Geoscience Reference
In-Depth Information
Interpolation
models
Parameter
Specification
Interpolation functions
Weight vector(W)
Constant (m)
a
: area of
Thiessen
polygon(Pi);
a
: the total
areas of all
Thiessen
polygons
NNI, Nature
Neighbor
Interpolation
n
a
a
i
i
Z
z
w
0
p
p
i
a
i
a
i
1
Q
: a
quadratic
polynomial
at the
interpolated
point Pi;
d
: the
distance
between P
0
and P
i
;
k
: a power
parameter
MSM,
Modified
Shepard's
Method
k
n
d
i
w
Z
Q
0
i
p
i
i
n
k
d
i
1
i
i
1
A
: position
vector of
unknown
point;
P
: position
vector of
known points
LP, Local
Polynomial
T
1
T
Z[
AP P
]
P Z
]
T T
1
WAPPP
[
0
p
A
: position
vector of
unknown
point;
P
: position
vector of
known points
TLI,
Triangulation
with Linear
Interpolation
1
p
Z
PZ
WAP
1
0
d
: the
distance
between P
0
and P
i
;
: the
optimal
parameter
* In this study, the power parameter k of IDW function is set as 2, as well as MSM; the
quadratic polynomial is applied in LP interpolation.
Table 1. Unified interpolation models of common spatial interpolation algorithms
n
TPS, Thin
Plate Spline
w
w
Z
wd
(
.
)ln(
.
dw
)
p
i
i
i
n
1
1
i
1
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