Rupture surfaces¶
Package openquake.hazardlib.geo.surface
contains base and specific
implementations of earthquake rupture surfaces.
Base surface¶
Module openquake.hazardlib.geo.surface.base
implements
BaseSurface
and BaseQuadrilateralSurface
.

class
openquake.hazardlib.geo.surface.base.
BaseQuadrilateralSurface
[source]¶ Base class for a quadrilateral surface in 3Dspace.
Subclasses must implement
_create_mesh()
, and superclass methodsget_strike()
,get_dip()
andget_width()
, and can override any others just for the sake of performance
_create_mesh
()[source]¶ Create and return the mesh of points covering the surface.
Returns: An instance of openquake.hazardlib.geo.mesh.RectangularMesh
.

get_bounding_box
()[source]¶ Compute surface bounding box from surface mesh representation. That is extract longitudes and latitudes of mesh points and calls:
openquake.hazardlib.geo.utils.get_spherical_bounding_box()
Returns: 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.

get_closest_points
(mesh)[source]¶ See
superclass method
for spec of input and result values.Base class implementation calls the
corresponding
method of the surface’smesh
.

get_hypo_location
(mesh_spacing, hypo_loc=None)[source]¶ The method determines the location of the hypocentre within the rupture
Parameters:  mesh –
Mesh
of points  mesh_spacing – The desired distance between two adjacent points in source’s ruptures’ mesh, in km. Mainly this parameter allows to balance the tradeoff between time needed to compute the distance between the rupture surface and a site and the precision of that computation.
 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
Point
 mesh –

get_joyner_boore_distance
(mesh)[source]¶ See
superclass method
for spec of input and result values.Base class calls surface mesh’s method
get_joyner_boore_distance()
.

get_mesh
()[source]¶ Return surface’s mesh.
Uses
_create_mesh()
for creating the mesh for the first time. All subsequent calls toget_mesh()
return the same mesh object.Warning
It is required that the mesh is constructed “toptobottom”. That is, the first row of points should be the shallowest.

get_middle_point
()[source]¶ Compute middle point from surface mesh representation. Calls
openquake.hazardlib.geo.mesh.RectangularMesh.get_middle_point()

get_min_distance
(mesh)[source]¶ See
superclass method
for spec of input and result values.Base class implementation calls the
corresponding
method of the surface’smesh
.Subclasses may override this method in order to make use of knowledge of a specific surface shape and thus perform better.

get_resampled_top_edge
(angle_var=0.1)[source]¶ 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.
Parameters: angle_var (float) – Number representing the maximum deviation (in degrees) admitted without the creation of a new segment Returns: A Line
representing the rupture surface’s top edge.

get_rx_distance
(mesh)[source]¶ See
superclass method
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
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.

get_ry0_distance
(mesh)[source]¶ Parameters: mesh – Mesh
of points to calculate Ry0distance to.Returns: Numpy array of distances in km. See also
superclass method
for spec of input and result values.This method uses an average strike direction to compute ry0.


class
openquake.hazardlib.geo.surface.base.
BaseSurface
[source]¶ Base class for a surface in 3Dspace.

get_bounding_box
()[source]¶ Compute surface geographical bounding box.
Returns: 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.

get_closest_points
(mesh)[source]¶ For each point from
mesh
find a closest point belonging to surface.Parameters: mesh – Mesh
of points to find closest points to.Returns: Mesh
of the same shape asmesh
with closest surface’s points on respective indices.

get_dip
()[source]¶ 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

get_joyner_boore_distance
(mesh)[source]¶ Compute and return JoynerBoore (also known as
Rjb
) distance to each point ofmesh
.Parameters: mesh – Mesh
of points to calculate JoynerBoore distance to.Returns: Numpy array of closest distances between the projections of surface and each point of the mesh
to the earth surface.

get_middle_point
()[source]¶ Compute coordinates of surface middle point.
The actual definition of
middle point
depends on the type of surface geometry.Returns: instance of openquake.hazardlib.geo.point.Point
representing surface middle point.

get_min_distance
(mesh)[source]¶ Compute and return the minimum distance from the surface to each point of
mesh
. This distance is sometimes calledRrup
.Parameters: mesh – Mesh
of points to calculate minimum distance to.Returns: A numpy array of distances in km.

get_rx_distance
(mesh)[source]¶ 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.
Parameters: mesh – Mesh
of points to calculate Rxdistance to.Returns: Numpy array of distances in km.

get_ry0_distance
(mesh)[source]¶ 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 endpoints of the trace.
Parameters: mesh – Mesh
of points to calculate Ry0distance to.Returns: Numpy array of distances in km.

get_strike
()[source]¶ 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


openquake.hazardlib.geo.surface.base.
_find_turning_points
(mesh, tol=1.0)[source]¶ 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)
Parameters:  mesh – Mesh for downsampling as instance of :class: openquake.hazardlib.geo.mesh.RectangularMesh
 tol (float) – Maximum difference in azimuth (decimal degrees) between successive points to identify a turning point
Returns: Column indices of turning points (as numpy array)

openquake.hazardlib.geo.surface.base.
downsample_mesh
(mesh, tol=1.0)[source]¶ 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
Planar surface¶
Module openquake.hazardlib.geo.surface.planar
contains
PlanarSurface
.

class
openquake.hazardlib.geo.surface.planar.
PlanarSurface
(mesh_spacing, strike, dip, top_left, top_right, bottom_right, bottom_left)[source]¶ Planar rectangular surface with two sides parallel to the Earth surface.
Parameters:  mesh_spacing – The desired distance between two adjacent points in the surface mesh in both horizontal and vertical directions, in km.
 strike – Strike of the surface is the azimuth from
top_left
totop_right
points.  dip – Dip is the angle between the surface itself and the earth surface.
Other parameters are points (instances of
Point
) defining the surface corners in clockwise direction starting from top left corner. Top and bottom edges of the polygon must be parallel to earth surface and to each other.See
NodalPlane
for more detailed definition ofstrike
anddip
. Note that these parameters are supposed to match the factual surface geometry (defined by corner points), but this is not enforced or even checked.Raises: ValueError – If either top or bottom points differ in depth or if top edge is not parallel to the bottom edge, if top edge differs in length from the bottom one, or if mesh spacing is not positive. 
IMPERFECT_RECTANGLE_TOLERANCE
= 0.0008¶ Maximum difference in surface’s rectangle side lengths, maximum offset of a bottom right corner from a plane that contains other corners, as well as maximum offset of a bottom left corner from a line drawn downdip perpendicular to top edge from top left corner, expressed as a fraction of the surface’s area.

_create_mesh
()[source]¶ See
openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface._create_mesh()
.

_get_top_edge_centroid
()[source]¶ Overrides
superclass' method
in order to avoid creating a mesh.

_init_plane
()[source]¶ Prepare everything needed for projecting arbitrary points on a plane containing the surface.

_project
(lons, lats, depths)[source]¶ Project points to a surface’s plane.
Parameters are lists or numpy arrays of coordinates of points to project.
Returns: A tuple of three items: distances between original points and surface’s plane in km, “x” and “y” coordinates of points’ projections to the plane (in a surface’s coordinate space).

_project_back
(dists, xx, yy)[source]¶ Convert coordinates in plane’s Cartesian space back to spherical coordinates.
Parameters are numpy arrays, as returned from
_project()
, which this method does the opposite to.Returns: Tuple of longitudes, latitudes and depths numpy arrays.

classmethod
from_corner_points
(mesh_spacing, top_left, top_right, bottom_right, bottom_left)[source]¶ Create and return a planar surface from four corner points.
The azimuth of the line connecting the top left and the top right corners define the surface strike, while the angle between the line connecting the top left and bottom left corners and a line parallel to the earth surface defines the surface dip.
Parameters:  mesh_spacing – Distance between two subsequent points in the mesh representing the planar surface, in km.
 top_left (openquake.hazardlib.geo.point.Point) – Upper left corner
 top_right (openquake.hazardlib.geo.point.Point) – Upper right corner
 bottom_right (openquake.hazardlib.geo.point.Point) – Lower right corner
 bottom_left (openquake.hazardlib.geo.point.Point) – Lower left corner
Returns: An instance of
PlanarSurface
.

get_area
()[source]¶ Return surface’s area value (in squared km) obtained as the product of surface lenght and width.

get_bounding_box
()[source]¶ Compute surface bounding box from plane’s corners coordinates. Calls
openquake.hazardlib.geo.utils.get_spherical_bounding_box()
Returns: 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.

get_closest_points
(mesh)[source]¶ See
superclass' method
.This is an optimized version specific to planar surface that doesn’t make use of the mesh.

get_joyner_boore_distance
(mesh)[source]¶ See
superclass' method
.This is an optimized version specific to planar surface that doesn’t make use of the mesh.

get_middle_point
()[source]¶ Compute middle point from surface’s corners coordinates. Calls
openquake.hazardlib.geo.utils.get_middle_point()

get_min_distance
(mesh)[source]¶ See
superclass' method
.This is an optimized version specific to planar surface that doesn’t make use of the mesh.

get_rx_distance
(mesh)[source]¶ See
superclass method
for spec of input and result values.This is an optimized version specific to planar surface that doesn’t make use of the mesh.

get_top_edge_depth
()[source]¶ Overrides
superclass' method
in order to avoid creating a mesh.

get_width
()[source]¶ Return surface’s width value (in km) as computed in the constructor (that is mean value of left and right surface sides).

translate
(p1, p2)[source]¶ Translate the surface for a specific distance along a specific azimuth direction.
Parameters are two points (instances of
openquake.hazardlib.geo.point.Point
) representing the direction and an azimuth for translation. The resulting surface corner points will be that far along that azimuth from respective corner points of this surface asp2
is located with respect top1
.Returns: A new PlanarSurface
object with the same mesh spacing, dip, strike, width, length and depth but with corners longitudes and latitudes translated.
Simple fault surface¶
Module openquake.hazardlib.geo.surface.simple_fault
defines
SimpleFaultSurface
.

class
openquake.hazardlib.geo.surface.simple_fault.
SimpleFaultSurface
(mesh)[source]¶ Represent a fault surface as regular (uniformly spaced) 3D mesh of points.
Parameters: mesh – Instance of RectangularMesh
representing surface geometry.Another way to construct the surface object is to call
from_fault_data()
.
classmethod
check_fault_data
(fault_trace, upper_seismogenic_depth, lower_seismogenic_depth, dip, mesh_spacing)[source]¶ Verify the fault data and raise
ValueError
if anything is wrong.This method doesn’t have to be called by hands before creating the surface object, because it is called from
from_fault_data()
.

classmethod
from_fault_data
(fault_trace, upper_seismogenic_depth, lower_seismogenic_depth, dip, mesh_spacing)[source]¶ Create and return a fault surface using fault source data.
Parameters:  fault_trace (openquake.hazardlib.geo.line.Line) – Geographical line representing the intersection between the fault surface and the earth surface.
 upper_seismo_depth – Minimum depth ruptures can reach, in km (i.e. depth to fault’s top edge).
 lower_seismo_depth – Maximum depth ruptures can reach, in km (i.e. depth to fault’s bottom edge).
 dip – Dip angle (i.e. angle between fault surface and earth surface), in degrees.
 mesh_spacing – Distance between two subsequent points in a mesh, in km.
Returns: An instance of
SimpleFaultSurface
created using that data.Uses
check_fault_data()
for checking parameters.

get_dip
()[source]¶ Return the fault dip as the average dip over the fault surface mesh.
The average dip is defined as the weighted mean inclination of top row of mesh cells. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_inclination_and_azimuth()
Returns: The average dip, in decimal degrees.

classmethod
get_fault_patch_vertices
(rupture_top_edge, upper_seismogenic_depth, lower_seismogenic_depth, dip, index_patch=1)[source]¶ Get surface main vertices. Parameters are the same as for
from_fault_data()
, excluding fault_trace, and mesh spacing.Parameters:  rupture_top_edge – A instances of
openquake.hazardlib.geo.line.Line
representing the rupture surface’s top edge.  index_patch – Indicate the patch of the fault in order to output the vertices. The fault patch numbering follows the same logic of the righthand rule i.e. patch with index 1 is the first patch along the trace.
Returns: Four :class:~openquake.hazardlib.geo.point.Point objects representing the four vertices of the target patch.
 rupture_top_edge – A instances of

get_strike
()[source]¶ Return the fault strike as the average strike along the fault trace.
The average strike is defined as the weighted mean azimuth of top row of mesh cells. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_inclination_and_azimuth()
Returns: The average strike, in decimal degrees.

classmethod
get_surface_vertexes
(fault_trace, upper_seismogenic_depth, lower_seismogenic_depth, dip)[source]¶ Get surface main vertexes.
Parameters are the same as for
from_fault_data()
, excluding mesh spacing.Returns: Instance of Polygon
describing the surface projection of the simple fault with specified parameters.

get_width
()[source]¶ Return surface’s width (that is surface extension along the dip direction) in km.
The width is computed as the average width along the surface. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_width()

classmethod
hypocentre_patch_index
(hypocentre, rupture_top_edge, upper_seismogenic_depth, lower_seismogenic_depth, dip)[source]¶ This methods finds the index of the fault patch including the hypocentre.
Parameters:  hypocentre –
Point
object representing the location of hypocentre.  rupture_top_edge – A instances of
openquake.hazardlib.geo.line.Line
representing the rupture surface’s top edge.  upper_seismo_depth – Minimum depth ruptures can reach, in km (i.e. depth to fault’s top edge).
 lower_seismo_depth – Maximum depth ruptures can reach, in km (i.e. depth to fault’s bottom edge).
 dip – Dip angle (i.e. angle between fault surface and earth surface), in degrees.
Returns: An integer corresponding to the index of the fault patch which contains the hypocentre.
 hypocentre –

classmethod
surface_projection_from_fault_data
(fault_trace, upper_seismogenic_depth, lower_seismogenic_depth, dip)[source]¶ Get a surface projection of the simple fault surface.
Parameters are the same as for
from_fault_data()
, excluding mesh spacing.Returns: Instance of Polygon
describing the surface projection of the simple fault with specified parameters.

classmethod
Complex fault surface¶
Module openquake.hazardlib.geo.surface.complex_fault
defines
ComplexFaultSurface
.

class
openquake.hazardlib.geo.surface.complex_fault.
ComplexFaultSurface
(mesh)[source]¶ Represent a complex fault surface as 3D mesh of points (not necessarily uniformly spaced across the surface area).
Parameters: mesh – Instance of RectangularMesh
representing surface geometry.Another way to construct the surface object is to call
from_fault_data()
.
classmethod
check_aki_richards_convention
(edges)[source]¶ Verify that surface (as defined by corner points) conforms with Aki and Richard convention (i.e. surface dips right of surface strike)
This method doesn’t have to be called by hands before creating the surface object, because it is called from
from_fault_data()
.

classmethod
check_fault_data
(edges, mesh_spacing)[source]¶ Verify the fault data and raise
ValueError
if anything is wrong.This method doesn’t have to be called by hands before creating the surface object, because it is called from
from_fault_data()
.

classmethod
check_surface_validity
(edges)[source]¶ Check validity of the surface.
Project edge points to vertical plane anchored to surface upper left edge and with strike equal to top edge strike. Check that resulting polygon is valid.
This method doesn’t have to be called by hands before creating the surface object, because it is called from
from_fault_data()
.

classmethod
from_fault_data
(edges, mesh_spacing)[source]¶ Create and return a fault surface using fault source data.
Parameters:  edges – A list of at least two horizontal edges of the surface
as instances of
openquake.hazardlib.geo.line.Line
. The list should be in toptobottom order (the shallowest edge first).  mesh_spacing – Distance between two subsequent points in a mesh, in km.
Returns: An instance of
ComplexFaultSurface
created using that data.Raises: ValueError – If requested mesh spacing is too big for the surface geometry (doesn’t allow to put a single mesh cell along length and/or width).
Uses
check_fault_data()
for checking parameters. edges – A list of at least two horizontal edges of the surface
as instances of

get_dip
()[source]¶ Return the fault dip as the average dip over the mesh.
The average dip is defined as the weighted mean inclination of all the mesh cells. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_inclination_and_azimuth()
Returns: The average dip, in decimal degrees.

get_strike
()[source]¶ Return the fault strike as the average strike over the mesh.
The average strike is defined as the weighted mean azimuth of all the mesh cells. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_inclination_and_azimuth()
Returns: The average strike, in decimal degrees.

get_width
()[source]¶ Return surface’s width (that is surface extension along the dip direction) in km.
The width is computed as the average width along the surface. See
openquake.hazardlib.geo.mesh.RectangularMesh.get_mean_width()

classmethod
surface_projection_from_fault_data
(edges)[source]¶ Get a surface projection of the complex fault surface.
Parameters: edges – A list of horizontal edges of the surface as instances of openquake.hazardlib.geo.line.Line
.Returns: Instance of Polygon
describing the surface projection of the complex fault.

classmethod
Multi surface¶
Module openquake.hazardlib.geo.surface.multi
defines
MultiSurface
.

class
openquake.hazardlib.geo.surface.multi.
MultiSurface
(surfaces, tol=0.1)[source]¶ Represent a surface as a collection of independent surface elements.
Parameters:  surfaces – List of instances of subclasses of
BaseSurface
each representing a surface geometry element.  edge_set – Retains list of upper edges from all of the surfaces, with each edge given as a numpy array of [longitude, latitude, depth]
 cartesian_edges – For GC2, this holds the list of edge sets in an orthographic projection such that the coordinates are all cartesian.
 cartesian_endpoints – For GC2, this hold the list of endpoints of the edges in an orthographic projection
 proj – For GC2, instance of :class: ~openquake.hazardlib.geo.utils.OrthographicProjection instantiated with the bounding box limits of the fault
 length_set – List of lengths of upper edges of each surface
 cum_length_set – List of cumulative lengths of edges along fault
 gc2_config – For GC2, dictionary holding fault specific parameters for GC2 configuration
 p0 – For GC2, reference origin point of the fault
 gc2t – GC2 Tcoordinate
 gc2u – GC2 Ucoordinate
 tmp_mesh – If fed with the same mesh twice (e.g. calling get_rx_distance and then get_ry0_distance in sequence) does not repeat GC2 calculations, this hold the last mesh it was fed with
 gc_length – For GC2, determines the length of the fault (km) in its own GC2 configuration

_get_cartesian_edge_set
()[source]¶ For the GC2 calculations a set of cartesian representations of the fault edges are needed. In this present case we use a common cartesian framework for all edges, as opposed to defining a separate orthographic projection per edge

_get_edge_set
(tol=0.1)[source]¶ Retrieve set of top edges from all of the individual surfaces, downsampling the upper edge based on the specified tolerance

_get_gc2_coordinates_for_rupture
(edge_sets)[source]¶ Calculates the GC2 coordinates for the nodes of the upper edge of the fault

_get_ut_i
(seg, sx, sy)[source]¶ Returns the U and T coordinate for a specific trace segment
Parameters:  seg – End points of the segment edge
 sx – Sites longitudes rendered into coordinate system
 sy – Sites latitudes rendered into coordinate system

_setup_gc2_framework
()[source]¶ This method establishes the GC2 framework for a multisegment (and indeed multitypology) case based on the description in Spudich & Chiou (2015)  see section on Generalized Coordinate System for Multiple Rupture Traces

get_bounding_box
()[source]¶ Compute bounding box for each surface element, and then return the bounding box of all surface elements’ bounding boxes.
Returns: 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.

get_closest_points
(mesh)[source]¶ For each point in
mesh
find the closest surface element, and return the corresponding closest point.See
superclass method
for spec of input and result values.

get_dip
()[source]¶ Compute dip of each surface element and return areaweighted average value (in range
(0, 90]
).Given that dip values are constrained in the range (0, 90], the simple formula for weighted mean is used.

get_generalised_coordinates
(lons, lats)[source]¶ Transforms the site positions into the generalised coordinate form described by Spudich and Chiou (2015) for the multirupture and/or discordant case
Spudich, Paul and Chiou, Brian (2015) Strikeparallel and strikenormal coordinate system around geometrically complicated rupture traces — Use by NGAWest2 and further improvements: U.S. Geological Survey OpenFile Report 20151028

get_joyner_boore_distance
(mesh)[source]¶ For each point in mesh compute the JoynerBoore distance to all the surface elements and return the smallest value.
See
superclass method
for spec of input and result values.

get_middle_point
()[source]¶ If
MultiSurface
is defined by a single surface, simply returns surface’s middle point, otherwise find surface element closest to the surface’s bounding box centroid and return corresponding middle point.Note that the concept of middle point for a multi surface is ambiguous and alternative definitions may be possible. However, this method is mostly used to define the hypocenter location for ruptures described by a multi surface (see
openquake.hazardlib.source.characteristic.CharacteristicFaultSource.iter_ruptures()
). This is needed because when creating fault based sources, the rupture’s hypocenter locations are not explicitly defined, and therefore an automated way to define them is required.

get_min_distance
(mesh)[source]¶ For each point in
mesh
compute the minimum distance to each surface element and return the smallest value.See
superclass method
for spec of input and result values.

get_rx_distance
(mesh)[source]¶ For each point determine the corresponding rx distance using the GC2 configuration.
See
superclass method
for spec of input and result values.

get_ry0_distance
(mesh)[source]¶ For each point determine the corresponding Ry0 distance using the GC2 configuration.
See
superclass method
for spec of input and result values.

get_strike
()[source]¶ Compute strike of each surface element and return areaweighted average value (in range
[0, 360]
) using formula from: http://en.wikipedia.org/wiki/Mean_of_circular_quantitiesNote that the original formula has been adapted to compute a weighted rather than arithmetic mean.
 surfaces – List of instances of subclasses of