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Contained applications
======================
Pyrocko contains a few standalone applications for everyday seismological
practice.
* Snuffler: an extensible seismogram browser and workbench
* Cake: travel-time and ray-path computations for 1D layered earthmodels
* Fomosto: a tool to manage pre-calculated Green's function stores
* Jackseis: a command-line tool for common waveform archive data manipulations
.. toctree::
:maxdepth: 2
apps_snuffler
apps_cake
apps_fomosto

@ -0,0 +1,11 @@
Cake
====
Cake is a command line tool contained in Pyrocko, which can solve some
classical seismic ray theory problems for 1D layered earth models (layer cake
models).
.. toctree::
:maxdepth: 2
apps_cake_manual

@ -1,7 +1,7 @@
Cake
====
Cake manual
===========
Cake is a module which can be used to solve classical seismic ray theory
Cake is a tool which can be used to solve classical seismic ray theory
problems for layered earth models (layer cake models).
For various seismic phases it can calculate:
@ -21,58 +21,58 @@ Invocation
.. program:: cake
::
::
cake <subcommand> [options]
cake <subcommand> [options]
Subcommands:
.. describe:: print
.. describe:: print
get information on model/phase/material properties
.. describe:: arrivals
.. describe:: arrivals
print list of phase arrivals
.. describe:: paths
.. describe:: paths
print ray path details
.. describe:: plot-xt
.. describe:: plot-xt
plot traveltime vs distance curves
.. describe:: plot-xp
.. describe:: plot-xp
plot ray parameter vs distance curves
.. describe:: plot-rays
.. describe:: plot-rays
plot ray propagation paths
.. describe:: plot
.. describe:: plot
plot combination of ray and traveltime curves
.. describe:: plot-model
.. describe:: plot-model
plot velocity model
.. describe:: list-models
.. describe:: list-models
list builtin velocity models
.. describe:: list-phase-map
.. describe:: list-phase-map
show translation table for classic phase names
.. describe:: simplify-model
.. describe:: simplify-model
create a simplified version of a layered model
.. describe:: scatter
show details about scattering at model interfaces
To get further help and a list of available options for any subcommand run::
@ -90,35 +90,35 @@ above.
Phases:
"""""""
Seismic phase arrivals may be either specified as traditional phase names
(e.g. P, S, PP, PcP, ...) or in Cake's own syntax which is more powerful.
(e.g. P, S, PP, PcP, ...) or in Cake's own syntax which is more powerful.
Use the :option:`--classic` option, for traditional phase names. Use the :option:`--phase`
option if you want to define phases in Cake's syntax.
.. option:: --phase=PHASE1,PHASE2,..., --phases=PHASE1,PHASE2,...
Comma separated list of seismic phases in Cake's syntax.
The definition of a seismic propagation path in Cake's phase syntax is
a string consisting of an alternating sequence of *legs* and *knees*.
A *leg* represents seismic wave propagation without any conversions,
encountering only super-critical reflections. Legs are denoted by ``P``,
``p``, ``S``, or ``s``. The capital letters are used when the take-off of
the *leg* is in downward direction, while the lower case letters
indicate a take-off in upward direction.
A *knee* is an interaction with an interface. It can be a mode
conversion, a reflection, or propagation as a headwave or diffracted
wave.
* conversion is simply denoted as: ``(INTERFACE)`` or ``DEPTH``
* upperside reflection: ``v(INTERFACE)`` or ``vDEPTH``
* underside reflection: ``^(INTERFACE)`` or ``^DEPTH``
* normal kind headwave or diffracted wave: ``v_(INTERFACE)`` or
``v_DEPTH``
The interface may be given by name or by depth: INTERFACE is the name
of an interface defined in the model, DEPTH is the depth of an
interface in [km] (the interface closest to that depth is chosen). If
@ -128,7 +128,7 @@ option if you want to define phases in Cake's syntax.
The preferred standard interface names in cake are ``conrad``,
``moho``, ``cmb`` (core-mantle boundary), and ``icb`` (inner core
boundary).
The phase definition may end with a backslash ``\``, to indicate that
the ray should arrive at the receiver from above instead of from
below. It is possible to restrict the maximum and minimum depth of a
@ -161,11 +161,11 @@ Source-receiver geometry:
"""""""""""""""""""""""""
.. option:: --sdepth=FLOAT
Source depth [km] (default: 0)
.. option:: --rdepth=FLOAT
Receiver depth [km] (default: 0)
.. option:: --distances=DISTANCES
@ -179,15 +179,15 @@ An isotropic elastic material may be specified by giving a combination of
some of the following options.
.. option:: --vp=FLOAT
P-wave velocity [km/s]
.. option:: --vs=FLOAT
S-wave velocity [km/s]
.. option:: --rho=FLOAT
density [g/cm**3]
.. option:: --qp=FLOAT
@ -246,10 +246,10 @@ General:
Name or depth [km] of interface to select
Command Line Examples
Command line examples
---------------------
Plot P and p Phases
Plot P and p phases
^^^^^^^^^^^^^^^^^^^
Ten receiver distances ranging from 100 km to 1000 km and a source depth of 10km.
@ -277,7 +277,7 @@ Receivers may be at any depth. Arbitrary reflection/conversion histories may be
.. figure:: _static/cake_plot_example_2.png
:scale: 80%
To print arrival times and other ray parameters, replace ``plot-rays`` with
To print arrival times and other ray parameters, replace ``plot-rays`` with
``arrivals`` in the command line above.
::
@ -285,14 +285,14 @@ To print arrival times and other ray parameters, replace ``plot-rays`` with
> cake arrivals --sdepth=15 --distances=10 --rdepth=4.443 --crust2loc=0,0 \
--phase='pP\,pPv3pP\,pPv3pPv3pP\,p'
slow dist time take inci effi spre phase used
s/km km s deg deg % %
slow dist time take inci effi spre phase used
s/km km s deg deg % %
----------------------------------------------------------------------------
0.09711 10.00 2.3147 128 10.6 58.7 103 p (p)
0.09099 10.00 8.1792 132 97.8 49.2 725 pP\ (p^0P\)
0.09711 10.00 2.3147 128 10.6 58.7 103 p (p)
0.09099 10.00 8.1792 132 97.8 49.2 725 pP\ (p^0P\)
0.08461 10.00 14.052 136 97.3 8.03 729 pPv3pP\ (p^0Pv4.443p^0P\)
0.07835 10.00 19.931 140 96.8 1.32 710 pPv3pPv3pP\ (p^0Pv4.443p^0Pv4.443p^0P\)
Classic phase names
^^^^^^^^^^^^^^^^^^^
@ -320,7 +320,7 @@ Cake phases
It is possible to see the exact definition of a phase using ``cake print ...``::
> cake print --classic=Pg
Phase definition "P<(moho)":
- P mode propagation, departing downward (may not propagate deeper than interface moho)
@ -353,12 +353,12 @@ Here's another example to illustrate why cake needs its special phase definition
Material calculator
^^^^^^^^^^^^^^^^^^^
Cake can also be used to convert between different material parameters::
Cake can also be used to convert between different material parameters::
> cake print --vp=5 --poisson=0.25
P wave velocity [km/s] : 5
S wave velocity [km/s] : 2.88675
P/S wave vel. ratio : 1.73205
P/S wave vel. ratio : 1.73205
Lame lambda [GPa] : 21.6667
Lame shear modulus [GPa] : 21.6667
Poisson ratio : 0.25
@ -377,15 +377,15 @@ Energy scatter at interface
The ``scatter`` subcommand may be used to see how much energy (in percent) is
transmitted through or reflected by an interface for any given surface
slowness (P-SV case)::
> cake scatter --interface=moho --slowness=0.0
interface "moho" (35 km)
4.349 3.209 95.65 96.79
\P /P \S /S /P /S
4.349 3.209 95.65 96.79
\P /P \S /S /P /S
---------------- ---------------- ---------------- ----------------
\P \S /P \P /S \S
95.65 96.79 4.349 3.209
\P \S /P \P /S \S
95.65 96.79 4.349 3.209
@ -393,15 +393,15 @@ slowness (P-SV case)::
interface "moho" (35 km)
3.899 92.69 1.859 3.899 94.24 3.411
\P /S /P \S /S /P /S /P
\P /S /P \S /S /P /S /P
---------------- ---------------- ----------------
\S \S /S \S
3.411 94.24 2.347
\S \S /S \S
3.411 94.24 2.347
Python Script Examples
Python script examples
----------------------
Calculate P-phase arrivals
@ -410,7 +410,7 @@ Calculate P-phase arrivals
The following Python script calculates arrival times for the P-phase emitted by an event in a depth of 300km.
::
'''
Calculate P-phase arrivals.
'''

@ -0,0 +1,10 @@
Fomosto
=======
Fomosto is a command line tool contained in the Pyrocko package to manage
pre-calculated Green's function stores.
.. toctree::
:maxdepth: 2
apps_fomosto_tutorial

@ -1,4 +1,4 @@
Fomosto Tutorial
Fomosto tutorial
================
Fomosto is a tool to help create and work with pre-calculated and stored
@ -13,7 +13,7 @@ seismogram calculation over source imaging techniques to source inversion
methods. Calculation of Green's functions is a computationally expensive
operation and it can be of advantage to calculate them in advance. The same
Green's function traces can then be reused several or many times as required in
a typical application.
a typical application.
Regarding Green's function creation as an independent step in a use-case's
processing chain encourages to store these in an application independant form.
@ -31,7 +31,7 @@ Pyrocko contains a flexible framework to store and work with pre-calculated
Green's functions. It is implemented in the :py:mod:`pyrocko.gf` subpackage.
Also included, is a powerful front end tool to create, inspect, and manipulate
Green's function stores: the :program:`fomosto` tool ("*forward model storage
tool*").
tool*").
Invocation and online help
--------------------------
@ -44,7 +44,7 @@ started without any arguments.
::
$ fomosto
Usage: fomosto <subcommand> <arguments> ... [options]
Usage: fomosto <subcommand> <arguments> ... [options]
Subcommands:
@ -108,7 +108,7 @@ is created::
|-- config # (1)
`-- extra/
`-- qseis # (2)
The file ``config`` (1) contains general settings and the file ``extra/qseis``
(2) contains extra settings which are specific to the QSEIS modelling code.
@ -116,7 +116,7 @@ These files are in the `YAML <http://yaml.org/>`_ format, which is good
compromise between human and computer readability. The contents of the
configuration files are disussed in the next section. The default
configuration produced by the ``fomosto init`` command can be used without any
modifications for a quick functional test.
modifications for a quick functional test.
First step is to create tabulated phase arrivals::
@ -134,13 +134,13 @@ Now, we can calculate the Green's function traces::
$ fomosto build
Green's functions are built in parallel, if possible. The number of worker processes
may be limited with the ``--nworkers=N`` option.
may be limited with the ``--nworkers=N`` option.
We now have a complete Green's function store, ready to be used. This is the
directory structure of the store::
my_first_gfs/ # this directory represents the GF store
|-- config # general settings
|-- config # general settings
|-- decimated/ # directory for decimated variants of the store
|-- extra/ # any extra meta information is in here
| `-- qseis # e.g. parameters used for the initial modelling
@ -155,17 +155,17 @@ directory structure of the store::
`-- traces # big binary file with the actual GF data samples
We may now want to change some configuration values and rebuild the Green's
functions.
functions.
Configuration
-------------
.. highlight :: yaml
These are the initial contents of the ``config`` file::
--- !pyrocko.gf.meta.ConfigTypeA # this type is for cylindrical symmetry with
--- !pyrocko.gf.meta.ConfigTypeA # this type is for cylindrical symmetry with
# receivers all at the same depth
# this label should be set to something unique if the GF store should be published
@ -174,8 +174,8 @@ These are the initial contents of the ``config`` file::
# indicates, that QSEIS is/was used for the modelling
modelling_code_id: qseis
# a layered earth model, used for modelling of the Green's functions
# and for calculation of phase arrivals. Format is the 'nd' format
# a layered earth model, used for modelling of the Green's functions
# and for calculation of phase arrivals. Format is the 'nd' format
# as used in cake.
earthmodel_1d: |2 # '|2' means that a text block indented with 2 blanks follows
@ -185,16 +185,16 @@ These are the initial contents of the ``config`` file::
35. 6.5 3.85 2.9 1283. 600.
mantle
35. 8.04 4.48 3.58 1449. 600.
...
sample_rate: 0.2 # [Hz]
ncomponents: 10 # number of Green's function components (always use 10 with QSEIS).
# travel time tables are calculated for the phase arrivals defined below
# travel time tables are calculated for the phase arrivals defined below
# the travel time tables can be referenced at other points in the configuration
# by their id
tabulated_phases:
tabulated_phases:
- !pyrocko.gf.meta.TPDef
id: begin
definition: p,P,p\,P\,Pv_(cmb)p # phase defintions in *cake* syntax, first available arrival is used
@ -208,7 +208,7 @@ These are the initial contents of the ``config`` file::
...
# uniform receiver depth with this type of GF config
receiver_depth: 0.0 # [m]
receiver_depth: 0.0 # [m]
# extents and spacing of the GF traces [m]
source_depth_min: 10000.0
@ -230,7 +230,7 @@ The initial contents of the QSEIS specific configuration file ``extra/qseis``::
# with the folowing setting, Green's functions will be calculated for (at
# least) the time region between 'begin' minus 50 seconds to 'end' plus 100
# seconds, where 'begin' and 'end' are tabulated phases as defined in the
# main main configuration
# main main configuration
time_region: [begin-50, end+100] # see note below
@ -238,7 +238,7 @@ The initial contents of the QSEIS specific configuration file ``extra/qseis``::
cut: [begin-50, end+100] # see note below
# following docs are excerpts from the QSEIS documentation
# following docs are excerpts from the QSEIS documentation
# select slowness integration algorithm (0 = suggested for full wave-field
# modelling; 1 or 2 = suggested when using a slowness window with narrow
@ -295,15 +295,15 @@ The initial contents of the QSEIS specific configuration file ``extra/qseis``::
gradient_resolution_vp: 0.0
gradient_resolution_vs: 0.0
gradient_resolution_density: 0.0
# wavelet duration [unit = time sample rather than sec!], that is about
# equal to the half-amplitude cut-off period of the wavelet (> 0. if <= 0,
# then default value = 2 time samples will be used)
# then default value = 2 time samples will be used)
wavelet_duration_samples: 0.001
# switch for the wavelet form (0 = user's own wavelet; 1 = default wavelet:
# normalized square half-sinusoid for simulating a physical delta impulse;
# switch for the wavelet form (0 = user's own wavelet; 1 = default wavelet:
# normalized square half-sinusoid for simulating a physical delta impulse;
# 2 = tapered Heaviside wavelet, i.e. integral of wavelet 1)
wavelet_type: 2
@ -311,7 +311,7 @@ The initial contents of the QSEIS specific configuration file ``extra/qseis``::
.. highlight:: console
.. note::
The syntax for the timings in the ``time_region`` and ``cut`` in the above
example configuration is described in :py:class:`pyrocko.gf.meta.Timing`.
@ -351,7 +351,7 @@ the surface and *f_max* is the highest frequency to be analysed. For example if
we want to study waveforms in a frequency range of up to 2 Hz and the slowest
horizontal velocities are 2 km/s, we need a grid spacing well below 1 km so we
may try with 250 m. The Green's functions should be calculated with a temporal
sampling rate of at least 4 Hz in this example, better more.
sampling rate of at least 4 Hz in this example, better more.
Typically there is some trial and error involved in determining a stable and
efficient set of parameters for a new modelling setup. The strategy is to first
@ -448,11 +448,11 @@ example if we want to extend an existing store with more additional source
depths, or if we wish to extract a subset of an existing database. This is
done with Fomosto by creating an empty target store with the desired extents
and by then copying the relevant traces from the source stores to the target
store.
store.
1) Create empty copy of ``my_first_gfs``::
$ fomosto init redeploy my_first_gfs derived
$ fomosto init redeploy my_first_gfs derived
2) Adjust parameters in ``derived/config``; e.g. change the extents of the
store.
@ -464,33 +464,33 @@ store.
$ fomosto redeploy my_first_gfs derived
Python Script Examples
Python script examples
----------------------
Retrieve synthetic seismograms from a local store
Retrieve synthetic seismograms from a local store
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. highlight:: python
It is assumed that a :py:class:`pyrocko.gf.store.Store` with store ID
*crust2_dd* has been downloaded in advance. A list of currently available
stores can be found at http://kinherd.org/gfs.html as well as how to download
such stores.
It is assumed that a :py:class:`pyrocko.gf.store.Store` with store ID
*crust2_dd* has been downloaded in advance. A list of currently available
stores can be found at http://kinherd.org/gfs.html as well as how to download
such stores.
::
from pyrocko.gf import LocalEngine, Target, DCSource
from pyrocko import trace
from pyrocko.gui_util import PhaseMarker
# We need a pyrocko.gf.Engine object which provides us with the traces
# extracted from the store. In this case we are going to use a local
# engine since we are going to query a local store.
engine = LocalEngine(store_superdirs=['/media/usb/stores'])
# The store we are going extract data from:
store_id = 'crust2_dd'
# Define a list of pyrocko.gf.Target objects, representing the recording
# devices. In this case one station with a three component sensor will
# serve fine for demonstation.
@ -502,7 +502,7 @@ such stores.
store_id=store_id,
codes=('', 'STA', '', channel_code))
for channel_code in channel_codes]
# Let's use a double couple source representation.
source_dc = DCSource(
lat=11.,
@ -512,34 +512,34 @@ such stores.
dip=40.,
rake=60.,
magnitude=4.)
# Processing that data will return a pyrocko.gf.Reponse object.
response = engine.process(source_dc, targets)
# This will return a list of the requested traces:
synthetic_traces = response.pyrocko_traces()
# In addition to that it is also possible to extract interpolated travel times
# In addition to that it is also possible to extract interpolated travel times
# of phases which have been defined in the store's config file.
store = engine.get_store(store_id)
markers = []
for t in targets:
dist = t.distance_to(source_dc)
depth = source_dc.depth
arrival_time = store.t('p', (depth, dist))
m = PhaseMarker(tmin=arrival_time,
m = PhaseMarker(tmin=arrival_time,
tmax=arrival_time,
phasename='p',
nslc_ids=(t.codes,))
markers.append(m)
# Processing that data will return a pyrocko.gf.Response object.
response = engine.process(source_dc, targets)
# This will return a list of the requested traces:
synthetic_traces = response.pyrocko_traces()
# Finally, let's scrutinize these traces.
trace.snuffle(synthetic_traces, markers=markers)

@ -0,0 +1,11 @@
Snuffler
========
Snuffler is a seismogram browser and workbench.
.. toctree::
:maxdepth: 2
apps_snuffler_manual
apps_snuffler_tutorial
apps_snuffler_extensions

@ -1,6 +1,6 @@
Writing a Snuffling
===================
Extending Snuffler with plugins: Snufflings
===========================================
Snufflings are small Python scripts which extend the functionality of Snuffler.
Snuffler looks into the directory ``$HOME/.snufflings`` for snufflings.
@ -9,12 +9,8 @@ in the main menu of Snuffler - no need to restart Snuffler when a snuffling is
modified or added.
An example snuffling to show earthquake catalog information within Snuffler
---------------------------------------------------------------------------
Example Snuffling to show earthquake catalog information within Snuffler
------------------------------------------------------------------------
Put the following code into ``$HOME/.snufflings/geofon.py``. It will add four
items into the *Snufflings* sub-menu of Snuffler (*Get GEOFON events*, *Get

@ -1,8 +1,8 @@
Snuffler
========
Snuffler manual
===============
Snuffler is a seismogram browser.
Snuffler is a seismogram browser and workbench.
* read waveforms in Mini-SEED, SAC and other file formats
* visually browse through seismic waveform archives

@ -1,5 +1,5 @@
Snuffler Tutorial
Snuffler tutorial
=================
This document describes basic usage of Snuffler.

@ -1,12 +1,11 @@
.. image:: _static/snuffler.png
.. image:: _static/pyrocko_shadow.png
:align: left
Pyrocko Manual
==============
This document describes Pyrocko, an open source toolbox and library for
seismology.
Pyrocko is open source toolbox and library for seismology.
.. raw:: html

@ -0,0 +1,10 @@
Library
=======
The Pyrocko library can be used as a framework for own developments.
.. toctree::
:maxdepth: 2
examples
reference

@ -0,0 +1,24 @@
Overview
========
Pyrocko is an open source seismology toolbox and library. Most of Pyrocko is
written in the Python programming language, a few parts are written in C.
.. raw:: html
<div style="clear:both"></div>
It can be used as a framework for own developments but also contains a few
standalone tools for everyday seismological practice:
* Snuffler: an extensible seismogram browser and workbench
* Cake: travel-time and ray-path computations for 1D layered earthmodels
* Fomosto: a tool to manage pre-calculated Green's function stores
* Jackseis: a command-line tool for common waveform archive data manipulations
To download the software or if you wish to contribute, please use the `Pyrocko
project page on GitHub <https://github.com/pyrocko/pyrocko>`_. If you want to
file a bug report or need help, please use the `GitHub issues page
<https://github.com/pyrocko/pyrocko/issues>`_.

@ -5,26 +5,27 @@ Library Reference
.. toctree::
:maxdepth: 1
trace
io
pile
util
model
hamster_pile
crust2x2
cake
moment_tensor
beachball
evalresp
pz
orthodrome
catalog
rdseed
snuffling
pile_viewer
gui_util
slink
gf
fdsn
ims
plot
reference_trace
reference_io
reference_pile
reference_util
reference_model
reference_hamster_pile
reference_crust2x2
reference_cake
reference_moment_tensor
reference_beachball
reference_evalresp
reference_pz
reference_orthodrome
reference_catalog
reference_rdseed
reference_snuffling
reference_pile_viewer
reference_gui_util
reference_slink
reference_gf
reference_fdsn
reference_ims
reference_plot
reference_gmtpy

@ -0,0 +1,9 @@
The :mod:`gmtpy` Module
=======================
.. automodule:: pyrocko.gmtpy
:members:
:special-members:
:show-inheritance:

@ -0,0 +1,22 @@
import sys, re
for fn in sys.argv[1:]:
with open(fn, 'r') as f:
s = f.read()
xx = re.findall(r'([^\n]+)\s+\'\'\'(.*?)\'\'\'', s, re.M|re.S)
for (obj, doc) in xx:
s = re.findall('[^:`]\B(([`*])[a-zA-Z_][a-zA-Z0-9_]*\\2)\B', doc)
if s:
print '-'*50
print fn, obj
print '.'*50
print doc
print '.'*50
print [ss[0] for ss in s]
# for vim:
# :s/\([^`:]\)\([`*]\)\([a-zA-Z0-9_]\+\)\2/\1``\3``/

@ -2950,37 +2950,38 @@ class GMT:
The standard input of the GMT process is fed by data selected with one
of the following ``in_*`` keyword arguments:
============== ========================================================
``in_stream`` Data is read from an open file like object.
``in_filename`` Data is read from the given file.
``in_string`` String content is dumped to the process.
``in_columns`` A 2D nested iterable whose elements can be accessed as
``in_columns[icolumn][irow]`` is converted into an ascii
table, which is fed to the process.
``in_rows`` A 2D nested iterable whos elements can be accessed as
``in_rows[irow][icolumn]`` is converted into an ascii
table, which is fed to the process.
============== ========================================================
=============== =======================================================
``in_stream`` Data is read from an open file like object.
``in_filename`` Data is read from the given file.
``in_string`` String content is dumped to the process.
``in_columns`` A 2D nested iterable whose elements can be accessed as
``in_columns[icolumn][irow]`` is converted into an
ascii
table, which is fed to the process.
``in_rows`` A 2D nested iterable whos elements can be accessed as
``in_rows[irow][icolumn]`` is converted into an ascii
table, which is fed to the process.
=============== =======================================================
The standard output of the GMT process may be redirected by one of the
following options:
============= =========================================================
out_stream Output is fed to an open file like object.
out_filename Output is dumped to the given file.
out_discard If True, output is dumped to :file:`/dev/null`.
============= =========================================================
================= =====================================================
``out_stream`` Output is fed to an open file like object.
``out_filename`` Output is dumped to the given file.
``out_discard`` If True, output is dumped to :file:`/dev/null`.
================= =====================================================
Additional keyword arguments:
===================== =================================================
config Dict with GMT defaults which override the
``config`` Dict with GMT defaults which override the
currently active set of defaults exclusively
during this call.
finish If True, the postscript file, which is maintained
``finish`` If True, the postscript file, which is maintained
by the GMT instance is finished, and no further
plotting is allowed.
suppress_defaults Suppress appending of the ``'+gmtdefaults'``
``suppress_defaults`` Suppress appending of the ``'+gmtdefaults'``
option to the command.
===================== =================================================

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