1
×
+
V
8
(8.10)
V
+
20 23
.
+
8
exp.
−
941
V
+
V
5
8
V
2
Equation 8.11 - Simplified probabilistic-based equation
(
)
V
2
exp.
.
−
005
V
2
5
T
ij
=
(8.11)
12
V
6
SoS values calculated for the GP models are provided in Table 8.10. The results are also compared
and contrasted against a conventional spatial interaction model. The standard model was specified as
(
)
α
TAOW
=⋅
⋅
⋅ −⋅
exp
β
C
(8.12)
ij
i
i
ij
j
where
i
is the origin
j
is the destination
T
is a trip
O
is the size of the origin
W
is the attractiveness of the destination
C
is a distance or cost measure
the β parameter controls the willingness to travel
A
is a balancing factor, so that the origin totals match, defined as
−
1
n
∑
(
)
A W C
i
=
⋅ −⋅
exp
β
(8.13)
j
ij
j
=
1
The parameters α and β are optimised according to an error function.
