Page 174 - MATLAB Recipes for Earth Sciences

7.8 Comparison of Methods and Potential Artifacts 169

The biharmonic spline interpolation described in this chapter provides a so-
lution to most gridding problems. It therefore was the only gridding method
that came with MATLAB for quite a long time. However, different applica-
tions in earth sciences require different methods for interpolation. However,
there is no method without problems. The next chapter compares biharmon-
ic splines with other gridding methods and summarizes their strengths and
weaknesses.

7.8 Comparison of Methods and Potential Artifacts

The first example illustrates the use of the bilinear interpolation technique
for gridding irregular-spaced data. Bilinear interpolation is an extension of
the one-dimensional linear interpolation. In the two-dimensional case, linear
interpolation is performed in one direction fi rst, then in the other direction.
Intuitively, the bilinear method is one of the simplest interpolation tech-
niques. One would not expect serious artifacts and distortions of the data.
On the contrary, this method has a number of disadvantages and therefore
other methods are used in many applications.
The sample data used in the previous chapter can be loaded to study the
performance of a bilinear interpolation.

data = load('normalfault.txt');
labels = num2str(data(:,3),2);

We now choose the option linear while using the function griddata to
interpolate the data.
[XI,YI] = meshgrid(420:0.25:470,70:0.25:120);
ZI = griddata(data(:,1),data(:,2),data(:,3),XI,YI,'linear');

The result are plotted as fi lled contours. The plot also includes the location
of the control points.

contourf(XI,YI,ZI), colorbar, hold on
plot(data(:,1),data(:,2),'ko')
The new surface is restricted to the area that contains control points. By
default, bilinear interpolation does not extrapolate beyond this region.
Furthermore, the contours are rather angular compared to the smooth out-
line of the biharmonic spline interpolation. The most important character of
the bilinear gridding technique, however, is illustrated by a projection of the
data in a vertical plane.