tau.py

# -*- coding: utf-8 -*-
"""
High-level interface to travel-time calculation routines.
"""
import copy
import warnings

import matplotlib as mpl
import matplotlib.cbook
from matplotlib.cm import get_cmap
import matplotlib.text
import numpy as np

from .helper_classes import Arrival
from .tau_model import TauModel
from .taup_path import TauPPath
from .taup_pierce import TauPPierce
from .taup_time import TauPTime
from .taup_geo import calc_dist, add_geo_to_arrivals
from .utils import parse_phase_list
import obspy.geodetics.base as geodetics

# Pretty paired colors. Reorder to have saturated colors first and remove
# some colors at the end.
cmap = get_cmap('Paired', lut=12)
COLORS = ['#%02x%02x%02x' % tuple(int(col * 255) for col in cmap(i)[:3])
          for i in range(12)]
COLORS = COLORS[1:][::2][:-1] + COLORS[::2][:-1]


class _SmartPolarText(matplotlib.text.Text):
    """
    Automatically align text on polar plots to be away from axes.

    This class automatically sets the horizontal and vertical alignments
    based on which sides of the spherical axes the text is located.
    """
    def draw(self, renderer, *args, **kwargs):
        fig = self.get_figure()
        midx = fig.get_figwidth() * fig.dpi / 2
        midy = fig.get_figheight() * fig.dpi / 2

        extent = self.get_window_extent(renderer, dpi=fig.dpi)
        points = extent.get_points()

        is_left = points[0, 0] < midx
        is_top = points[0, 1] > midy
        updated = False

        ha = 'right' if is_left else 'left'
        if self.get_horizontalalignment() != ha:
            self.set_horizontalalignment(ha)
            updated = True
        va = 'bottom' if is_top else 'top'
        if self.get_verticalalignment() != va:
            self.set_verticalalignment(va)
            updated = True

        if updated:
            self.update_bbox_position_size(renderer)

        matplotlib.text.Text.draw(self, renderer, *args, **kwargs)


class Arrivals(list):
    """
    List like object of arrivals returned by :class:`TauPyModel` methods.

    :param arrivals: Initial arrivals to store.
    :type arrivals: :class:`list` of
        :class:`~obspy.taup.helper_classes.Arrival`
    :param model: The model used to calculate the arrivals.
    :type model: :class:`~TauPyModel`
    """
    __slots__ = ["model"]

    def __init__(self, arrivals, model):
        super(Arrivals, self).__init__()
        self.model = model
        self.extend(arrivals)

    def __add__(self, other):
        if isinstance(other, Arrival):
            other = Arrivals([other], model=self.model)
        if not isinstance(other, Arrivals):
            raise TypeError
        return self.__class__(super(Arrivals, self).__add__(other),
                              model=self.model)

    def __iadd__(self, other):
        if isinstance(other, Arrival):
            other = Arrivals([other], model=self.model)
        if not isinstance(other, Arrivals):
            raise TypeError
        self.extend(other)
        return self

    def __mul__(self, num):
        if not isinstance(num, int):
            raise TypeError("Integer expected")
        arr = self.copy()
        for _i in range(num - 1):
            arr += self.copy()
        return arr

    def __imul__(self, num):
        if not isinstance(num, int):
            raise TypeError("Integer expected")
        arr = self.copy()
        for _i in range(num - 1):
            self += arr
        return self

    def __setitem__(self, index, arrival):
        if (isinstance(index, slice) and
                all(isinstance(x, Arrival) for x in arrival)):
            super(Arrivals, self).__setitem__(index, arrival)
        elif isinstance(arrival, Arrival):
            super(Arrivals, self).__setitem__(index, arrival)
        else:
            msg = 'Only Arrival objects can be assigned.'
            raise TypeError(msg)

    def __setslice__(self, i, j, seq):
        if all(isinstance(x, Arrival) for x in seq):
            super(Arrivals, self).__setslice__(i, j, seq)
        else:
            msg = 'Only Arrival objects can be assigned.'
            raise TypeError(msg)

    def __getitem__(self, index):
        if isinstance(index, slice):
            return self.__class__(super(Arrivals, self).__getitem__(index),
                                  model=self.model)
        else:
            return super(Arrivals, self).__getitem__(index)

    def __getslice__(self, i, j):
        return self.__class__(super(Arrivals, self).__getslice__(i, j),
                              model=self.model)

    def __str__(self):
        return (
            "{count} arrivals\n\t{arrivals}"
        ).format(
            count=len(self),
            arrivals="\n\t".join([str(_i) for _i in self]))

    def __repr__(self):
        return "[%s]" % (", ".join([repr(_i) for _i in self]))

    def append(self, arrival):
        if isinstance(arrival, Arrival):
            super(Arrivals, self).append(arrival)
        else:
            msg = 'Append only supports a single Arrival object as argument.'
            raise TypeError(msg)

    def copy(self):
        return self.__class__(super(Arrivals, self).copy(),
                              model=self.model)

    def plot_times(self, phase_list=None, plot_all=True, legend=False,
                   show=True, fig=None, ax=None):
        """
        Plot arrival times if any have been calculated.

        :param phase_list: List of phases for which travel times are plotted,
            if they exist. See `phase_taup`_ for details on
            phase naming and convenience keys like ``'ttbasic'``. Defaults to
            ``'ttall'``.
        :type phase_list: list[str]
        :param plot_all: By default all rays, even those travelling in the
            other direction and thus arriving at a distance of *360 - x*
            degrees are shown. Set this to ``False`` to only show rays
            arriving at exactly *x* degrees.
        :type plot_all: bool
        :param legend: If boolean, specify whether or not to show the legend
            (at the default location.) If a str, specify the location of the
            legend.
        :type legend: bool or str
        :param show: Show the plot.
        :type show: bool
        :param fig: Figure instance to plot in. If not given, a new figure
            will be created.
        :type fig: :class:`matplotlib.figure.Figure`
        :param ax: Axes to plot in. If not given, a new figure with an axes
            will be created.
        :type ax: :class:`matplotlib.axes.Axes`
        :returns: Matplotlib axes with the plot
        :rtype: :class:`matplotlib.axes.Axes`
        """
        import matplotlib.pyplot as plt

        if not self:
            raise ValueError("No travel times.")

        if phase_list is None:
            phase_list = ("ttall",)

        phase_names = sorted(parse_phase_list(phase_list))

        # create an axis/figure, if there is none yet:
        if fig and ax:
            pass
        elif not fig and not ax:
            fig, ax = plt.subplots()
        elif not ax:
            ax = fig.add_subplot(1, 1, 1)
        elif not fig:
            fig = ax.figure

        # extract the time/distance for each phase, and for each distance:
        for arrival in self:
            if plot_all is False:
                dist = arrival.purist_distance % 360.0
                distance = arrival.distance
                if distance < 0:
                    distance = (distance % 360)
                if abs(dist - distance) / dist > 1E-5:
                    continue
            if arrival.name in phase_names:
                ax.plot(arrival.distance, arrival.time / 60, '.',
                        label=arrival.name,
                        color=COLORS[phase_names.index(arrival.name)
                                     % len(COLORS)])
            else:
                ax.plot(arrival.distance, arrival.time / 60, '.',
                        label=arrival.name, color='k')
        if legend:
            if isinstance(legend, bool):
                if 0 <= arrival.distance <= 180.0:
                    loc = "upper left"
                else:
                    loc = "upper right"
            else:
                loc = legend
            ax.legend(loc=loc, prop=dict(size="small"), numpoints=1)

        ax.grid()
        ax.set_xlabel('Distance (degrees)')
        ax.set_ylabel('Time (minutes)')
        if show:
            plt.show()
        return ax

    def plot_rays(self, phase_list=None, plot_type="spherical",
                  plot_all=True, legend=False, label_arrivals=False,
                  show=True, fig=None, ax=None):
        """
        Plot ray paths if any have been calculated.

        :param phase_list: List of phases for which ray paths are plotted,
            if they exist. See `phase_taup`_ for details on
            phase naming and convenience keys like ``'ttbasic'``. Defaults to
            ``'ttall'``.
        :type phase_list: list[str]
        :param plot_type: Either ``"spherical"`` or ``"cartesian"``.
            A spherical plot is always global whereas a Cartesian one can
            also be local.
        :type plot_type: str
        :param plot_all: By default all rays, even those travelling in the
            other direction and thus arriving at a distance of *360 - x*
            degrees are shown. Set this to ``False`` to only show rays
            arriving at exactly *x* degrees.
        :type plot_all: bool
        :param legend: If boolean, specify whether or not to show the legend
            (at the default location.) If a str, specify the location of the
            legend. If you are plotting a single phase, you may consider using
            the ``label_arrivals`` argument.
        :type legend: bool or str
        :param label_arrivals: Label the arrivals with their respective phase
            names. This setting is only useful if you are plotting a single
            phase as otherwise the names could be large and possibly overlap
            or clip. Consider using the ``legend`` parameter instead if you
            are plotting multiple phases.
        :type label_arrivals: bool
        :param show: Show the plot
        :type show: bool
        :param fig: Figure to plot in. If not given, a new figure will be
            created.
        :type fig: :class:`matplotlib.figure.Figure`
        :param ax: Axes to plot in. If not given, a new figure with an axes
            will be created. Must be a polar axes for the spherical plot and
            a regular one for the Cartesian plot.
        :type ax: :class:`matplotlib.axes.Axes`
        :returns: Matplotlib axes with the plot
        :rtype: :class:`matplotlib.axes.Axes`
        """
        import matplotlib.pyplot as plt

        # I don't get this, but without sorting, I get a different
        # order each call:

        if phase_list is None:
            phase_list = ("ttall",)

        requested_phase_names = parse_phase_list(phase_list)
        requested_phase_name_map = {}
        i = 0
        for phase_name in requested_phase_names:
            if phase_name in requested_phase_name_map:
                continue
            requested_phase_name_map[phase_name] = i
            i += 1

        phase_names = sorted(parse_phase_list(phase_list))
        arrivals = []
        for arrival in self:
            if arrival.path is None:
                continue
            dist = arrival.purist_distance % 360.0
            distance = arrival.distance
            if distance < 0:
                distance = (distance % 360)
            if abs(dist - distance) / dist > 1E-5:
                if plot_all is False:
                    continue
                # Mirror on axis.
                arrival = copy.deepcopy(arrival)
                arrival.path["dist"] *= -1.0
            arrivals.append(arrival)

        if not arrivals:
            raise ValueError("Can only plot arrivals with calculated ray "
                             "paths.")

        # get the velocity discontinuities in your model, for plotting:
        discons = self.model.s_mod.v_mod.get_discontinuity_depths()

        if plot_type == "spherical":
            if ax and not isinstance(ax, mpl.projections.polar.PolarAxes):
                msg = ("Axes instance provided for plotting with "
                       "`plot_type='spherical'` but it seems the axes is not "
                       "a polar axes.")
                warnings.warn(msg)
            if fig and ax:
                pass
            elif not fig and not ax:
                fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))
            elif not ax:
                ax = fig.add_subplot(1, 1, 1, polar=True)
            elif not fig:
                fig = ax.figure

            ax.set_theta_zero_location('N')
            ax.set_theta_direction(-1)
            ax.set_xticks([])
            ax.set_yticks([])

            intp = matplotlib.cbook.simple_linear_interpolation
            radius = self.model.radius_of_planet
            phase_names_encountered = {ray.name for ray in arrivals}
            colors = {
                name: COLORS[i % len(COLORS)]
                for name, i in requested_phase_name_map.items()}
            i = len(colors)
            for name in sorted(phase_names_encountered):
                if name in colors:
                    continue
                colors[name] = COLORS[i % len(COLORS)]
                i += 1
            for ray in arrivals:
                color = colors.get(ray.name, 'k')
                # Requires interpolation,or diffracted phases look funny.
                ax.plot(intp(ray.path["dist"], 100),
                        radius - intp(ray.path["depth"], 100),
                        color=color, label=ray.name, lw=2.0)
                ax.set_yticks(radius - discons)
                ax.xaxis.set_major_formatter(plt.NullFormatter())
                ax.yaxis.set_major_formatter(plt.NullFormatter())

            # Pretty earthquake marker.
            ax.plot([0], [radius - arrivals[0].source_depth],
                    marker="*", color="#FEF215", markersize=20, zorder=10,
                    markeredgewidth=1.5, markeredgecolor="0.3",
                    clip_on=False)

            # Pretty station marker.
            arrowprops = dict(arrowstyle='-|>,head_length=0.8,'
                              'head_width=0.5',
                              color='#C95241', lw=1.5)
            station_radius = radius - arrivals[0].receiver_depth
            ax.annotate('',
                        xy=(np.deg2rad(distance), station_radius),
                        xycoords='data',
                        xytext=(np.deg2rad(distance),
                                station_radius + radius * 0.02),
                        textcoords='data',
                        arrowprops=arrowprops,
                        clip_on=False)
            arrowprops = dict(arrowstyle='-|>,head_length=1.0,'
                              'head_width=0.6',
                              color='0.3', lw=1.5, fill=False)
            ax.annotate('',
                        xy=(np.deg2rad(distance), station_radius),
                        xycoords='data',
                        xytext=(np.deg2rad(distance),
                                station_radius + radius * 0.01),
                        textcoords='data',
                        arrowprops=arrowprops,
                        clip_on=False)
            if label_arrivals:
                name = ','.join(sorted(set(ray.name for ray in arrivals)))
                # We cannot just set the text of the annotations above because
                # it changes the arrow path.
                t = _SmartPolarText(np.deg2rad(distance),
                                    station_radius + radius * 0.1,
                                    name, clip_on=False)
                ax.add_artist(t)

            ax.set_rmax(radius)
            ax.set_rmin(0.0)

            if legend:
                if isinstance(legend, bool):
                    if 0 <= distance <= 180.0:
                        loc = "upper left"
                    else:
                        loc = "upper right"
                else:
                    loc = legend
                ax.legend(loc=loc, prop=dict(size="small"))

        elif plot_type == "cartesian":
            if ax and isinstance(ax, mpl.projections.polar.PolarAxes):
                msg = ("Axes instance provided for plotting with "
                       "`plot_type='cartesian'` but it seems the axes is "
                       "a polar axes.")
                warnings.warn(msg)
            if fig and ax:
                pass
            elif not fig and not ax:
                fig, ax = plt.subplots()
                ax.invert_yaxis()
            elif not ax:
                ax = fig.add_subplot(1, 1, 1)
                ax.invert_yaxis()
            elif not fig:
                fig = ax.figure

            # Plot the ray paths:
            for ray in arrivals:
                if ray.name in phase_names:
                    ax.plot(np.rad2deg(ray.path["dist"]), ray.path["depth"],
                            color=COLORS[phase_names.index(ray.name) %
                                         len(COLORS)],
                            label=ray.name, lw=2.0)
                else:
                    ax.plot(np.rad2deg(ray.path["dist"]), ray.path["depth"],
                            color='k', label=ray.name, lw=2.0)

            # Pretty station marker:
            ms = 14
            station_marker_transform = matplotlib.transforms.offset_copy(
                ax.transData,
                fig=ax.get_figure(),
                y=ms / 2.0,
                units="points")
            ax.plot([distance], [arrivals[0].receiver_depth],
                    marker="v", color="#C95241",
                    markersize=ms, zorder=10, markeredgewidth=1.5,
                    markeredgecolor="0.3", clip_on=False,
                    transform=station_marker_transform)
            if label_arrivals:
                name = ','.join(sorted(set(ray.name for ray in arrivals)))
                ax.annotate(name,
                            xy=(distance, arrivals[0].receiver_depth),
                            xytext=(0, ms * 1.5),
                            textcoords='offset points',
                            ha='center', annotation_clip=False)

            # Pretty earthquake marker.
            ax.plot([0], [arrivals[0].source_depth], marker="*",
                    color="#FEF215", markersize=20, zorder=10,
                    markeredgewidth=1.5, markeredgecolor="0.3",
                    clip_on=False)

            # lines of major discontinuities:
            x = ax.get_xlim()
            y = ax.get_ylim()
            for depth in discons:
                if not (y[1] <= depth <= y[0]):
                    continue
                ax.hlines(depth, x[0], x[1], color="0.5", zorder=-1)

            # Plot some more station markers if necessary.
            possible_distances = [_i * (distance + 360.0)
                                  for _i in range(1, 10)]
            possible_distances += [-_i * (360.0 - distance) for _i in
                                   range(1, 10)]
            possible_distances = [_i for _i in possible_distances
                                  if x[0] <= _i <= x[1]]
            if possible_distances:
                ax.plot(possible_distances,
                        [arrivals[0].receiver_depth] * len(possible_distances),
                        marker="v", color="#C95241",
                        markersize=ms, zorder=10, markeredgewidth=1.5,
                        markeredgecolor="0.3", clip_on=False, lw=0,
                        transform=station_marker_transform)
            if legend:
                if isinstance(legend, bool):
                    loc = "lower left"
                else:
                    loc = legend
                ax.legend(loc=loc, prop=dict(size="small"))
            ax.set_xlabel("Distance [deg]")
            ax.set_ylabel("Depth [km]")
        else:
            msg = "Plot type '{}' is not a valid option.".format(plot_type)
            raise ValueError(msg)
        if show:
            plt.show()
        return ax

    def plot(self, plot_type="spherical", plot_all=True, legend=True,
             label_arrivals=False, ax=None, show=True):
        """
        Plot ray paths if any have been calculated.

        :param plot_type: Either ``"spherical"`` or ``"cartesian"``.
            A spherical plot is always global whereas a Cartesian one can
            also be local.
        :type plot_type: str
        :param plot_all: By default all rays, even those travelling in the
            other direction and thus arriving at a distance of *360 - x*
            degrees are shown. Set this to ``False`` to only show rays
            arriving at exactly *x* degrees.
        :type plot_all: bool
        :param legend: If boolean, specify whether or not to show the legend
            (at the default location.) If a str, specify the location of the
            legend. If you are plotting a single phase, you may consider using
            the ``label_arrivals`` argument.
        :type legend: bool or str
        :param label_arrivals: Label the arrivals with their respective phase
            names. This setting is only useful if you are plotting a single
            phase as otherwise the names could be large and possibly overlap
            or clip. Consider using the ``legend`` parameter instead if you
            are plotting multiple phases.
        :type label_arrivals: bool
        :param show: Show the plot.
        :type show: bool
        :param fig: Figure to plot in. If not given, a new figure will be
            created.
        :type fig: :class:`matplotlib.figure.Figure`
        :param ax: Axes to plot in. If not given, a new figure with an axes
            will be created. Must be a polar axes for the spherical plot and
            a regular one for the Cartesian plot.
        :type ax: :class:`matplotlib.axes.Axes`
        :returns: Matplotlib axes with the plot
        :rtype: :class:`matplotlib.axes.Axes`

        .. versionchanged:: 1.1.0

            Deprecated.

            With the introduction of plot_times(), plot() has been renamed to
            plot_rays()
        """

        # display warning
        from obspy.core.util.deprecation_helpers import ObsPyDeprecationWarning
        warnings.warn("The plot() function is deprecated. Please use "
                      "arrivals.plot_rays()",
                      ObsPyDeprecationWarning, stacklevel=2)

        # call plot_rays, but with added fig and phase_list parameters:
        return self.plot_rays(plot_type=plot_type,
                              plot_all=plot_all,
                              legend=legend,
                              label_arrivals=label_arrivals,
                              ax=ax,
                              fig=None,
                              show=show,
                              phase_list=("ttall",))


class TauPyModel(object):
    """
    Representation of a seismic model and methods for ray paths through it.
    """

    def __init__(self, model="iasp91", verbose=False, planet_flattening=0.0,
                 cache=None):
        """
        Loads an already created TauPy model.

        :param model: The model name. Either an internal TauPy model or a
            filename in the case of custom models.
        :param planet_flattening: Flattening parameter for the planet's
            ellipsoid (i.e. (a-b)/a, where a is the semimajor equatorial radius
            and b is the semiminor polar radius). A value of 0 (the default)
            gives a spherical planet. Note that this is only used to convert
            from geographical positions (source and receiver latitudes and
            longitudes) to epicentral distances - the actual traveltime and
            raypath calculations are performed on a spherical planet.
        :type planet_flattening: float
        :param cache: An object to use to cache models split at source depths.
            Generating results requires splitting a model at the source depth,
            which may be expensive. The cache allows faster calculation when
            multiple results are requested for the same source depth. The
            dictionary must be ordered, otherwise the LRU cache will not
            behave correctly. If ``False`` is specified, then no cache will be
            used.
        :type cache: :class:`collections.OrderedDict` or bool

        Usage:

        >>> from obspy.taup import tau
        >>> i91 = tau.TauPyModel()
        >>> print(i91.get_travel_times(10, 20)[0].name)
        P
        >>> i91.get_travel_times(10, 20)[0].time  # doctest: +ELLIPSIS
        272.675...
        >>> len(i91.get_travel_times(100, 50, phase_list = ["P", "S"]))
        2
        """
        self.verbose = verbose
        self.model = TauModel.from_file(model, cache=cache)
        self.planet_flattening = planet_flattening

    def get_travel_times(self, source_depth_in_km, distance_in_degree=None,
                         phase_list=("ttall",), receiver_depth_in_km=0.0):
        """
        Return travel times of every given phase.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param distance_in_degree: Epicentral distance in degrees.
        :type distance_in_degree: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]
        :param receiver_depth_in_km: Receiver depth in km
        :type receiver_depth_in_km: float

        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        # Accessing the arrivals not just by list indices but by phase name
        # might be useful, but also difficult: several arrivals can have the
        # same phase.
        tt = TauPTime(self.model, phase_list, source_depth_in_km,
                      distance_in_degree, receiver_depth_in_km)
        tt.run()
        return Arrivals(sorted(tt.arrivals, key=lambda x: x.time),
                        model=self.model)

    def get_pierce_points(self, source_depth_in_km, distance_in_degree,
                          phase_list=("ttall",), receiver_depth_in_km=0.0):
        """
        Return pierce points of every given phase.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param distance_in_degree: Epicentral distance in degrees.
        :type distance_in_degree: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]
        :param receiver_depth_in_km: Receiver depth in km
        :type receiver_depth_in_km: float

        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        pp = TauPPierce(self.model, phase_list, source_depth_in_km,
                        distance_in_degree, receiver_depth_in_km)
        pp.run()
        return Arrivals(sorted(pp.arrivals, key=lambda x: x.time),
                        model=self.model)

    def get_ray_paths(self, source_depth_in_km, distance_in_degree=None,
                      phase_list=("ttall",), receiver_depth_in_km=0.0):
        """
        Return ray paths of every given phase.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param distance_in_degree: Epicentral distance in degrees.
        :type distance_in_degree: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]
        :param receiver_depth_in_km: Receiver depth in km
        :type receiver_depth_in_km: float

        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        rp = TauPPath(self.model, phase_list, source_depth_in_km,
                      distance_in_degree, receiver_depth_in_km)
        rp.run()
        return Arrivals(sorted(rp.arrivals, key=lambda x: x.time),
                        model=self.model)

    def get_travel_times_geo(self, source_depth_in_km, source_latitude_in_deg,
                             source_longitude_in_deg, receiver_latitude_in_deg,
                             receiver_longitude_in_deg, phase_list=("ttall",)):
        """
        Return travel times of every given phase given geographical data.

        .. note::

            Note that the conversion from source and receiver latitudes and
            longitudes to epicentral distances respects the model's flattening
            parameter, so this calculation can be performed for a ellipsoidal
            or spherical planet. However, the actual traveltime and raypath
            calculations are performed on a spherical planet. Ellipticity
            corrections of e.g. [Dziewonski1976]_ are not made.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param source_latitude_in_deg: Source latitude in degrees
        :type source_latitude_in_deg: float
        :param source_longitude_in_deg: Source longitude in degrees
        :type source_longitude_in_deg: float
        :param receiver_latitude_in_deg: Receiver latitude in degrees
        :type receiver_latitude_in_deg: float
        :param receiver_longitude_in_deg: Receiver longitude in degrees
        :type receiver_longitude_in_deg: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]

        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        distance_in_deg = calc_dist(source_latitude_in_deg,
                                    source_longitude_in_deg,
                                    receiver_latitude_in_deg,
                                    receiver_longitude_in_deg,
                                    self.model.radius_of_planet,
                                    self.planet_flattening)
        arrivals = self.get_travel_times(source_depth_in_km, distance_in_deg,
                                         phase_list)
        return arrivals

    def get_pierce_points_geo(self, source_depth_in_km, source_latitude_in_deg,
                              source_longitude_in_deg,
                              receiver_latitude_in_deg,
                              receiver_longitude_in_deg,
                              phase_list=("ttall",),
                              resample=False):
        """
        Return pierce points of every given phase with geographical info.

        .. note::

            Note that the conversion from source and receiver latitudes and
            longitudes to epicentral distances respects the model's flattening
            parameter, so this calculation can be performed for a ellipsoidal
            or spherical planet. However, the actual traveltime and raypath
            calculations are performed on a spherical planet. Ellipticity
            corrections of e.g. [Dziewonski1976]_ are not made.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param source_latitude_in_deg: Source latitude in degrees
        :type source_latitude_in_deg: float
        :param source_longitude_in_deg: Source longitue in degrees
        :type source_longitude_in_deg: float
        :param receiver_latitude_in_deg: Receiver latitude in degrees
        :type receiver_latitude_in_deg: float
        :param receiver_longitude_in_deg: Receiver longitude in degrees
        :type receiver_longitude_in_deg: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]
        :param resample: adds sample points to allow for easy cartesian
                         interpolation. This is especially useful for phases
                         like Pdiff.
        :type resample: bool
        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        distance_in_deg = calc_dist(source_latitude_in_deg,
                                    source_longitude_in_deg,
                                    receiver_latitude_in_deg,
                                    receiver_longitude_in_deg,
                                    self.model.radius_of_planet,
                                    self.planet_flattening)

        arrivals = self.get_pierce_points(source_depth_in_km, distance_in_deg,
                                          phase_list)

        if geodetics.HAS_GEOGRAPHICLIB:
            arrivals = add_geo_to_arrivals(arrivals, source_latitude_in_deg,
                                           source_longitude_in_deg,
                                           receiver_latitude_in_deg,
                                           receiver_longitude_in_deg,
                                           self.model.radius_of_planet,
                                           self.planet_flattening,
                                           resample=resample)
        else:
            msg = "Not able to evaluate positions of pierce points. " + \
                  "Arrivals object will not be modified. " + \
                  "Install the Python module 'geographiclib' to solve " + \
                  "this issue."
            warnings.warn(msg)

        return arrivals

    def get_ray_paths_geo(self, source_depth_in_km, source_latitude_in_deg,
                          source_longitude_in_deg, receiver_latitude_in_deg,
                          receiver_longitude_in_deg, phase_list=("ttall",),
                          resample=False):
        """
        Return ray paths of every given phase with geographical info.

        .. note::

            Note that the conversion from source and receiver latitudes and
            longitudes to epicentral distances respects the model's flattening
            parameter, so this calculation can be performed for a ellipsoidal
            or spherical planet. However, the actual traveltime and raypath
            calculations are performed on a spherical planet. Ellipticity
            corrections of e.g. [Dziewonski1976]_ are not made.

        :param source_depth_in_km: Source depth in km
        :type source_depth_in_km: float
        :param source_latitude_in_deg: Source latitude in degrees
        :type source_latitude_in_deg: float
        :param source_longitude_in_deg: Source longitue in degrees
        :type source_longitude_in_deg: float
        :param receiver_latitude_in_deg: Receiver latitude in degrees
        :type receiver_latitude_in_deg: float
        :param receiver_longitude_in_deg: Receiver longitude in degrees
        :type receiver_longitude_in_deg: float
        :param phase_list: List of phases for which travel times should be
            calculated. If this is empty, all phases in arrivals object
            will be used.
        :type phase_list: list[str]
        :return: List of ``Arrival`` objects, each of which has the time,
            corresponding phase name, ray parameter, takeoff angle, etc. as
            attributes.
        :rtype: :class:`Arrivals`
        """
        distance_in_deg = calc_dist(source_latitude_in_deg,
                                    source_longitude_in_deg,
                                    receiver_latitude_in_deg,
                                    receiver_longitude_in_deg,
                                    self.model.radius_of_planet,
                                    self.planet_flattening)

        arrivals = self.get_ray_paths(source_depth_in_km, distance_in_deg,
                                      phase_list)

        if geodetics.HAS_GEOGRAPHICLIB:
            arrivals = add_geo_to_arrivals(arrivals, source_latitude_in_deg,
                                           source_longitude_in_deg,
                                           receiver_latitude_in_deg,
                                           receiver_longitude_in_deg,
                                           self.model.radius_of_planet,
                                           self.planet_flattening,
                                           resample=resample)
        else:
            msg = "Not able to evaluate positions of points on path. " + \
                  "Arrivals object will not be modified. " + \
                  "Install the Python module 'geographiclib' to solve " + \
                  "this issue."
            warnings.warn(msg)

        return arrivals


def plot_travel_times(source_depth, phase_list=("ttbasic",), min_degrees=0,
                      max_degrees=180, npoints=50, model='iasp91',
                      plot_all=True, legend=True, verbose=False, fig=None,
                      ax=None, show=True):
    """
    Returns a travel time plot and any created axis instance of this
    plot.

    :param source_depth: Source depth in kilometers.
    :type source_depth: float
    :param min_degrees: minimum distance from the source (in degrees)
    :type min_degrees: float
    :param max_degrees: maximum distance from the source (in degrees)
    :type max_degrees: float
    :param npoints: Number of points to plot.
    :type npoints: int
    :param phase_list: List of phase names to plot.
    :type phase_list: list[str], optional
    :param model: string containing the model to use.
    :type model: str
    :param plot_all: By default all rays, even those travelling in the
        other direction and thus arriving at a distance of *360 - x*
        degrees are shown. Set this to ``False`` to only show rays
        arriving at exactly *x* degrees.
    :type plot_all: bool
    :param legend: Whether or not to show the legend
    :type legend: bool
    :param verbose: Whether to print information about epicentral distances
        that did not have an arrival.
    :type verbose: bool
    :param fig: Figure to plot into. If not given, a new figure instance
        will be created.
    :type fig: :class:`matplotlib.figure.Figure`
    :param ax: Axes to plot in. If not given, a new figure with an axes
        will be created.
    :param show: Show the plot.
    :type show: bool
    :param ax: Axes to plot in. If not given, a new figure with an axes
        will be created.
    :type ax: :class:`matplotlib.axes.Axes`
    :returns: Matplotlib axes with the plot
    :rtype: :class:`matplotlib.axes.Axes`

    .. rubric:: Example

    >>> from obspy.taup import plot_travel_times
    >>> ax = plot_travel_times(source_depth=10, phase_list=['P', 'S', 'PP'])

    .. plot::

        from obspy.taup import plot_travel_times
        ax = plot_travel_times(source_depth=10, phase_list=['P','S','PP'])
    """
    import matplotlib.pyplot as plt

    # compute the requested arrivals:
    if not isinstance(model, TauPyModel):
        model = TauPyModel(model)

    # a list of epicentral distances without a travel time, and a flag:
    notimes = []
    plotted = False

    # calculate the arrival times and plot vs. epicentral distance:
    degrees = np.linspace(min_degrees, max_degrees, npoints)
    for degree in degrees:
        try:
            arrivals = model.get_ray_paths(source_depth, degree,
                                           phase_list=phase_list)
            ax = arrivals.plot_times(phase_list=phase_list, show=False,
                                     ax=ax, plot_all=plot_all)
            plotted = True
        except ValueError:
            notimes.append(degree)

    if plotted:
        if verbose:
            if len(notimes) == 1:
                tmpl = "There was {} epicentral distance without an arrival"
            else:
                tmpl = "There were {} epicentral distances without an arrival"
            print(tmpl.format(len(notimes)))
    else:
        raise ValueError("No arrival times to plot.")

    if legend:
        # merge all arrival labels of a certain phase:
        handles, labels = ax.get_legend_handles_labels()
        labels, ids = np.unique(labels, return_index=True)
        handles = [handles[i] for i in ids]
        ax.legend(handles, labels, loc=2, numpoints=1)

    if show:
        plt.show()
    return ax


def plot_ray_paths(source_depth, min_degrees=0, max_degrees=360, npoints=10,
                   plot_type='spherical', phase_list=['P', 'S', 'PP'],
                   model='iasp91', plot_all=True, legend=False,
                   label_arrivals=False, verbose=False, fig=None, show=True,
                   ax=None):
    """
    Plot ray paths for seismic phases.

    :param source_depth: Source depth in kilometers.
    :type source_depth: float
    :param min_degrees: minimum distance from the source (in degrees).
    :type min_degrees: float
    :param max_degrees: maximum distance from the source (in degrees).
    :type max_degrees: float
    :param npoints: Number of receivers to plot.
    :type npoints: int
    :param plot_type: type of plot to create. Options are 'spherical' (default)
        and 'cartesian'.
    :type plot_type: str
    :param phase_list: List of phase names.
    :type phase_list: list[str]
    :param model: Model name.
    :type model: str
    :param plot_all: By default all rays, even those travelling in the
        other direction and thus arriving at a distance of *360 - x*
        degrees are shown. Set this to ``False`` to only show rays
        arriving at exactly *x* degrees.
    :type plot_all: bool
    :param legend: Whether or not to show the legend
    :type legend: bool
    :param label_arrivals: Label the arrivals with their respective phase
        names. This setting is only useful if you are plotting a single
        phase as otherwise the names could be large and possibly overlap
        or clip. Consider using the ``legend`` parameter instead if you
        are plotting multiple phases.
    :type label_arrivals: bool
    :param verbose: Whether to print information about selected phases that
        were not encountered at individual epicentral distances.
    :type verbose: bool
    :param fig: Figure to plot into. If not given, a new figure instance
        will be created.
    :type fig: :class:`matplotlib.figure.Figure`
    :param show: Show the plot.
    :type show: bool
    :param ax: Axes to plot in. If not given, a new figure with an axes
        will be created.
    :type ax: :class:`matplotlib.axes.Axes`
    :returns: Matplotlib axes with the plot
    :rtype: :class:`matplotlib.axes.Axes`

    .. rubric:: Example

    >>> from obspy.taup import plot_ray_paths
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(figsize=(10, 10), subplot_kw=dict(polar=True))
    >>> ax = plot_ray_paths(source_depth=10, ax=ax, fig=fig, legend=True,
    ...                     phase_list=['P', 'S', 'PP'], verbose=True)
    There were rays for all but the following epicentral distances:
     [0.0, 360.0]

    .. plot::

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

        fig, ax = plt.subplots(figsize=(10, 10), subplot_kw=dict(polar=True))
        ax = plot_ray_paths(source_depth=10, plot_type="spherical",
                        ax=ax, fig=fig, legend=True,
                        phase_list=['P','S','PP'])
    """
    import matplotlib.pyplot as plt
    model = TauPyModel(model)

    # set up a list of epicentral distances without a ray, and a flag:
    norays = []
    plotted = False

    # calculate the arrival times and plot vs. epicentral distance:
    degrees = np.linspace(min_degrees, max_degrees, npoints)
    for degree in degrees:
        try:
            arrivals = model.get_ray_paths(source_depth, degree,
                                           phase_list=phase_list)
            ax = arrivals.plot_rays(phase_list=phase_list, show=False,
                                    ax=ax, plot_type=plot_type,
                                    plot_all=plot_all, legend=False)
            plotted = True
        except ValueError:
            norays.append(degree)

    if plotted:
        if verbose:
            print("There were rays for all but the following epicentral "
                  "distances:\n", norays)
    else:
        raise ValueError("No ray paths to plot.")

    if legend:
        # merge all arrival labels of a certain phase:
        handles, labels = ax.get_legend_handles_labels()
        labels, ids = np.unique(labels, return_index=True)
        handles = [handles[i] for i in ids]
        ax.legend(handles, labels, loc=2, numpoints=1)

    if show:
        plt.show()
    return ax