Geoscience Reference
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least six adjacent control points. h e i nal surface is a composite comprising
dif erent portions of these splines. MATLAB has, from the start, provided a
biharmonic spline interpolation method, which was developed by Sandwell
(1987). h is gridding method is particularly well suited for producing smooth
surfaces from noisy data sets with unevenly-distributed control points. As an
example we use synthetic xyz data representing the vertical distance between
the surface of an imaginary stratigraphic horizon that has been displaced
by a normal fault, and a reference surface. h e foot wall of the fault shows
roughly horizontal strata, whereas the hanging wall is characterized by the
development of two large sedimentary basins. h e xyz data are irregularly
distributed and so need to be interpolated onto a regular grid. h e xyz data
are stored as a three-column table in a i le named normalfault.txt .
4.3229698e+02 7.4641694e+01 9.7283620e-01
4.4610209e+02 7.2198697e+01 6.0655065e-01
4.5190255e+02 7.8713355e+01 1.4741054e+00
4.6617169e+02 8.7182410e+01 2.2842172e+00
4.6524362e+02 9.7361564e+01 1.1295175e-01
4.5526682e+02 1.1454397e+02 1.9007110e+00
4.2930233e+02 7.3175896e+01 3.3647807e+00
(cont'd)
h e i rst and second column contain the coordinates x (between 420 and 470
of an arbitrary spatial coordinate system) and y (between 70 and 120), while
the third column contains the vertical z -values. h e data are loaded using
clear
data = load('normalfault.txt');
Initially, we wish to create an overview plot of the spatial distribution of the
control points. In order to label the points in the plot, numerical z -values of
the third column are converted into character string representations with a
maximum of two digits.
labels = num2str(data(:,3),2);
h e 2D plot of our data is generated in two steps. Firstly, the data are
displayed as empty circles using the plot command. Secondly, the data are
labeled using the function text(x,y,'string') , which adds text contained in
string to the xy locations. h e value 1 is added to all x coordinates in order
to produce a small of set between the circles and the text.
plot(data(:,1),data(:,2),'o'), hold on
text(data(:,1)+1,data(:,2),labels), hold off
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