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

# -*- coding: utf-8 -*-
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"""
Module :mod:`openquake.hazardlib.geo.surface.base` implements
:class:`BaseSurface` and :class:`BaseQuadrilateralSurface`.
"""
import abc

import numpy
import math
from openquake.hazardlib.geo import geodetic, utils, Point, Line,\
    RectangularMesh
from openquake.baselib.python3compat import with_metaclass


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)
    azimuths = geodetic.azimuth(mesh.lons[0, :-1], mesh.lats[0, :-1],
                                mesh.lons[0, 1:], mesh.lats[0, 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 not 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(with_metaclass(abc.ABCMeta)): """ Base class for a surface in 3D-space. """
[docs] @abc.abstractmethod 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. """
[docs] @abc.abstractmethod 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. """
[docs] @abc.abstractmethod 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. """
[docs] @abc.abstractmethod 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. """
[docs] @abc.abstractmethod 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. """
[docs] @abc.abstractmethod def get_top_edge_depth(self): """ Compute 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. """
[docs] @abc.abstractmethod def get_strike(self): """ Compute surface's strike as decimal degrees in a range ``[0, 360)``. The actual definition of the strike might depend on surface geometry. :returns: Float value, the azimuth (in degrees) of the surface top edge """
[docs] @abc.abstractmethod def get_dip(self): """ Compute surface's dip as decimal degrees in a range ``(0, 90]``. The actual definition of the dip might depend on surface geometry. :returns: Float value, the inclination (in degrees) of the surface with respect to the Earth surface """
[docs] @abc.abstractmethod def get_width(self): """ Compute surface's width (that is surface extension along the dip direction) in km. The actual definition depends on the type of surface geometry. :returns: Float value, the surface width """
[docs] @abc.abstractmethod def get_area(self): """ Compute surface's area in squared km. :returns: Float value, the surface area """
[docs] @abc.abstractmethod def get_bounding_box(self): """ Compute surface geographical 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. """
[docs] @abc.abstractmethod 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. """
[docs]class BaseQuadrilateralSurface(with_metaclass(abc.ABCMeta, BaseSurface)): """ Base class for a quadrilateral surface in 3D-space. Subclasses must implement :meth:`_create_mesh`, and superclass methods :meth:`get_strike() <.base.BaseSurface.get_strike>`, :meth:`get_dip() <.base.BaseSurface.get_dip>` and :meth:`get_width() <.base.BaseSurface.get_width>`, and can override any others just for the sake of performance """ def __init__(self): self.mesh = None
[docs] def get_min_distance(self, mesh): """ See :meth:`superclass method <.base.BaseSurface.get_min_distance>` for spec of input and result values. Base class implementation calls the :meth:`corresponding <openquake.hazardlib.geo.mesh.Mesh.get_min_distance>` method of the surface's :meth:`mesh <get_mesh>`. Subclasses may override this method in order to make use of knowledge of a specific surface shape and thus perform better. """ return self.get_mesh().get_min_distance(mesh)
[docs] def get_closest_points(self, mesh): """ See :meth:`superclass method <.base.BaseSurface.get_closest_points>` for spec of input and result values. Base class implementation calls the :meth:`corresponding <openquake.hazardlib.geo.mesh.Mesh.get_closest_points>` method of the surface's :meth:`mesh <get_mesh>`. """ return self.get_mesh().get_closest_points(mesh)
[docs] def get_joyner_boore_distance(self, mesh): """ See :meth:`superclass method <.base.BaseSurface.get_joyner_boore_distance>` for spec of input and result values. Base class calls surface mesh's method :meth:`~openquake.hazardlib.geo.mesh.RectangularMesh.get_joyner_boore_distance`. """ return self.get_mesh().get_joyner_boore_distance(mesh)
[docs] def get_ry0_distance(self, mesh): """ :param mesh: :class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate Ry0-distance to. :returns: Numpy array of distances in km. See also :meth:`superclass method <.base.BaseSurface.get_ry0_distance>` for spec of input and result values. This method uses an average strike direction to compute ry0. """ # This computes ry0 by using an average strike direction top_edge = self.get_mesh()[0:1] mean_strike = self.get_strike() dst1 = geodetic.distance_to_arc(top_edge.lons[0, 0], top_edge.lats[0, 0], (mean_strike + 90.) % 360, mesh.lons, mesh.lats) dst2 = geodetic.distance_to_arc(top_edge.lons[0, -1], top_edge.lats[0, -1], (mean_strike + 90.) % 360, mesh.lons, mesh.lats) # Find the points on the rupture # 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])) return dst
[docs] def get_rx_distance(self, mesh): """ See :meth:`superclass method <.base.BaseSurface.get_rx_distance>` for spec of input and result values. The method extracts the top edge of the surface. For each point in mesh it computes the Rx distance to each segment the top edge is made of. The calculation is done by calling the function :func:`openquake.hazardlib.geo.geodetic.distance_to_arc`. The final Rx distance matrix is then constructed by taking, for each point in mesh, the minimum Rx distance value computed. """ top_edge = self.get_mesh()[0:1] dists = [] if top_edge.lons.shape[1] < 3: i = 0 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): 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 == 0 or i == top_edge.lons.shape[1] - 2: 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]))] 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.get_mesh()[0:1] if top_edge.depths is None: return 0 else: return numpy.min(top_edge.depths)
def _get_top_edge_centroid(self): """ Return :class:`~openquake.hazardlib.geo.point.Point` representing the surface's top edge centroid. """ top_edge = self.get_mesh()[0:1] return top_edge.get_middle_point()
[docs] def get_mesh(self): """ Return surface's mesh. Uses :meth:`_create_mesh` for creating the mesh for the first time. All subsequent calls to :meth:`get_mesh` return the same mesh object. .. warning:: It is required that the mesh is constructed "top-to-bottom". That is, the first row of points should be the shallowest. """ if self.mesh is None: self.mesh = self._create_mesh() assert ( self.mesh.depths is None or len(self.mesh.depths) == 1 or self.mesh.depths[0][0] < self.mesh.depths[-1][0] ), "the first row of points in the mesh must be the shallowest" return self.mesh
[docs] def get_area(self): """ Compute area as the sum of the mesh cells area values. """ mesh = self.get_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 = self.get_mesh() return utils.get_spherical_bounding_box(mesh.lons, mesh.lats)
[docs] def get_middle_point(self): """ Compute middle point from surface mesh representation. Calls :meth:`openquake.hazardlib.geo.mesh.RectangularMesh.get_middle_point` """ mesh = self.get_mesh() return mesh.get_middle_point()
[docs] def get_surface_boundaries(self): """ Returns the boundaries in the same format as a multiplanar surface, with two one-element lists of lons and lats """ mesh = self.get_mesh() lons = numpy.concatenate((mesh.lons[0, :], mesh.lons[1:, -1], mesh.lons[-1, :-1][::-1], mesh.lons[:-1, 0][::-1])) lats = numpy.concatenate((mesh.lats[0, :], mesh.lats[1:, -1], mesh.lats[-1, :-1][::-1], mesh.lats[:-1, 0][::-1])) return [lons], [lats]
[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.get_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
@abc.abstractmethod def _create_mesh(self): """ Create and return the mesh of points covering the surface. :returns: An instance of :class:`openquake.hazardlib.geo.mesh.RectangularMesh`. """
[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.get_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