def __computeD(self, i):
"""Compute d for the i-th quad/segment.
Y = d/W, where d is the portion (in km) of the width of the fault which
ruptures up-dip from the hypocenter to the top of the fault.
Args:
i (int): index of segment for which d is to be computed.
"""
hyp_ecef = self.phyp[i] # already in ECEF
hyp_col = np.array([[hyp_ecef.x], [hyp_ecef.y], [hyp_ecef.z]])
# First compute "updip" vector
P0, P1, P2 = self._rup.getQuadrilaterals()[i][0:3]
p1 = Vector.fromPoint(P1) # convert to ECEF
p2 = Vector.fromPoint(P2)
e21 = p1 - p2
e21norm = e21.norm()
hp1 = p1 - hyp_ecef
# convert to km (used as max later)
udip_len = Vector.dot(hp1, e21norm) / 1000.0
udip_col = np.array([[e21norm.x], [e21norm.y],
[e21norm.z]]) # ECEF coords
# Sites
slat = self._lat
slon = self._lon
# Convert sites to ECEF:
site_ecef_x = np.ones_like(slat)
site_ecef_y = np.ones_like(slat)
site_ecef_z = np.ones_like(slat)
# Make a 3x(#number of sites) matrix of site locations
# (rows are x, y, z) in ECEF
site_ecef_x, site_ecef_y, site_ecef_z = ecef.latlon2ecef(
slat, slon, np.zeros(slon.shape))
site_mat = np.array([
np.reshape(site_ecef_x, (-1, )),
np.reshape(site_ecef_y, (-1, )),
np.reshape(site_ecef_z, (-1, ))
])
# Hypocenter-to-site matrix
h2s_mat = site_mat - hyp_col # in ECEF
# Dot hypocenter-to-site with updip vector
d_raw = np.abs(np.sum(h2s_mat * udip_col, axis=0)) / \
1000.0 # convert to km
d_raw = np.reshape(d_raw, self._lat.shape)
self.d = d_raw.clip(min=1.0, max=udip_len)
def __computeD(self, i):
"""Compute d for the i-th quad/segment.
Y = d/W, where d is the portion (in km) of the width of the fault which
ruptures up-dip from the hypocenter to the top of the fault.
Args:
i (int): index of segment for which d is to be computed.
"""
hyp_ecef = self.phyp[i] # already in ECEF
hyp_col = np.array([[hyp_ecef.x], [hyp_ecef.y], [hyp_ecef.z]])
# First compute "updip" vector
P0, P1, P2 = self._rup.getQuadrilaterals()[i][0:3]
p1 = Vector.fromPoint(P1) # convert to ECEF
p2 = Vector.fromPoint(P2)
e21 = p1 - p2
e21norm = e21.norm()
hp1 = p1 - hyp_ecef
# convert to km (used as max later)
udip_len = Vector.dot(hp1, e21norm) / 1000.0
udip_col = np.array(
[[e21norm.x], [e21norm.y], [e21norm.z]]) # ECEF coords
# Sites
slat = self._lat
slon = self._lon
# Convert sites to ECEF:
site_ecef_x = np.ones_like(slat)
site_ecef_y = np.ones_like(slat)
site_ecef_z = np.ones_like(slat)
# Make a 3x(#number of sites) matrix of site locations
# (rows are x, y, z) in ECEF
site_ecef_x, site_ecef_y, site_ecef_z = ecef.latlon2ecef(
slat, slon, np.zeros(slon.shape))
site_mat = np.array([np.reshape(site_ecef_x, (-1,)),
np.reshape(site_ecef_y, (-1,)),
np.reshape(site_ecef_z, (-1,))])
# Hypocenter-to-site matrix
h2s_mat = site_mat - hyp_col # in ECEF
# Dot hypocenter-to-site with updip vector
d_raw = np.abs(np.sum(h2s_mat * udip_col, axis=0)) / \
1000.0 # convert to km
d_raw = np.reshape(d_raw, self._lat.shape)
self.d = d_raw.clip(min=1.0, max=udip_len)
def getDip(self):
"""
Return average dip of all quadrilaterals in the rupture.
Returns:
float: Average dip in degrees.
"""
dipsum = 0.0
for quad in self._quadrilaterals:
N = utils.get_quad_normal(quad)
V = utils.get_vertical_vector(quad)
dipsum = dipsum + np.degrees(np.arccos(Vector.dot(N, V)))
dip = dipsum / len(self._quadrilaterals)
return dip
def get_quad_dip(q):
"""
Dip of a quadrilateral.
Args:
q (list): A quadrilateral; list of four points.
Returns:
float: Dip in degrees.
"""
N = get_quad_normal(q)
V = get_vertical_vector(q)
dip = np.degrees(np.arccos(Vector.dot(N, V)))
return dip
def get_quad_dip(q):
"""
Dip of a quadrilateral.
Args:
q (list): A quadrilateral; list of four points.
Returns:
float: Dip in degrees.
"""
N = get_quad_normal(q)
V = get_vertical_vector(q)
dip = np.degrees(np.arccos(Vector.dot(N, V)))
return dip
def __computeWrup(self):
"""
Compute the the portion (in km) of the width of the rupture which
ruptures up-dip from the hypocenter to the top of the rupture.
Wrup is the portion (in km) of the width of the rupture which
ruptures up-dip from the hypocenter to the top of the rupture.
* This is ambiguous for ruptures with varible top of rupture (not
allowed in NGA). For now, lets just compute this for the
quad where the hypocenter is located.
* Alternative is to compute max Wrup for the different quads.
"""
nquad = len(self._rup.getQuadrilaterals())
# ---------------------------------------------------------------------
# First find which quad the hypocenter is on
# ---------------------------------------------------------------------
x, y, z = latlon2ecef(self._hyp.latitude, self._hyp.longitude,
self._hyp.depth)
hyp_ecef = np.array([[x, y, z]])
qdist = np.zeros(nquad)
for i in range(0, nquad):
qdist[i] = utils._quad_distance(self._rup.getQuadrilaterals()[i],
hyp_ecef)
ind = int(np.where(qdist == np.min(qdist))[0][0])
# *** check that this doesn't break with more than one quad
q = self._rup.getQuadrilaterals()[ind]
# ---------------------------------------------------------------------
# Compute Wrup on that quad
# ---------------------------------------------------------------------
pp0 = Vector.fromPoint(
geo.point.Point(q[0].longitude, q[0].latitude, q[0].depth))
hyp_ecef = Vector.fromPoint(
geo.point.Point(self._hyp.longitude, self._hyp.latitude,
self._hyp.depth))
hp0 = hyp_ecef - pp0
ddv = utils.get_quad_down_dip_vector(q)
self._Wrup = Vector.dot(ddv, hp0) / 1000
def __computeWrup(self):
"""
Compute the the portion (in km) of the width of the rupture which
ruptures up-dip from the hypocenter to the top of the rupture.
Wrup is the portion (in km) of the width of the rupture which
ruptures up-dip from the hypocenter to the top of the rupture.
* This is ambiguous for ruptures with varible top of rupture (not
allowed in NGA). For now, lets just compute this for the
quad where the hypocenter is located.
* Alternative is to compute max Wrup for the different quads.
"""
nquad = len(self._rup.getQuadrilaterals())
# ---------------------------------------------------------------------
# First find which quad the hypocenter is on
# ---------------------------------------------------------------------
x, y, z = latlon2ecef(
self._hyp.latitude, self._hyp.longitude, self._hyp.depth)
hyp_ecef = np.array([[x, y, z]])
qdist = np.zeros(nquad)
for i in range(0, nquad):
qdist[i] = utils._quad_distance(
self._rup.getQuadrilaterals()[i], hyp_ecef)
ind = int(np.where(qdist == np.min(qdist))[0][0])
# *** check that this doesn't break with more than one quad
q = self._rup.getQuadrilaterals()[ind]
# ---------------------------------------------------------------------
# Compute Wrup on that quad
# ---------------------------------------------------------------------
pp0 = Vector.fromPoint(geo.point.Point(
q[0].longitude, q[0].latitude, q[0].depth))
hyp_ecef = Vector.fromPoint(geo.point.Point(
self._hyp.longitude, self._hyp.latitude, self._hyp.depth))
hp0 = hyp_ecef - pp0
ddv = utils.get_quad_down_dip_vector(q)
self._Wrup = Vector.dot(ddv, hp0) / 1000
def _computeStrikeDip(self):
"""
Loop over all triangles and get the average normal, north, and up
vectors in ECEF. Use these to compute a representative strike and dip.
"""
seg = self._group_index
groups = np.unique(seg)
ng = len(groups)
norm_vec = Vector(0, 0, 0)
north_vec = Vector(0, 0, 0)
up_vec = Vector(0, 0, 0)
for i in range(ng):
group_segments = np.where(groups[i] == seg)[0]
nseg = len(group_segments) - 1
for j in range(nseg):
ind = group_segments[j]
P0 = Point(self._toplons[ind], self._toplats[ind],
self._topdeps[ind])
P1 = Point(self._toplons[ind + 1], self._toplats[ind + 1],
self._topdeps[ind + 1])
P2 = Point(self._botlons[ind + 1], self._botlats[ind + 1],
self._botdeps[ind + 1])
P3 = Point(self._botlons[ind], self._botlats[ind],
self._botdeps[ind])
P1up = Point(self._toplons[ind + 1], self._toplats[ind + 1],
self._topdeps[ind + 1] - 1.0)
P1N = Point(self._toplons[ind + 1],
self._toplats[ind + 1] + 0.001,
self._topdeps[ind + 1])
P3up = Point(self._botlons[ind], self._botlats[ind],
self._botdeps[ind] - 1.0)
P3N = Point(self._botlons[ind], self._botlats[ind] + 0.001,
self._botdeps[ind])
p0 = Vector.fromPoint(P0)
p1 = Vector.fromPoint(P1)
p2 = Vector.fromPoint(P2)
p3 = Vector.fromPoint(P3)
p1up = Vector.fromPoint(P1up)
p1N = Vector.fromPoint(P1N)
p3up = Vector.fromPoint(P3up)
p3N = Vector.fromPoint(P3N)
# Sides
s01 = p1 - p0
s02 = p2 - p0
s03 = p3 - p0
s21 = p1 - p2
s23 = p3 - p2
# First triangle
t1norm = (s02.cross(s01)).norm()
a = s01.mag()
b = s02.mag()
c = s21.mag()
s = (a + b + c) / 2
A1 = np.sqrt(s * (s - a) * (s - b) * (s - c)) / 1000
# Second triangle
t2norm = (s03.cross(s02)).norm()
a = s03.mag()
b = s23.mag()
c = s02.mag()
s = (a + b + c) / 2
A2 = np.sqrt(s * (s - a) * (s - b) * (s - c)) / 1000
# Up and North
p1up = (p1up - p1).norm()
p3up = (p3up - p3).norm()
p1N = (p1N - p1).norm()
p3N = (p3N - p3).norm()
# Combine
norm_vec = norm_vec + A1 * t1norm + A2 * t2norm
north_vec = north_vec + A1 * p1N + A2 * p3N
up_vec = up_vec + A1 * p1up + A2 * p3up
norm_vec = norm_vec.norm()
north_vec = north_vec.norm()
up_vec = up_vec.norm()
# Do I need to flip the vector because it is pointing down (i.e.,
# right-hand rule is violated)?
flip = np.sign(up_vec.dot(norm_vec))
norm_vec = flip * norm_vec
# Angle between up_vec and norm_vec is dip
self._dip = np.arcsin(up_vec.cross(norm_vec).mag()) * 180 / np.pi
# Normal vector projected to horizontal plane
nvph = (norm_vec - up_vec.dot(norm_vec) * up_vec).norm()
# Dip direction is angle between nvph and north; strike is orthogonal.
cp = nvph.cross(north_vec)
sign = np.sign(cp.dot(up_vec))
dp = nvph.dot(north_vec)
strike = np.arctan2(sign * cp.mag(), dp) * 180 / np.pi - 90
if strike < -180:
strike = strike + 360
self._strike = strike
def _computeStikeDip(self):
"""
Loop over all triangles and get the average normal, north, and up
vectors in ECEF. Use these to compute a representative strike and dip.
"""
seg = self._group_index
groups = np.unique(seg)
ng = len(groups)
norm_vec = Vector(0, 0, 0)
north_vec = Vector(0, 0, 0)
up_vec = Vector(0, 0, 0)
for i in range(ng):
group_segments = np.where(groups[i] == seg)[0]
nseg = len(group_segments) - 1
for j in range(nseg):
ind = group_segments[j]
P0 = Point(self._toplons[ind],
self._toplats[ind],
self._topdeps[ind])
P1 = Point(self._toplons[ind + 1],
self._toplats[ind + 1],
self._topdeps[ind + 1])
P2 = Point(self._botlons[ind + 1],
self._botlats[ind + 1],
self._botdeps[ind + 1])
P3 = Point(self._botlons[ind],
self._botlats[ind],
self._botdeps[ind])
P1up = Point(self._toplons[ind + 1],
self._toplats[ind + 1],
self._topdeps[ind + 1] - 1.0)
P1N = Point(self._toplons[ind + 1],
self._toplats[ind + 1] + 0.001,
self._topdeps[ind + 1])
P3up = Point(self._botlons[ind],
self._botlats[ind],
self._botdeps[ind] - 1.0)
P3N = Point(self._botlons[ind],
self._botlats[ind] + 0.001,
self._botdeps[ind])
p0 = Vector.fromPoint(P0)
p1 = Vector.fromPoint(P1)
p2 = Vector.fromPoint(P2)
p3 = Vector.fromPoint(P3)
p1up = Vector.fromPoint(P1up)
p1N = Vector.fromPoint(P1N)
p3up = Vector.fromPoint(P3up)
p3N = Vector.fromPoint(P3N)
# Sides
s01 = p1 - p0
s02 = p2 - p0
s03 = p3 - p0
s21 = p1 - p2
s23 = p3 - p2
# First triangle
t1norm = (s02.cross(s01)).norm()
a = s01.mag()
b = s02.mag()
c = s21.mag()
s = (a + b + c) / 2
A1 = np.sqrt(s * (s - a) * (s - b) * (s - c)) / 1000
# Second triangle
t2norm = (s03.cross(s02)).norm()
a = s03.mag()
b = s23.mag()
c = s02.mag()
s = (a + b + c) / 2
A2 = np.sqrt(s * (s - a) * (s - b) * (s - c)) / 1000
# Up and North
p1up = (p1up - p1).norm()
p3up = (p3up - p3).norm()
p1N = (p1N - p1).norm()
p3N = (p3N - p3).norm()
# Combine
norm_vec = norm_vec + A1 * t1norm + A2 * t2norm
north_vec = north_vec + A1 * p1N + A2 * p3N
up_vec = up_vec + A1 * p1up + A2 * p3up
norm_vec = norm_vec.norm()
north_vec = north_vec.norm()
up_vec = up_vec.norm()
# Do I need to flip the vector because it is pointing down (i.e.,
# right-hand rule is violated)?
flip = np.sign(up_vec.dot(norm_vec))
norm_vec = flip * norm_vec
# Angle between up_vec and norm_vec is dip
self._dip = np.arcsin(up_vec.cross(norm_vec).mag()) * 180 / np.pi
# Normal vector projected to horizontal plane
nvph = (norm_vec - up_vec.dot(norm_vec) * up_vec).norm()
# Dip direction is angle between nvph and north; strike is orthogonal.
cp = nvph.cross(north_vec)
sign = np.sign(cp.dot(up_vec))
dp = nvph.dot(north_vec)
strike = np.arctan2(sign * cp.mag(), dp) * 180 / np.pi - 90
if strike < -180:
strike = strike + 360
self._strike = strike
def __computeThetaAndS(self, i):
"""
Args:
i (int): Compute d for the i-th quad/segment.
"""
# self.phyp is in ECEF
tmp = ecef.ecef2latlon(self.phyp[i].x, self.phyp[i].y, self.phyp[i].z)
epi_ecef = Vector.fromPoint(geo.point.Point(tmp[1], tmp[0], 0.0))
epi_col = np.array([[epi_ecef.x], [epi_ecef.y], [epi_ecef.z]])
# First compute along strike vector
P0, P1, P2, P3 = self._rup.getQuadrilaterals()[i]
p0 = Vector.fromPoint(P0) # convert to ECEF
p1 = Vector.fromPoint(P1)
e01 = p1 - p0
e01norm = e01.norm()
hp0 = p0 - epi_ecef
hp1 = p1 - epi_ecef
strike_min = Vector.dot(hp0, e01norm) / 1000.0 # convert to km
strike_max = Vector.dot(hp1, e01norm) / 1000.0 # convert to km
strike_col = np.array(
[[e01norm.x], [e01norm.y], [e01norm.z]]) # ECEF coords
# Sites
slat = self._lat
slon = self._lon
# Convert sites to ECEF:
site_ecef_x = np.ones_like(slat)
site_ecef_y = np.ones_like(slat)
site_ecef_z = np.ones_like(slat)
# Make a 3x(#number of sites) matrix of site locations
# (rows are x, y, z) in ECEF
site_ecef_x, site_ecef_y, site_ecef_z = ecef.latlon2ecef(
slat, slon, np.zeros(slon.shape))
site_mat = np.array([np.reshape(site_ecef_x, (-1,)),
np.reshape(site_ecef_y, (-1,)),
np.reshape(site_ecef_z, (-1,))])
# Epicenter-to-site matrix
e2s_mat = site_mat - epi_col # in ECEF
mag = np.sqrt(np.sum(e2s_mat * e2s_mat, axis=0))
# Avoid division by zero
mag[mag == 0] = 1e-12
e2s_norm = e2s_mat / mag
# Dot epicenter-to-site with along-strike vector
s_raw = np.sum(e2s_mat * strike_col, axis=0) / 1000.0 # conver to km
# Put back into a 2d array
s_raw = np.reshape(s_raw, self._lat.shape)
self.s = np.abs(s_raw.clip(min=strike_min,
max=strike_max)).clip(min=np.exp(1))
# Compute theta
sdots = np.sum(e2s_norm * strike_col, axis=0)
theta_raw = np.arccos(sdots)
# But theta is defined to be the reference angle
# (i.e., the equivalent angle between 0 and 90 deg)
sintheta = np.abs(np.sin(theta_raw))
costheta = np.abs(np.cos(theta_raw))
theta = np.arctan2(sintheta, costheta)
self.theta = np.reshape(theta, self._lat.shape)
def __setPseudoHypocenters(self):
""" Set a pseudo-hypocenter.
Adapted from ShakeMap 3.5 src/contour/directivity.c
From Bayless and Somerville:
"Define the pseudo-hypocenter for rupture of successive segments as
the point on the side edge of the rupture segment that is closest to
the side edge of the previous segment, and that lies half way
between the top and bottom of the rupture. We assume that the rupture
is segmented along strike, not updip. All geometric parameters are
computed relative to the pseudo-hypocenter."
"""
hyp_ecef = Vector.fromPoint(geo.point.Point(
self._hyp.longitude, self._hyp.latitude, self._hyp.depth))
# Loop over each quad
self.phyp = [None] * self._nq
for i in range(self._nq):
P0, P1, P2, P3 = self._rup.getQuadrilaterals()[i]
p0 = Vector.fromPoint(P0) # convert to ECEF
p1 = Vector.fromPoint(P1)
p2 = Vector.fromPoint(P2)
p3 = Vector.fromPoint(P3)
# Create 4 planes with normals pointing outside rectangle
hpnp = Vector.cross(p1 - p0, p2 - p0).norm()
hpp = -hpnp.x * p0.x - hpnp.y * p0.y - hpnp.z * p0.z
n0 = Vector.cross(p1 - p0, hpnp)
n1 = Vector.cross(p2 - p1, hpnp)
n2 = Vector.cross(p3 - p2, hpnp)
n3 = Vector.cross(p0 - p3, hpnp)
# -----------------------------------------------------------------
# Is the hypocenter inside the projected rectangle?
# Dot products show which side the origin is on.
# If origin is on same side of all the planes, then it is 'inside'
# -----------------------------------------------------------------
sgn0 = np.signbit(Vector.dot(n0, p0 - hyp_ecef))
sgn1 = np.signbit(Vector.dot(n1, p1 - hyp_ecef))
sgn2 = np.signbit(Vector.dot(n2, p2 - hyp_ecef))
sgn3 = np.signbit(Vector.dot(n3, p3 - hyp_ecef))
if (sgn0 == sgn1) and (sgn1 == sgn2) and (sgn2 == sgn3):
# Origin is inside. Use distance-to-plane formula.
d = Vector.dot(hpnp, hyp_ecef) + hpp
d = d * d
# Put the pseudo hypocenter on the plane
D = Vector.dot(hpnp, hyp_ecef) + hpp
self.phyp[i] = hyp_ecef - hpnp * D
else:
# Origin is outside. Find distance to edges
p0p = np.reshape(p0.getArray() - hyp_ecef.getArray(), [1, 3])
p1p = np.reshape(p1.getArray() - hyp_ecef.getArray(), [1, 3])
p2p = np.reshape(p2.getArray() - hyp_ecef.getArray(), [1, 3])
p3p = np.reshape(p3.getArray() - hyp_ecef.getArray(), [1, 3])
s1 = _distance_sq_to_segment(p1p, p2p)
s3 = _distance_sq_to_segment(p3p, p0p)
# Assuming that the rupture is segmented along strike and not
# updip (as described by Bayless and somerville), we only
# need to consider s1 and s3:
if s1 > s3:
e30 = p0 - p3
e30norm = e30.norm()
mag = e30.mag()
self.phyp[i] = p3 + e30norm * (0.5 * mag)
else:
e21 = p1 - p2
e21norm = e21.norm()
mag = e21.mag()
self.phyp[i] = p2 + e21norm * (0.5 * mag)
def __computeThetaAndS(self, i):
"""
Args:
i (int): Compute d for the i-th quad/segment.
"""
# self.phyp is in ECEF
tmp = ecef.ecef2latlon(self.phyp[i].x, self.phyp[i].y, self.phyp[i].z)
epi_ecef = Vector.fromPoint(geo.point.Point(tmp[1], tmp[0], 0.0))
epi_col = np.array([[epi_ecef.x], [epi_ecef.y], [epi_ecef.z]])
# First compute along strike vector
P0, P1, P2, P3 = self._rup.getQuadrilaterals()[i]
p0 = Vector.fromPoint(P0) # convert to ECEF
p1 = Vector.fromPoint(P1)
e01 = p1 - p0
e01norm = e01.norm()
hp0 = p0 - epi_ecef
hp1 = p1 - epi_ecef
strike_min = Vector.dot(hp0, e01norm) / 1000.0 # convert to km
strike_max = Vector.dot(hp1, e01norm) / 1000.0 # convert to km
strike_col = np.array([[e01norm.x], [e01norm.y],
[e01norm.z]]) # ECEF coords
# Sites
slat = self._lat
slon = self._lon
# Convert sites to ECEF:
site_ecef_x = np.ones_like(slat)
site_ecef_y = np.ones_like(slat)
site_ecef_z = np.ones_like(slat)
# Make a 3x(#number of sites) matrix of site locations
# (rows are x, y, z) in ECEF
site_ecef_x, site_ecef_y, site_ecef_z = ecef.latlon2ecef(
slat, slon, np.zeros(slon.shape))
site_mat = np.array([
np.reshape(site_ecef_x, (-1, )),
np.reshape(site_ecef_y, (-1, )),
np.reshape(site_ecef_z, (-1, ))
])
# Epicenter-to-site matrix
e2s_mat = site_mat - epi_col # in ECEF
mag = np.sqrt(np.sum(e2s_mat * e2s_mat, axis=0))
# Avoid division by zero
mag[mag == 0] = 1e-12
e2s_norm = e2s_mat / mag
# Dot epicenter-to-site with along-strike vector
s_raw = np.sum(e2s_mat * strike_col, axis=0) / 1000.0 # conver to km
# Put back into a 2d array
s_raw = np.reshape(s_raw, self._lat.shape)
self.s = np.abs(s_raw.clip(min=strike_min,
max=strike_max)).clip(min=np.exp(1))
# Compute theta
sdots = np.sum(e2s_norm * strike_col, axis=0)
theta_raw = np.arccos(sdots)
# But theta is defined to be the reference angle
# (i.e., the equivalent angle between 0 and 90 deg)
sintheta = np.abs(np.sin(theta_raw))
costheta = np.abs(np.cos(theta_raw))
theta = np.arctan2(sintheta, costheta)
self.theta = np.reshape(theta, self._lat.shape)
def __setPseudoHypocenters(self):
""" Set a pseudo-hypocenter.
Adapted from ShakeMap 3.5 src/contour/directivity.c
From Bayless and Somerville:
"Define the pseudo-hypocenter for rupture of successive segments as
the point on the side edge of the rupture segment that is closest to
the side edge of the previous segment, and that lies half way
between the top and bottom of the rupture. We assume that the rupture
is segmented along strike, not updip. All geometric parameters are
computed relative to the pseudo-hypocenter."
"""
hyp_ecef = Vector.fromPoint(
geo.point.Point(self._hyp.longitude, self._hyp.latitude,
self._hyp.depth))
# Loop over each quad
self.phyp = [None] * self._nq
for i in range(self._nq):
P0, P1, P2, P3 = self._rup.getQuadrilaterals()[i]
p0 = Vector.fromPoint(P0) # convert to ECEF
p1 = Vector.fromPoint(P1)
p2 = Vector.fromPoint(P2)
p3 = Vector.fromPoint(P3)
# Create 4 planes with normals pointing outside rectangle
hpnp = Vector.cross(p1 - p0, p2 - p0).norm()
hpp = -hpnp.x * p0.x - hpnp.y * p0.y - hpnp.z * p0.z
n0 = Vector.cross(p1 - p0, hpnp)
n1 = Vector.cross(p2 - p1, hpnp)
n2 = Vector.cross(p3 - p2, hpnp)
n3 = Vector.cross(p0 - p3, hpnp)
# -----------------------------------------------------------------
# Is the hypocenter inside the projected rectangle?
# Dot products show which side the origin is on.
# If origin is on same side of all the planes, then it is 'inside'
# -----------------------------------------------------------------
sgn0 = np.signbit(Vector.dot(n0, p0 - hyp_ecef))
sgn1 = np.signbit(Vector.dot(n1, p1 - hyp_ecef))
sgn2 = np.signbit(Vector.dot(n2, p2 - hyp_ecef))
sgn3 = np.signbit(Vector.dot(n3, p3 - hyp_ecef))
if (sgn0 == sgn1) and (sgn1 == sgn2) and (sgn2 == sgn3):
# Origin is inside. Use distance-to-plane formula.
d = Vector.dot(hpnp, hyp_ecef) + hpp
d = d * d
# Put the pseudo hypocenter on the plane
D = Vector.dot(hpnp, hyp_ecef) + hpp
self.phyp[i] = hyp_ecef - hpnp * D
else:
# Origin is outside. Find distance to edges
p0p = np.reshape(p0.getArray() - hyp_ecef.getArray(), [1, 3])
p1p = np.reshape(p1.getArray() - hyp_ecef.getArray(), [1, 3])
p2p = np.reshape(p2.getArray() - hyp_ecef.getArray(), [1, 3])
p3p = np.reshape(p3.getArray() - hyp_ecef.getArray(), [1, 3])
s1 = _distance_sq_to_segment(p1p, p2p)
s3 = _distance_sq_to_segment(p3p, p0p)
# Assuming that the rupture is segmented along strike and not
# updip (as described by Bayless and somerville), we only
# need to consider s1 and s3:
if s1 > s3:
e30 = p0 - p3
e30norm = e30.norm()
mag = e30.mag()
self.phyp[i] = p3 + e30norm * (0.5 * mag)
else:
e21 = p1 - p2
e21norm = e21.norm()
mag = e21.mag()
self.phyp[i] = p2 + e21norm * (0.5 * mag)
def getDepthAtPoint(self, lat, lon):
SMALL_DISTANCE = 2e-03 # 2 meters
depth = np.nan
tmp, _ = self.computeRjb(np.array([lon]), np.array([lat]),
np.array([0]))
if tmp > SMALL_DISTANCE:
return depth
i = 0
imin = -1
dmin = 9999999999999999
for quad in self.getQuadrilaterals():
pX = Vector.fromPoint(Point(lon, lat, 0))
points = np.reshape(np.array([pX.x, pX.y, pX.z]), (1, 3))
rjb = utils._quad_distance(quad, points, horizontal=True)
if rjb[0][0] < dmin:
dmin = rjb[0][0]
imin = i
i += 1
quad = self._quadrilaterals[imin]
P0, P1, P2, P3 = quad
# project the quad and the point in question to orthographic defined by
# quad
xmin = np.min([P0.x, P1.x, P2.x, P3.x])
xmax = np.max([P0.x, P1.x, P2.x, P3.x])
ymin = np.min([P0.y, P1.y, P2.y, P3.y])
ymax = np.max([P0.y, P1.y, P2.y, P3.y])
proj = OrthographicProjection(xmin, xmax, ymax, ymin)
# project each vertex of quad (at 0 depth)
s0x, s0y = proj(P0.x, P0.y)
s1x, s1y = proj(P1.x, P1.y)
s2x, s2y = proj(P2.x, P2.y)
s3x, s3y = proj(P3.x, P3.y)
sxx, sxy = proj(lon, lat)
# turn these to vectors
s0 = Vector(s0x, s0y, 0)
s1 = Vector(s1x, s1y, 0)
s3 = Vector(s3x, s3y, 0)
sx = Vector(sxx, sxy, 0)
# Compute vector from s0 to s1
s0s1 = s1 - s0
# Compute the vector from s0 to s3
s0s3 = s3 - s0
# Compute the vector from s0 to sx
s0sx = sx - s0
# cross products
s0normal = s0s3.cross(s0s1)
dd = s0s1.cross(s0normal)
# normalize dd (down dip direction)
ddn = dd.norm()
# dot product
sxdd = ddn.dot(s0sx)
# get width of quad (convert from km to m)
w = utils.get_quad_width(quad) * 1000
# Get weights for top and bottom edge depths
N = utils.get_quad_normal(quad)
V = utils.get_vertical_vector(quad)
dip = np.degrees(np.arccos(Vector.dot(N, V)))
ws = (w * np.cos(np.radians(dip)))
wtt = (ws - sxdd) / ws
wtb = sxdd / ws
# Compute the depth of of the plane at Px:
depth = wtt * P0.z + wtb * P3.z * 1000
return depth
