Geoscience Reference
In-Depth Information
clear
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');
h e results are plotted as contours. h e plot also includes the locations of the
control points.
v = -40 : 10 : 20;
contourf(XI,YI,ZI,v), colorbar, hold on
plot(data(:,1),data(:,2),'o'), hold off
h e 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
shape of the contours from the biharmonic spline interpolation. h e most
important character of the bilinear gridding technique, however, is illustrated
by a projection of the data in a vertical plane.
plot(XI,ZI,'k'), hold on
plot(data(:,1),data(:,3),'ro')
text(data(:,1)+1,data(:,3),labels)
title('Linear Interpolation'), hold off
h is plot shows the projection of the estimated surface (vertical lines) and
the labeled control points. h e
z
-values at the grid points never exceed the
z
-values of the control points. As with the linear interpolation of time series
(Section 5.5), bilinear interpolation causes signii cant smoothing of the data
and a reduction in high-frequency variations.
Biharmonic spline interpolations are, in many ways, the other extreme.
h ey are ot en used for extremely irregular-spaced and noisy data.
[XI,YI] = meshgrid(420:0.25:470,70:0.25:120);
ZI = griddata(data(:,1),data(:,2),data(:,3),XI,YI,'v4');
v = -40 : 10 : 20;
contourf(XI,YI,ZI,v), colorbar, hold on
plot(data(:,1),data(:,2),'o'), hold off
h e contours suggest an extremely smooth surface. h is solution is very
useful in many applications but the method also produces a number of
artifacts. As we can see from the next plot, the estimated values at the grid
