Skip to content

Commit

Permalink
More formatting of references
Browse files Browse the repository at this point in the history
  • Loading branch information
PaulWessel committed Jun 18, 2023
1 parent bb0eefd commit 8bf949a
Show file tree
Hide file tree
Showing 14 changed files with 23 additions and 22 deletions.
2 changes: 1 addition & 1 deletion doc/rst/source/rose.rst
Original file line number Diff line number Diff line change
Expand Up @@ -174,7 +174,7 @@ Optional Arguments
**-Q**\ [*alpha*]
Sets the confidence level used to determine if the mean resultant
is significant (i.e., Lord Rayleigh test for uniformity) [0.05].
**Note**: The critical values are approximated [Berens, 2009] and
**Note**: The critical values are approximated [*Berens*, 2009] and
requires at least 10 points; the critical resultants are accurate
to at least 3 significant digits. For smaller data sets you
should consult exact statistical tables.
Expand Down
12 changes: 6 additions & 6 deletions doc/rst/source/spectrum1d.rst
Original file line number Diff line number Diff line change
Expand Up @@ -36,8 +36,8 @@ columns on standard input [or *x[y]file*]. These values are treated as
timeseries X(t) [Y(t)] sampled at equal intervals spaced *dt* units
apart. There may be any number of lines of input. **spectrum1d** will
create file[s] containing auto- [and cross- ] spectral density estimates
by Welch's method of ensemble averaging of multiple overlapped windows,
using standard error estimates from Bendat and Piersol.
by *Welch*\ 's [1967] method of ensemble averaging of multiple overlapped windows,
using standard error estimates from *Bendat and Piersol* [1986].

The output files have 3 columns: f or w, p, and e. f or w is the
frequency or wavelength, p is the spectral density estimate, and e is
Expand Down Expand Up @@ -229,7 +229,7 @@ Another is to form a parametric model for the auto-correlation structure in x(t)
the spectrum of that model. This last approach is what is done in what is called the
"maximum entropy" or "Berg" or "Box-Jenkins" or "ARMA" or "ARIMA" methods.

Welch's method is a tried-and-true method. In his method, you choose a segment length,
*Welch*\ 's method is a tried-and-true method. In his method, you choose a segment length,
**-S**\ *N*, so that estimates will be made from segments of length *N*. The frequency samples
(in cycles per delta_t unit) of your P_useful will then be at *k* /(*N* \* *delta_t*),
where *k* is an integer, and you will get *N* samples (since the spectrum is an even
Expand All @@ -246,17 +246,17 @@ the spectral bandwidth of each estimate, because the estimate at frequency sampl
is now a little correlated with the estimate at frequency sample k+1. (Of course this
would also happen if you simply formed P_raw and then smoothed it.)

Finally, Welch's method also uses overlapped processing. Since the Von Hann window is
Finally, *Welch*\ 's method also uses overlapped processing. Since the Von Hann window is
large in the middle and tapers to near zero at the ends, only the middle of the segment
of length *N* contributes much to its estimate. Therefore in taking the next segment
of data, we move ahead in the x(t) sequence only *N*/2 points. In this way, the next
segment gets large weight where the segments on either side of it will get little weight,
and vice versa. This doubles the smoothing effect and ensures that (if *N* << *M*)
nearly every point in x(t) contributes with nearly equal weight in the final answer.

Welch's method of spectral estimation has been widely used and widely studied. It is very
*Welch*\ 's method of spectral estimation has been widely used and widely studied. It is very
reliable and its statistical properties are well understood. It is highly recommended in
such textbooks as "Random Data: Analysis and Measurement Procedures" by Bendat and Piersol.
such textbooks as "Random Data: Analysis and Measurement Procedures" [*Bendat and Piersol*, 1986].

In all problems of estimating parameters from data, there is a classic trade-off between
resolution and variance. If you want to try to squeeze more resolution out of your data
Expand Down
3 changes: 2 additions & 1 deletion doc/rst/source/sph2grd.rst
Original file line number Diff line number Diff line change
Expand Up @@ -34,7 +34,8 @@ Description
-----------

**sph2grd** reads a spherical harmonics coefficient table with records of
L, M, C[L,M], S[L,M] and evaluates the spherical harmonic model on the specified grid.
L, M, C[L,M], S[L,M] and evaluates the spherical harmonic model on the specified grid
[*Holmes and Featherstone*, 2002].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/mgd77/mgd77convert.rst
Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ Description

**mgd77convert** reads versions of MGD77 files and writes the same data
in (probably) another format to a new file in the current directory.
Both pre- and post-Y2K MGD77 formats can be processed.
Both pre- and post-Y2K MGD77 formats can be processed [*Wessel and Chandler*, 2007].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/mgd77/mgd77info.rst
Original file line number Diff line number Diff line change
Expand Up @@ -31,7 +31,7 @@ record of information about each cruise specified. The information
includes beginning and end times, total track distances in km, longitude
and latitude range, and the total number of geophysical observations.
Optionally, choose instead to see the original MGD77 header meta-data
section or its individual members.
section or its individual members [*Wessel and Chandler*, 2007].

If you need to know which tracks are crossing through a given region and
what kinds of geophysical observations are available, consider using the
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/mgd77/mgd77manage.rst
Original file line number Diff line number Diff line change
Expand Up @@ -42,7 +42,7 @@ obtained by sampling a grid (choose between GMT grid or a Sandwell/Smith
Mercator \*.img grid) along track. The new data will be appended to the
MGD77+ file in the form of an extra data column of specified type. The
data file will be modified; no new file will be created. For the big
issues, see the DISCUSSION section below.
issues, see the DISCUSSION section below [*Wessel and Chandler*, 2007].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/mgd77/mgd77track.rst
Original file line number Diff line number Diff line change
Expand Up @@ -41,7 +41,7 @@ Description
-----------

**mgd77track** reads NCEI MGD77 cruises and plots one or more ship tracks
on a map using the specified projection.
on a map using the specified projection [*Wessel and Chandler*, 2007].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/potential/gmtflexure.rst
Original file line number Diff line number Diff line change
Expand Up @@ -43,7 +43,7 @@ Description
of user-selectable options, such as boundary conditions, pre-existing
deformations, variable rigidity and restoring force, and more. The solutions
are obtained using finite difference approximations to the differential
equations.
equations [*Bodine*,\ 1980].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/potential/talwani2d.rst
Original file line number Diff line number Diff line change
Expand Up @@ -43,7 +43,7 @@ We can compute anomalies on an equidistant lattice (by specifying a lattice with
**-T**) or provide arbitrary output points specified in a file via |-N|.
Choose between free-air anomalies, vertical gravity gradient anomalies, or geoid anomalies.
Options are available to control axes units and direction.

For theory, see references at the end.

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/potential/talwani3d.rst
Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ We can compute anomalies on an equidistant grid (by specifying a new grid with
**-R** and |-I| or provide an observation grid with desired elevations) or at arbitrary
output points specified via |-N|. Choose between free-air anomalies, vertical
gravity gradient anomalies, or geoid anomalies. Options are available to control
axes units and direction.
axes units and direction. For theory, see *Kim and Wessel* [2016] and *Talwani and Ewing* [1960].


Required Arguments
Expand Down
8 changes: 4 additions & 4 deletions doc/rst/source/supplements/spotter/backtracker.rst
Original file line number Diff line number Diff line change
Expand Up @@ -45,8 +45,8 @@ Description
**backtracker** reads (longitude, latitude, age) positions from
*infiles* [or standard input] and computes rotated (x,y,t) coordinates
using the specified rotation parameters. It can either calculate final
positions [Default] or create a sampled track (flowline or hotspot
track) between the initial and final positions. The former mode allows
positions [Default] or create a sampled track (flowline or hotspot track)
between the initial and final positions [*Wessel*, 1999]. The former mode allows
additional data fields after the first 3 columns which must have
(longitude,latitude,age). See option **-:** on how to read
(latitude,longitude,age) files.
Expand Down Expand Up @@ -208,14 +208,14 @@ total reconstruction rotations for the plate (PAC_APM.txt), try
echo 204 19 80 | gmt backtracker -Df -EPAC_APM.txt -Lb1 > path.txt

To predict Hawaiian-Emperor seamount trail using the Pacific absolute plate
and plume motion from Doubrovine et al. (2012), use
and plume motion from *Doubrovine et al.* [2012], use

::

echo -155.2872 19.3972 80 | gmt backtracker -Df -Lb1 -ED2012.txt -FD2012_HI_drift.txt > traildrift.txt

To predict the Hawaiian-Emperor seamount trail that would have resulted if no plume drift had been in effect,
using the Pacific absolute plate motion model from Doubrovine et al. (2012), use
using the Pacific absolute plate motion model from *Doubrovine et al.* [2012], use

::

Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/spotter/grdspotter.rst
Original file line number Diff line number Diff line change
Expand Up @@ -40,7 +40,7 @@ Description
calculates flowlines from each node that exceeds a minimum value using
the specified rotations file. These flowlines are then convolved with
the volume of the prism represented by each grid node and added up to
give a Cumulative Volcano Amplitude grid (CVA).
give a Cumulative Volcano Amplitude grid (CVA) [*Wessel*, 1999; 2008].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/spotter/hotspotter.rst
Original file line number Diff line number Diff line change
Expand Up @@ -43,7 +43,7 @@ using the specified stage or total reconstruction rotations. These
flowlines are convolved with the shape of the seamount (using a Gaussian
shape given amplitude and radius = 6 sigma) and added up to give a
Cumulative Volcano Amplitude grid (CVA). See option **-:** on how to
read (latitude,longitude,...) files.
read (latitude,longitude,...) files [*Wessel*, 1999; 2008].

Required Arguments
------------------
Expand Down
2 changes: 1 addition & 1 deletion doc/rst/source/supplements/spotter/originater.rst
Original file line number Diff line number Diff line change
Expand Up @@ -44,7 +44,7 @@ records from *table* [or standard input] and uses the given Absolute
Plate Motion (APM) stage or total reconstruction rotation file and the
list of hotspot locations to determine the most likely origin (hotspot)
for each seamount. It does so by calculating flowlines back in time and
determining the closest approach to all hotspots. The output consists of
determining the closest approach to all hotspots [*Wessel*, 1999]. The output consists of
the input records with four additional fields added for each of the
*n_hs* closest hotspots. The four fields are the hotspot id (e.g.,
HWI), the stage id of the flowline segment that came closest, the
Expand Down

0 comments on commit 8bf949a

Please sign in to comment.