# Source code for openquake.hazardlib.geo.surface.base

```# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.

"""
Module :mod:`openquake.hazardlib.geo.surface.base` implements
:class:`BaseSurface` and :class:`BaseSurface`.
"""
import numpy
import math
from openquake.hazardlib.geo.mesh import Mesh
from openquake.hazardlib.geo import geodetic, utils, Point, Line,\
RectangularMesh

def _get_finite_mesh(mesh):
ok = numpy.isfinite(mesh.lons.flat)
if numpy.all(ok):
return mesh
ok = numpy.reshape(ok, mesh.lons.shape)
return Mesh(mesh.lons[ok], mesh.lats[ok], mesh.depths[ok])

def _find_turning_points(mesh, tol=1.0):
"""
Identifies the turning points in a rectangular mesh based on the
deviation in the azimuth between successive points on the upper edge.
A turning point is flagged if the change in azimuth change is greater than
the specified tolerance (in degrees)

:param mesh:
Mesh for downsampling as instance of :class:
openquake.hazardlib.geo.mesh.RectangularMesh

:param float tol:
Maximum difference in azimuth (decimal degrees) between successive
points to identify a turning point

:returns:
Column indices of turning points (as numpy array)
"""
assert isinstance(mesh, RectangularMesh)
idx1 = numpy.isfinite(mesh.lons[0, :-1])
idx2 = numpy.isfinite(mesh.lons[0, 1:])
idx = numpy.where(numpy.logical_and(idx1, idx2))[0]
azimuths = geodetic.azimuth(mesh.lons[0, idx], mesh.lats[0, idx],
mesh.lons[0, idx+1], mesh.lats[0, idx+1])
naz = len(azimuths)
azim = azimuths[0]
# Retain initial point
idx = [0]
for i in range(1, naz):
if numpy.fabs(azimuths[i] - azim) > tol:
idx.append(i)
azim = azimuths[i]
# Add on last point - if not already in the set
if idx[-1] != mesh.lons.shape[1] - 1:
idx.append(mesh.lons.shape[1] - 1)
return numpy.array(idx)

[docs]def downsample_mesh(mesh, tol=1.0):
"""
Returns a mesh sampled at a lower resolution - if the difference
in azimuth is larger than the specified tolerance a turn is assumed

:returns:
Downsampled mesh as instance of :class:
openquake.hazardlib.geo.mesh.RectangularMesh
"""
idx = _find_turning_points(mesh, tol)
if mesh.depths is not None:
return RectangularMesh(lons=mesh.lons[:, idx],
lats=mesh.lats[:, idx],
depths=mesh.depths[:, idx])
else:
return RectangularMesh(lons=mesh.lons[:, idx],
lats=mesh.lats[:, idx])

[docs]def downsample_trace(mesh, tol=1.0):
"""
Downsamples the upper edge of a fault within a rectangular mesh, retaining
node points only if changes in direction on the order of tol are found

:returns:
Downsampled edge as a numpy array of [long, lat, depth]
"""
idx = _find_turning_points(mesh, tol)
if mesh.depths is not None:
return numpy.column_stack([mesh.lons[0, idx],
mesh.lats[0, idx],
mesh.depths[0, idx]])
else:
return numpy.column_stack([mesh.lons[0, idx], mesh.lats[0, idx]])

[docs]class BaseSurface:
"""
Base class for a surface in 3D-space.
"""

def __init__(self, mesh=None):
self.mesh = mesh

[docs]    def get_min_distance(self, mesh):
"""
Compute and return the minimum distance from the surface to each point
of ``mesh``. This distance is sometimes called ``Rrup``.

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate
minimum distance to.
:returns:
A numpy array of distances in km.
"""
fmesh = _get_finite_mesh(self.mesh)
return fmesh.get_min_distance(mesh)

[docs]    def get_closest_points(self, mesh):
"""
For each point from ``mesh`` find a closest point belonging to surface.

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to find
closest points to.
:returns:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of the same shape as
``mesh`` with closest surface's points on respective indices.
"""
fmesh = _get_finite_mesh(self.mesh)
return fmesh.get_closest_points(mesh)

[docs]    def get_joyner_boore_distance(self, mesh):
"""
Compute and return Joyner-Boore (also known as ``Rjb``) distance
to each point of ``mesh``.

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate
Joyner-Boore distance to.
:returns:
Numpy array of closest distances between the projections of surface
and each point of the ``mesh`` to the earth surface.
"""
fmesh = _get_finite_mesh(self.mesh)
return fmesh.get_joyner_boore_distance(mesh)

[docs]    def get_ry0_distance(self, mesh):
"""
Compute the minimum distance between each point of a mesh and the great
circle arcs perpendicular to the average strike direction of the
fault trace and passing through the end-points of the trace.

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate
Ry0-distance to.
:returns:
Numpy array of distances in km.
"""

# This computes ry0 by using an average strike direction
top_edge = self.mesh[0:1]
mean_strike = self.get_strike()

# Manage the case of kite fault surfaces
ia = 0
ib = -1
if (self.__class__.__name__ == 'KiteSurface'):
idx = numpy.nonzero(numpy.isfinite(top_edge.lons[0, :]))[0]
ia = min(idx)
ib = max(idx)

# Computing the distances between the sites and the two lines
# perpendicular to the strike passing trough the two extremes
# of the top of the rupture
dst1 = geodetic.distance_to_arc(top_edge.lons[0, ia],
top_edge.lats[0, ia],
(mean_strike + 90.) % 360,
mesh.lons, mesh.lats)

dst2 = geodetic.distance_to_arc(top_edge.lons[0, ib],
top_edge.lats[0, ib],
(mean_strike + 90.) % 360,
mesh.lons, mesh.lats)

# Get the shortest distance from the two lines
idx = numpy.sign(dst1) == numpy.sign(dst2)
dst = numpy.zeros_like(dst1)
dst[idx] = numpy.fmin(numpy.abs(dst1[idx]), numpy.abs(dst2[idx]))

if numpy.any(numpy.isnan(dst)):
raise ValueError('NaN in Ry0')

return dst

[docs]    def get_rx_distance(self, mesh):
"""
Compute distance between each point of mesh and surface's great circle
arc.

Distance is measured perpendicular to the rupture strike, from
the surface projection of the updip edge of the rupture, with
the down dip direction being positive (this distance is usually
called ``Rx``).

In other words, is the horizontal distance to top edge of rupture
measured perpendicular to the strike. Values on the hanging wall
are positive, values on the footwall are negative.

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate
Rx-distance to.
:returns:
Numpy array of distances in km.
"""
top_edge = self.mesh[0:1]
dists = []

ia = 0
ib = top_edge.lons.shape[1] - 2
if (self.__class__.__name__ == 'KiteSurface'):
idxs = numpy.nonzero(numpy.isfinite(top_edge.lons[0, :]))[0]
ia = min(idxs)
ib = sorted(idxs)[-2]

if top_edge.lons.shape[1] < 3:
i = 0

if ((self.__class__.__name__ == 'KiteSurface') and
(numpy.isnan(top_edge.lons[0, i]) or
numpy.isnan(top_edge.lons[0, i+1]))):
msg = 'Rx calculation. Top of rupture has less than two points'
raise ValueError(msg)

p1 = Point(
top_edge.lons[0, i],
top_edge.lats[0, i],
top_edge.depths[0, i])
p2 = Point(
top_edge.lons[0, i + 1], top_edge.lats[0, i + 1],
top_edge.depths[0, i + 1])
azimuth = p1.azimuth(p2)
dists.append(
geodetic.distance_to_arc(
p1.longitude, p1.latitude, azimuth,
mesh.lons, mesh.lats))

else:

for i in range(top_edge.lons.shape[1] - 1):

if ((self.__class__.__name__ == 'KiteSurface') and
(numpy.isnan(top_edge.lons[0, i]) or
numpy.isnan(top_edge.lons[0, i+1]))):
continue

p1 = Point(
top_edge.lons[0, i],
top_edge.lats[0, i],
top_edge.depths[0, i])
p2 = Point(
top_edge.lons[0, i + 1],
top_edge.lats[0, i + 1],
top_edge.depths[0, i + 1])

# Swapping
if i == 0:
pt = p1
p1 = p2
p2 = pt

# Computing azimuth and distance
if i == ia or i == ib:
azimuth = p1.azimuth(p2)
tmp = geodetic.distance_to_semi_arc(p1.longitude,
p1.latitude,
azimuth,
mesh.lons, mesh.lats)
else:
tmp = geodetic.min_distance_to_segment(
numpy.array([p1.longitude, p2.longitude]),
numpy.array([p1.latitude, p2.latitude]),
mesh.lons, mesh.lats)
# Correcting the sign of the distance
if i == 0:
tmp *= -1
dists.append(tmp)

# Computing distances
dists = numpy.array(dists)
iii = abs(dists).argmin(axis=0)
dst = dists[iii, list(range(dists.shape[1]))]

if numpy.any(numpy.isnan(dst)):
raise ValueError('NaN in Rx')

return dst

[docs]    def get_top_edge_depth(self):
"""
Return minimum depth of surface's top edge.

:returns:
Float value, the vertical distance between the earth surface
and the shallowest point in surface's top edge in km.
"""
top_edge = self.mesh[0:1]
if top_edge.depths is None:
return 0
else:
dep = numpy.min(top_edge.depths)
return dep

def _get_top_edge_centroid(self):
"""
Return :class:`~openquake.hazardlib.geo.point.Point` representing the
surface's top edge centroid.
"""
top_edge = self.mesh[0:1]

[docs]    def get_area(self):
"""
Compute area as the sum of the mesh cells area values.
"""
from openquake.hazardlib.geo.surface.kite_fault import KiteSurface
if isinstance(self, KiteSurface):
_, _, _, area = self.get_cell_dimensions()
else:
mesh = self.mesh
_, _, _, area = mesh.get_cell_dimensions()
return numpy.sum(area)

[docs]    def get_bounding_box(self):
"""
Compute surface bounding box from surface mesh representation. That is
extract longitudes and latitudes of mesh points and calls:
:meth:`openquake.hazardlib.geo.utils.get_spherical_bounding_box`

:return:
A tuple of four items. These items represent western, eastern,
northern and southern borders of the bounding box respectively.
Values are floats in decimal degrees.
"""
mesh = _get_finite_mesh(self.mesh)
return utils.get_spherical_bounding_box(mesh.lons, mesh.lats)

[docs]    def get_middle_point(self):
"""
Compute coordinates of surface middle point.

The actual definition of ``middle point`` depends on the type of
surface geometry.

:return:
instance of :class:`openquake.hazardlib.geo.point.Point`
representing surface middle point.
"""
return self.mesh.get_middle_point()

def _boundaries(self, name):
# name is one of lons, lats, mesh
arr = getattr(self.mesh, name)
return numpy.concatenate(
(arr[0, :], arr[1:, -1], arr[-1, :-1][::-1],  arr[:-1, 0][::-1]))

[docs]    def get_surface_boundaries(self):
"""
Returns the boundaries in the same format as a multiplanar
surface, with two lists of lons and lats
"""
return self._boundaries('lons'), self._boundaries('lats')

[docs]    def get_surface_boundaries_3d(self):
"""
Returns the boundaries as three lists of lons, lats, depths
"""
return (self._boundaries('lons'), self._boundaries('lats'),
self._boundaries('depths'))

[docs]    def get_resampled_top_edge(self, angle_var=0.1):
"""
This methods computes a simplified representation of a fault top edge
by removing the points that are not describing a change of direction,
provided a certain tolerance angle.

:param float angle_var:
Number representing the maximum deviation (in degrees) admitted
without the creation of a new segment
:returns:
A :class:`~openquake.hazardlib.geo.line.Line` representing the
rupture surface's top edge.
"""
mesh = self.mesh
top_edge = [Point(mesh.lons[0][0], mesh.lats[0][0], mesh.depths[0][0])]

for i in range(len(mesh.triangulate()[1][0]) - 1):
v1 = numpy.asarray(mesh.triangulate()[1][0][i])
v2 = numpy.asarray(mesh.triangulate()[1][0][i + 1])
cosang = numpy.dot(v1, v2)
sinang = numpy.linalg.norm(numpy.cross(v1, v2))
angle = math.degrees(numpy.arctan2(sinang, cosang))

if abs(angle) > angle_var:

top_edge.append(Point(mesh.lons[0][i + 1],
mesh.lats[0][i + 1],
mesh.depths[0][i + 1]))

top_edge.append(Point(mesh.lons[0][-1],
mesh.lats[0][-1], mesh.depths[0][-1]))
line_top_edge = Line(top_edge)

return line_top_edge

[docs]    def get_hypo_location(self, mesh_spacing, hypo_loc=None):
"""
The method determines the location of the hypocentre within the rupture

:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points
:param mesh_spacing:
The desired distance between two adjacent points in source's
ruptures' mesh, in km. Mainly this parameter allows to balance
the trade-off between time needed to compute the distance
between the rupture surface and a site and the precision of that
computation.
:param hypo_loc:
Hypocentre location as fraction of rupture plane, as a tuple of
(Along Strike, Down Dip), e.g. a hypocentre located in the centroid
of the rupture would be input as (0.5, 0.5), whereas a
hypocentre located in a position 3/4 along the length, and 1/4 of
the way down dip of the rupture plane would be entered as
(0.75, 0.25).
:returns:
Hypocentre location as instance of
:class:`~openquake.hazardlib.geo.point.Point`
"""
mesh = self.mesh
centroid = mesh.get_middle_point()
if hypo_loc is None:
return centroid

total_len_y = (len(mesh.depths) - 1) * mesh_spacing
y_distance = hypo_loc[1] * total_len_y
y_node = int(numpy.round(y_distance / mesh_spacing))
total_len_x = (len(mesh.lons[y_node]) - 1) * mesh_spacing
x_distance = hypo_loc[0] * total_len_x
x_node = int(numpy.round(x_distance / mesh_spacing))
hypocentre = Point(mesh.lons[y_node][x_node],
mesh.lats[y_node][x_node],
mesh.depths[y_node][x_node])
return hypocentre

[docs]    def get_azimuth(self, mesh):
"""
This method computes the azimuth of a set of points in a
:class:`openquake.hazardlib.geo.mesh` instance. The reference used for
the calculation of azimuth is the middle point and the strike of the
rupture. The value of azimuth computed corresponds to the angle
measured in a clockwise direction from the strike of the rupture.

:parameter mesh:
An instance of  :class:`openquake.hazardlib.geo.mesh`
:return:
An instance of `numpy.ndarray`
"""
# Get info about the rupture
strike = self.get_strike()
hypocenter = self.get_middle_point()
# This is the azimuth from the north of each point Vs. the middle of
# the rupture
azim = geodetic.azimuth(hypocenter.longitude, hypocenter.latitude,
mesh.lons, mesh.lats)
# Compute the azimuth from the fault strike
rel_azi = (azim - strike) % 360
return rel_azi

[docs]    def get_azimuth_of_closest_point(self, mesh):
"""
Compute the azimuth between point in `mesh` and the corresponding
closest point on the rupture surface.

:param mesh:
An instance of  :class:`openquake.hazardlib.geo.mesh`
:return:
An :class:`numpy.ndarray` instance with the azimuth values.
"""
mesh_closest = self.get_closest_points(mesh)
return geodetic.azimuth(mesh.lons, mesh.lats, mesh_closest.lons,
mesh_closest.lats)
```