Over the years my colleagues and I have written a number of useful programs that are in wide use in research institutions. They are all written in Fortran, come with extensive documentation. Several packages are briefly described below, with links to online documentation. On this page you will find information about plotxy (in the next section), and also color, magmap, dplus, psd, and contour.
Although matlab effortlessly generates simple graphics during the development stages of a project, production of publication-quality figures is much more tiresome. Control of figure and text size, arrangement on the page, annotation is handled in matlab by a confusing combination of pull-down menus, and function calls, some requiring handle graphics, others not, and documentation is diffuse. In contrast, plotxy offers full control within a uniform framework, documented in one place.
The example above is a figure drawn with plotxy (mapped to jpeg and somewhat degraded) by Andrew Barbour at IGPP, UCSD. Note the different fonts, line weights, the use of filled space, and the graceful numerical axis annotation. The plotxy script for a graph such as this is fairly complex.
The user manual in PDF form is available on this link: plotxydoc;
for quick reference see
quickplotxy.
The status command will report the date of the version you are running.
The Fortran-77 source code is available here.
A script and the data files for the examples given in the
PDF file can be found here.
For drawing contour maps over the surface of the earth, an automatic
mapping facility is provided to Hammer-Aitoff equal-area projection
from values on a standard latitude-longitude grid; see the magnetic field maps which were generated by the
script at this link. The jpeg conversion
of the original PostScript file has muted the colors in this plot.
Matlab's color contouring (contourc) is reasonably good, unlike its
plain contouring facilities, which are amateurish. But, as usual,
axis control, graph placement and sizing are tricky.
The user manual in PDF form is at the link:
colordoc;
for a quick reference see
quickcolor.
The Fortran-77 source code can be downloaded from
this link.
The best-fitting solutions to a finite set of admittance data is
computed by the program Dplus. It is very useful to determine the
smallest possible data misfit that a one-dimensional system can
generate without having to perform a nonlinear search in model space,
the general but uncertain procedure. Data quality control can be
assessed: for example, a large misfit at one frequency can be a clue
to the presence of an erroneous data point, or an unrealistic error
estimate. Data quality can also be checked in admittances for TE and
TM modes in 2-D conductivity structures, although then compatibility
with a 1-D profile under each station is only approximate.
Dplus accepts data in a variety of formats and units, and can also
generate a plot file for plotxy showing the
model response and the optimal profile in D+.
Documentation in PDF format is at the link:
dplusdoc;
Fortran-77 source code is here
and a Matlab M-file is here.
Please e-mail
me if you find this program useful.
Magmap creates
diskfiles containing regular two-dimensional arrays of numbers, sampling
the required element to be plotted, and also provides scripts for
mapping the contours of the function through the program color or contour.
Magmap also has facilities for calculating field elements for
any point, on or above the Earth's surface, or within the
body of the Earth. The program has available IGRF field
models from 1900 to 2000, but can also read
Gauss coefficients (spherical harmonics) from a diskfile.
All conventional normalizations of the spherical harmonics are
catered for.
The user manual in PDF form is at the link: magmapdoc;
for a quick reference see
quickmagmap.
Fortran-77 source is at this link.
Specifically, psd is based on the sine multitaper approach of Riedel
and Sidorenko to spectral estimation. All spectral estimators smooth
the spectrum in order to reduce variance; the S-R method applies
smoothing that varies with frequency to minimize the sum of variance
and bias at each point.
The user can leave all the choices to the program, or he or she can
request higher resolution (with smooth) at the expense of increased
variance, or apply a prewhitening FIR filter, among other options.
The input data need not be evenly spaced in time - spline
interpolation is provided. Graphical output (see below)
is generated during the run via plotxy.
The power spectrum shown in the example was created from a time series of the water level in
the Salton Sea, with a simple
script, which explores the effects of several
different parameter settings: in black, default settings; in red,
increased resolution by a factor of two; in blue, a fixed number of
tapers in each frequency band.
The user manual in PDF form is at the link: psddoc;
for quick reference see
quickpsd.
The Fortran-77 source can be found
on this link.
A slimmed-down matlab version is also available
here, but it performs only sine multitaper analysis
with a fixed set of parameters.
The example above was created with a contour
script. It shows two contour maps
superimposed, one
with solid, the other with dashed level lines, and
coastlines.
Color and contour are very similar, although
contour is somewhat more flexible in providing annotation and labels
as well as addition lines on the finished plot. The user manual in
PDF form can be found by going to the link
contourdoc;
the quick reference HTML file is at
quickcontour.
Fortran-77 source can be found
here.
f(z) = -1/(0.2 + i - [z2 - 1]1/2) .
You can see the pole and branch cut clearly in this graph.
Other kinds of displays, such as perspective plots, or graphs of the
real and imaginary parts are also provided. Simple scripts also
allow the user to zoom in or out and to move around the plane to
locate points of interest.
A script is provided to perform path integrals numerically in the
plane, on lines input with the mouse.
A brief description of the capabilities can be found at zlabdoc;
and the quick reference guide is at
quickzlab.
The matlab source scripts are in
zlab.m.
Top.
Color
Contour diagrams are not supported by plotxy. The program color
meets this need. The function to be contoured must be sampled on a
rectangular lattice of points. The program displays values between
specified levels with a uniform color. The levels can be outlined in
black, or not, as required. Operation follows the same model as
plotxy: commands entered at the terminal or via a script,
and a PostScript file describing the graphic is created. Notes can
be superimposed on the contour map, as can symbols and other curves,
such as coastlines.
Top.
Dplus
The one-dimensional magnetotelluric (MT) inverse problem with
discrete and noisy data has simple solution in terms of the spectral
function of the admittance, which is the ratio
Ey(&omega)/i&omega Bx(&omega) measured at the
surface over a range of frequencies &omega . See Chapter 5 in
Geophysical Inverse Theory, 1994, by R. L. Parker.
When the admittance observations are not exactly compatible with a
one-dimensional conductivity profile (which is usually the case) the
conductivity function with the smallest misfit to observation, in the
sense of the sum of squared discrepancies, is a singular profile, a
series of delta functions in conductivity, separated by insulating
layers. Structures of this type belong to a set called
D+.
Top.
Magmap
In geomagnetism and paleomagnetism is commonly desired to make maps
of magnetic field components or directions over the surface of the
Earth or the core, based on Spherical harmonic representations.
Magmap provides an easy interface to do this. The program supplies
several map projections, including Hammer-Aitoff equal area, Lambert
equal area, Mercator, and plain lat-long. The radial field
Br at the
core's surface is plotted in this graphic
for two spherical harmonic models: a new field model and for
IGRF1900. Here Hammer-Aitoff projection is used. The magmap script
making this plot can be found here.
Top.
PSD
P.S.D. stands for the Power Spectral Density,
often simply referred to as the power spectrum, a property of stationary
stochastic time series that usually provides remarkable insights into
the physical processes in question. Loosely speaking, the PSD
gives the energy density in each frequency band; it is a statistic of
the underlying random process, and so it can only be estimated from
a given realization, that is, a given finite collection of data.
There are probably dozens of different estimation algorithms for the
job. The program psd provides a small number of easily used methods,
with the intent of providing a good spectral estimate
without requiring the user to set too many tuning parameters.
Top.
Contour
As an alternative to color for contouring is the
old-fashioned approach of drawing labeled level lines without shaded
areas of colors or grey. For many purposes this is quite acceptable
and, since it is far cheaper to publish line drawings than color
plates, the program contour may be the method of choice.
Top.
Zlab
For a class in complex analysis I wrote a set of scripts for matlab
that enabled the student to explore analytic functions. The user has
the responsibility of writing a matlab function script defining the
function he or she wishes to explore. The main script, zmap.m,
generates an array and displays the results as a contour plot of
magnitude and phase, together with the site of the singularities and
branch cuts. An example is shown below. The function displayed is
