__init__.py

# -*- coding: utf-8 -*-
"""
obspy.taup - Ray theoretical travel times and paths
===================================================

:copyright:
    The ObsPy Development Team (devs@obspy.org)
:license:
    GNU Lesser General Public License, Version 3
    (https://www.gnu.org/copyleft/lesser.html)

This package started out as port of the Java TauP Toolkit by [Crotwell1999]_ so
please look there for more details about the algorithms used and further
information. It can be used to calculate theoretical arrival times for
arbitrary seismic phases in a 1D spherically symmetric background model.
Furthermore it can output ray paths for all phases and derive pierce points of
rays with model discontinuities.

Basic Usage
-----------

Let's start by initializing a :class:`~obspy.taup.tau.TauPyModel` instance.
Models can be initialized by specifying the name of a model provided by ObsPy.

>>> from obspy.taup import TauPyModel
>>> model = TauPyModel(model="iasp91")

ObsPy currently ships with the following 1D velocity models:

* ``1066a``, see [GilbertDziewonski1975]_
* ``1066b``, see [GilbertDziewonski1975]_
* ``ak135``, see [KennetEngdahlBuland1995]_
* ``ak135f``, see [KennetEngdahlBuland1995]_, [MontagnerKennett1995]_, and
  http://rses.anu.edu.au/seismology/ak135/ak135f.html (not supported)
* ``ak135f_no_mud``, ``ak135f`` with ``ak135`` used above the 120-km
  discontinuity; see the SPECFEM3D_GLOBE manual at
  https://geodynamics.org/cig/software/specfem3d_globe/
* ``herrin``, see [Herrin1968]_
* ``iasp91``, see [KennetEngdahl1991]_
* ``jb``, see [JeffreysBullen1940]_
* ``prem``, see [Dziewonski1981]_
* ``pwdk``, see [WeberDavis1990]_
* ``sp6``, see [MorelliDziewonski1993]_

Custom built models can be initialized by specifying an absolute
path to a model in ObsPy's ``.npz`` model format instead of just a model name.
Model initialization is a fairly expensive operation so make sure to do it only
if necessary. See below for information on how to build a ``.npz`` model file.

Travel Times
^^^^^^^^^^^^
The models' main method is the
:meth:`~obspy.taup.tau.TauPyModel.get_travel_times` method; as the name
suggests it returns travel times for the chosen phases, distance, source depth,
and model. By default it returns arrivals for a number of phases.

>>> arrivals = model.get_travel_times(source_depth_in_km=55,
...                                   distance_in_degree=67)
>>> print(arrivals)  # doctest: +NORMALIZE_WHITESPACE
28 arrivals
    P phase arrival at 647.041 seconds
    pP phase arrival at 662.233 seconds
    sP phase arrival at 668.704 seconds
    PcP phase arrival at 674.865 seconds
    PP phase arrival at 794.992 seconds
    PKiKP phase arrival at 1034.098 seconds
    pPKiKP phase arrival at 1050.529 seconds
    sPKiKP phase arrival at 1056.721 seconds
    S phase arrival at 1176.948 seconds
    pS phase arrival at 1195.508 seconds
    SP phase arrival at 1196.830 seconds
    sS phase arrival at 1203.129 seconds
    PS phase arrival at 1205.421 seconds
    SKS phase arrival at 1239.090 seconds
    SKKS phase arrival at 1239.109 seconds
    ScS phase arrival at 1239.512 seconds
    SKiKP phase arrival at 1242.388 seconds
    pSKS phase arrival at 1260.314 seconds
    sSKS phase arrival at 1266.921 seconds
    SS phase arrival at 1437.427 seconds
    PKIKKIKP phase arrival at 1855.271 seconds
    SKIKKIKP phase arrival at 2063.564 seconds
    PKIKKIKS phase arrival at 2069.756 seconds
    SKIKKIKS phase arrival at 2277.857 seconds
    PKIKPPKIKP phase arrival at 2353.934 seconds
    PKPPKP phase arrival at 2356.425 seconds
    PKPPKP phase arrival at 2358.899 seconds
    SKIKSSKIKS phase arrival at 3208.155 seconds

If you know which phases you are interested in, you can also specify them
directly which speeds up the calculation as unnecessary phases are not
calculated. Please note that it is possible to construct *any* phases that
adhere to the naming scheme which is detailed later.

>>> arrivals = model.get_travel_times(source_depth_in_km=100,
...                                   distance_in_degree=45,
...                                   phase_list=["P", "PSPSPS"])
>>> print(arrivals)  # doctest: +NORMALIZE_WHITESPACE
3 arrivals
    P phase arrival at 485.210 seconds
    PSPSPS phase arrival at 4983.041 seconds
    PSPSPS phase arrival at 5799.249 seconds

Each arrival is represented by an :class:`~obspy.taup.helper_classes.Arrival`
object which can be queried for various attributes.

>>> arr = arrivals[0]
>>> arr.ray_param, arr.time, arr.incident_angle  # doctest: +ELLIPSIS
(453.7535..., 485.2100..., 24.3988...)

Ray Paths
^^^^^^^^^

To also calculate the paths travelled by the rays to the receiver, use the
:meth:`~obspy.taup.tau.TauPyModel.get_ray_paths` method.

>>> arrivals = model.get_ray_paths(500, 130)
>>> arrival = arrivals[0]

The result is a NumPy record array containing ray parameter, time, distance
and depth to use however you see fit.

>>> arrival.path.dtype
dtype([('p', '<f8'), ('time', '<f8'), ('dist', '<f8'), ('depth', '<f8')])


Pierce Points
^^^^^^^^^^^^^

If you only need the pierce points of ray paths with model discontinuities,
use the :meth:`~obspy.taup.tau.TauPyModel.get_pierce_points` method which
results in pierce points being stored as a record array on the arrival object.

>>> arrivals = model.get_pierce_points(500, 130)
>>> arrivals[0].pierce.dtype
dtype([('p', '<f8'), ('time', '<f8'), ('dist', '<f8'), ('depth', '<f8')])


Plotting
--------

If ray paths have been calculated, they can be plotted using the
:meth:`Arrivals.plot_rays() <obspy.taup.tau.Arrivals.plot_rays>` method:

>>> arrivals = model.get_ray_paths(
...     source_depth_in_km=500, distance_in_degree=130, phase_list=["ttbasic"])
>>> ax = arrivals.plot_rays()

.. plot::
    :width: 50%
    :align: center

    from obspy.taup import TauPyModel
    TauPyModel().get_ray_paths(500, 130, phase_list=["ttbasic"]).plot_rays()

Plotting will only show the requested phases:

>>> arrivals = model.get_ray_paths(source_depth_in_km=500,
...                                distance_in_degree=130,
...                                phase_list=["Pdiff", "Sdiff",
...                                            "pPdiff", "sSdiff"])
>>> ax = arrivals.plot_rays()

.. plot::
    :width: 50%
    :align: center

    from obspy.taup import TauPyModel
    TauPyModel().get_ray_paths(500, 130,
                               phase_list=["Pdiff", "Sdiff", "pPdiff",
                                           "sSdiff"]).plot_rays()

Additionally, Cartesian coordinates may be used instead of a polar grid:

>>> arrivals = model.get_ray_paths(source_depth_in_km=500,
...                                distance_in_degree=130,
...                                phase_list=["ttbasic"])
>>> ax = arrivals.plot_rays(plot_type="cartesian")

.. plot::
    :width: 75%
    :align: center

    from obspy.taup import TauPyModel
    TauPyModel().get_ray_paths(500, 130,
                               phase_list=["ttbasic"]).plot_rays(plot_type=
                                                                 "cartesian")

Travel times for these ray paths can be plotted using the
:meth:`Arrivals.plot_times() <obspy.taup.tau.Arrivals.plot_times>` method:

>>> arrivals = model.get_ray_paths(source_depth_in_km=500,
...                                distance_in_degree=130)
>>> ax = arrivals.plot_times()

.. plot::
    :width: 50%
    :align: center

    from obspy.taup import TauPyModel
    ax = TauPyModel().get_ray_paths(500, 130).plot_times()

Alternatively, convenience wrapper functions plot the arrival times
and the ray paths for a range of epicentral distances.

The travel times wrapper function is :func:`~obspy.taup.tau.plot_travel_times`, 
creating the figure and axes first is optional to have control over e.g. figure
size or subplot setup:

>>> from obspy.taup import plot_travel_times
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(figsize=(9, 9))
>>> ax = plot_travel_times(source_depth=10, phase_list=["P", "S", "PP"],
...                        ax=ax, fig=fig, verbose=True)
There was 1 epicentral distance without an arrival

.. plot::
    :width: 50%
    :align: center

    from obspy.taup import plot_travel_times
    import matplotlib.pyplot as plt

    fig, ax = plt.subplots(figsize=(9, 9))
    ax = plot_travel_times(source_depth=10, ax=ax, phase_list=["P", "S", "PP"],
                           fig=fig)

The ray path plot wrapper function is :func:`~obspy.taup.tau.plot_ray_paths`.
Again, creating the figure and axes first is optional to have control over e.g.
figure size or subplot setup (note that a polar axes has to be set up when
aiming to do a plot with ``plot_type='spherical'`` and a normal matplotlib axes
when aiming to do a plot with ``plot_type='cartesian'``. An error will be
raised when mixing the two options):

>>> from obspy.taup import plot_ray_paths
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))
>>> ax = plot_ray_paths(source_depth=100, ax=ax, fig=fig, verbose=True)
There were rays for all but the following epicentral distances:
 [0.0, 360.0]

.. plot::
    :width: 50%
    :align: center

    from obspy.taup import plot_ray_paths
    import matplotlib.pyplot as plt

    fig, ax = plt.subplot(subplot_kw=dict(projection='polar'))
    ax = plot_ray_paths(source_depth=100, ax=ax, fig=fig)

More examples of plotting may be found in the :doc:`ObsPy tutorial
</tutorial/code_snippets/travel_time>`.

.. _`Phase naming in taup`:

Phase naming in obspy.taup
--------------------------

.. note::

    This section is a modified copy from the Java TauP Toolkit documentation so
    all credit goes to the authors of that.

A major feature of ``obspy.taup`` is the implementation of a phase name parser
that allows the user to define essentially arbitrary phases through a planet.
Thus, ``obspy.taup`` is extremely flexible in this respect since it is not
limited to a pre-defined set of phases. Phase names are not hard-coded into the
software, rather the names are interpreted and the appropriate propagation path
and resulting times are constructed at run time. Designing a phase-naming
convention that is general enough to support arbitrary phases and easy to
understand is an essential and somewhat challenging step. The rules that we
have developed are described here. Most of the phases resulting from these
conventions should be familiar to seismologists, e.g. ``pP``, ``PP``, ``PcS``,
``PKiKP``, etc.  However, the uniqueness required for parsing results in some
new names for other familiar phases.

In traditional "whole-Earth" seismology, there are 3 major interfaces: the free
surface, the core-mantle boundary, and the inner-outer core boundary. Phases
interacting with the core-mantle boundary and the inner core boundary are easy
to describe because the symbol for the wave type changes at the boundary (i.e.,
the symbol ``P`` changes to ``K`` within the outer core even though the wave
type is the same). Phase multiples for these interfaces and the free surface
are also easy to describe because the symbols describe a unique path. The
challenge begins with the description of interactions with interfaces within
the crust and upper mantle. We have introduced two new symbols to existing
nomenclature to provide unique descriptions of potential paths. Phase names are
constructed from a sequence of symbols and numbers (with no spaces) that either
describe the wave type, the interaction a wave makes with an interface, or the
depth to an interface involved in an interaction.

1. Symbols that describe wave-type are:
    * ``P`` - compressional wave, upgoing or downgoing; in the crust or mantle,
      ``p`` is a strictly upgoing *P*-wave in the crust or mantle
    * ``S`` - shear wave, upgoing or downgoing, in the crust or mantle
    * ``s`` - strictly upgoing *S*-wave in the crust or mantle
    * ``K`` - compressional wave in the outer core
    * ``I`` - compressional wave in the inner core
    * ``J`` - shear wave in the inner core
2. Symbols that describe interactions with interfaces are:
    * ``m`` - interaction with the Moho
    * ``g`` appended to ``P`` or ``S`` - ray turning in the crust
    * ``n`` appended to ``P`` or ``S`` - head wave along the Moho
    * ``c`` - topside reflection off the core mantle boundary
    * ``i`` - topside reflection off the inner core outer core boundary
    * ``ˆ`` - underside reflection, used primarily for crustal and mantle
      interfaces
    * ``v`` - topside reflection, used primarily for crustal and mantle
      interfaces
    * ``diff`` appended to ``P`` or ``S`` - diffracted wave along the core
      mantle boundary
    * ``kmps`` appended to a velocity - horizontal phase velocity (see 10
      below)
    * ``ed`` appended to ``P`` or ``S`` - an exclusively downgoing path, for a
      receiver below the source (see 3 below)
3. The characters ``p`` and ``s`` **always** represent up-going legs. An
   example is the source to surface leg of the phase ``pP`` from a source at
   depth. ``P`` and ``S`` can be turning waves, but always indicate downgoing
   waves leaving the source when they are the first symbol in a phase name.
   Thus, to get near-source, direct *P*-wave arrival times, you need to specify
   two phases ``p`` and ``P`` or use the "*ttimes* compatibility phases"
   described below. However, ``P`` may represent a upgoing leg in certain
   cases. For instance, ``PcP`` is allowed since the direction of the phase is
   unambiguously determined by the symbol ``c``, but would be named ``Pcp`` by
   a purist using our nomenclature.

   With the ability to have sources at depth, there is a need to specify the
   difference between a wave that is exclusively downgoing to the receiver from
   one that turns and is upgoing at the receiver. The suffix ``ed`` can be
   appended to indicate exclusively downgoing. So for a source at 10 km depth
   and a receiver at 20 km depth at 0 degree distance ``P`` does not have an
   arrival but ``Ped`` does.
4. Numbers, except velocities for ``kmps`` phases (see 10 below), represent
   depths at which interactions take place. For example, ``P410s`` represents a
   *P*-to-*S* conversion at a discontinuity at 410km depth. Since the *S*-leg
   is given by a lower-case symbol and no reflection indicator is included,
   this represents a *P*-wave converting to an *S*-wave when it hits the
   interface from below. The numbers given need not be the actual depth; the
   closest depth corresponding to a discontinuity in the model will be used.
   For example, if the time for ``P410s`` is requested in a model where the
   discontinuity was really located at 406.7 kilometers depth, the time
   returned would actually be for ``P406.7s``. The code would note that this
   had been done. Obviously, care should be taken to ensure that there are no
   other discontinuities closer than the one of interest, but this approach
   allows generic interface names like “410” and “660” to be used without
   knowing the exact depth in a given model.
5. If a number appears between two phase legs, e.g. ``S410P``, it represents a
   transmitted phase conversion, not a reflection. Thus, ``S410P`` would be a
   transmitted conversion from *S* to *P* at 410km depth. Whether the
   conversion occurs on the down-going side or up-going side is determined by
   the upper or lower case of the following leg. For instance, the phase
   ``S410P`` propagates down as an ``S``, converts at the 410 to a ``P``,
   continues down, turns as a *P*-wave, and propagates back across the 410 and
   to the surface. ``S410p`` on the other hand, propagates down as a ``S``
   through the 410, turns as an *S*-wave, hits the 410 from the bottom,
   converts to a ``p`` and then goes up to the surface. In these cases, the
   case of the phase symbol (``P`` vs. ``p``) is critical because the direction
   of propagation (upgoing or downgoing) is not unambiguously defined elsewhere
   in the phase name. The importance is clear when you consider a source depth
   below 410 compared to above 410. For a source depth greater than 410 km,
   ``S410P`` technically cannot exist while ``S410p`` maintains the same path
   (a receiver side conversion) as it does for a source depth above the 410.
   The first letter can be lower case to indicate a conversion from an up-going
   ray, e.g., ``p410S`` is a depth phase from a source at greater than 410
   kilometers depth that phase converts at the 410 discontinuity. It is
   strictly upgoing over its entire path, and hence could also be labeled
   ``p410s``. ``p410S`` is often used to mean a reflection in the literature,
   but there are too many possible interactions for the phase parser to allow
   this. If the underside reflection is desired, use the ``pˆ410S`` notation
   from rule 7.
6. Due to the two previous rules, ``P410P`` and ``S410S`` are over specified,
   but still legal. They are almost equivalent to ``P`` and ``S``,
   respectively, but restrict the path to phases transmitted through (turning
   below) the 410. This notation is useful to limit arrivals to just those that
   turn deeper than a discontinuity (thus avoiding travel time curve
   triplications), even though they have no real interaction with it.
7. The characters ``ˆ`` and ``v`` are new symbols introduced here to represent
   bottom-side and top-side reflections, respectively. They are followed by a
   number to represent the approximate depth of the reflection or a letter for
   standard discontinuities, ``m``, ``c`` or ``i``. Reflections from
   discontinuities besides the core-mantle boundary, ``c``, or inner-core
   outer-core boundary, ``i``, must use the ``ˆ`` and ``v`` notation. For
   instance, in the TauP convention, ``pˆ410S`` is used to describe a
   near-source underside reflection. Underside reflections, except at the
   surface (``PP``, ``sS``, etc.), core-mantle boundary (``PKKP``, ``SKKKS``,
   etc.), or outer-core-inner-core boundary (``PKIIKP``, ``SKJJKS``,
   ``SKIIKS``, etc.), must be specified with the ``ˆ`` notation. For example,
   ``Pˆ410P`` and ``PˆmP`` would both be underside reflections from the 410km
   discontinuity and the Moho, respectively. The phase ``PmP``, the traditional
   name for a top-side reflection from the Moho discontinuity, must change
   names under our new convention. The new name is ``PvmP`` or ``Pvmp`` while
   ``PmP`` just describes a *P*-wave that turns beneath the Moho. The reason
   why the Moho must be handled differently from the core-mantle boundary is
   that traditional nomenclature did not introduce a phase symbol change at the
   Moho. Thus, while ``PcP`` makes sense since a *P*-wave in the core would be
   labeled ``K``, ``PmP`` could have several meanings. The ``m`` symbol just
   allows the user to describe phases interaction with the Moho without knowing
   its exact depth. In all other respects, the ``ˆ`` - ``v`` nomenclature is
   maintained.
8. Currently, ``ˆ`` and ``v`` for non-standard discontinuities are allowed only
   in the crust and mantle. Thus there are no reflections off non-standard
   discontinuities within the core, (reflections such as ``PKKP``, ``PKiKP``
   and ``PKIIKP`` are still fine). There is no reason in principle to restrict
   reflections off discontinuities in the core, but until there is interest
   expressed, these phases will not be added. Also, a naming convention would
   have to be created since “``p`` is to ``P``” is not the same as “``i`` is to
   ``I``”.
9. Currently there is no support for ``PKPab``, ``PKPbc``, or ``PKPdf`` phase
   names. They lead to increased algorithmic complexity that at this point
   seems unwarranted. Currently, in regions where triplications develop, the
   triplicated phase will have multiple arrivals at a given distance. So,
   ``PKPab`` and ``PKPbc`` are both labeled just ``PKP`` while ``PKPdf`` is
   called ``PKIKP``.
10. The symbol ``kmps`` is used to get the travel time for a specific
    horizontal phase velocity. For example, ``2kmps`` represents a horizontal
    phase velocity of 2 kilometers per second. While the calculations for these
    are trivial, it is convenient to have them available to estimate surface
    wave travel times or to define windows of interest for given paths.
11. As a convenience, a ``ttimes`` phase name compatibility mode is available.
    So ``ttp`` gives you the phase list corresponding to ``P`` in ``ttimes``.
    Similarly there are ``tts``, ``ttp+``, ``tts+``, ``ttbasic`` and ``ttall``.

Building custom models
----------------------

Custom models can be built from ``.tvel`` and ``.nd`` files using the
:func:`~obspy.taup.taup_create.build_taup_model` function.
"""
from __future__ import (absolute_import, division, print_function,
                        unicode_literals)
from future.builtins import *  # NOQA

# Module wide default settings.
_DEFAULT_VALUES = {
    # Default depths for a couple of discontinuities in earth. These are
    # only used for the tvel files which have no named discontinuities.
    # Values are in km.
    "default_moho": 35,
    "default_cmb": 2889.0,
    "default_iocb": 5153.9,
    # Default material parameters if a model does not set them.
    "density": 2.6,
    "qp": 1000.0,
    "qs": 2000.0,
    # Slowness tolerance
    "slowness_tolerance": 1e-16
}


# Convenience imports.
from .tau import TauPyModel  # NOQA
from .tau import plot_travel_times  # NOQA
from .tau import plot_ray_paths  # NOQA

if __name__ == '__main__':
    import doctest
    doctest.testmod(exclude_empty=True)