Geoscience Reference
In-Depth Information
criteria (El-Sheimy et al.
2005
). For example, interpolation methods based on
surface coverage divided into local and global criteria. In the global methods, the
height of all control points are used to estimate the heights for the unknown points,
but in the local methods, calculation of unknown points' heights are derived from
the height of the neighbours' points. In this research, the different methods of
interpolation are used to estimate the heights at the unknown points within the
local methods, which are explained in the following sections.
4.1 Inverse Distance Weighting Method
In Inverse Distance Weighting (IDW) method, the height information of neigh-
bouring points according to the distance of unknown points and used based of
weight. Weight is a function of the distance from the unknown point and hence
closer points have higher weights. For height calculation, the following equation
is used:
i
=
1
z
i
d
i
z
=
i
=
1
1
d
j
In this equation, p is the speed reducer weight control rate according to distance,
where it is equal to 2, di
i
is the distance from unknown point to well-known point
and z
i
represents the height of point i (Lu and Wong
2008
; de Mesnard
2013
).
4.2 Polynomial Method
This method approximates the surface using polynomial terms plain elements x, y
in the form of z
=
f(x, y). The n power of this polynomial equation is:
n
n
a
ij
x
i
y
j
z
=
i
=
0
j
=
0
where x, y turned parts and plain components of known points and a
ij
are poly-
nomial coefficients, which are determined using the know elevation values in the
sample points and are obtained by least squares portion.
4.3 Kriging Method
Kriging method was introduced by Matheron (
1963
), based on the Krige variables
theory zone (Krige
1951
). This method is estimated based on a weighted moving
