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 _computeGC2(rupture, lon, lat, depth):
"""
Method for computing GC2 from a ShakeMap Rupture instance.
Args:
rupture (Rupture): ShakeMap rupture object.
lon (array): Numpy array of site longitudes.
lat (array): Numpy array of site latitudes.
depth (array): Numpy array of site depths.
Returns:
dict: Dictionary of GC2 distances. Keys include "T", "U", "rx"
"ry", "ry0".
"""
quadlist = rupture.getQuadrilaterals()
quadgc2 = copy.deepcopy(quadlist)
oldshape = lon.shape
if len(oldshape) == 2:
newshape = (oldshape[0] * oldshape[1], 1)
else:
newshape = (oldshape[0], 1)
# -------------------------------------------------------------------------
# Define a projection that spans sites and rupture
# -------------------------------------------------------------------------
all_lat = np.append(lat, rupture.lats)
all_lon = np.append(lon, rupture.lons)
west = np.nanmin(all_lon)
east = np.nanmax(all_lon)
south = np.nanmin(all_lat)
north = np.nanmax(all_lat)
proj = OrthographicProjection(west, east, north, south)
totweight = np.zeros(newshape, dtype=lon.dtype)
GC2T = np.zeros(newshape, dtype=lon.dtype)
GC2U = np.zeros(newshape, dtype=lon.dtype)
# -------------------------------------------------------------------------
# First sort out strike discordance and nominal strike prior to
# starting the loop if there is more than one group/trace.
# -------------------------------------------------------------------------
group_ind = rupture._getGroupIndex()
# Need group_ind as numpy array for sensible indexing...
group_ind_np = np.array(group_ind)
uind = np.unique(group_ind_np)
n_groups = len(uind)
if n_groups > 1:
# ---------------------------------------------------------------------
# The first thing we need to worry about is finding the coordinate
# shift. U's origin is "selected from the two endpoints most
# distant from each other."
# ---------------------------------------------------------------------
# Need to get index of first and last quad
# for each segment
iq0 = np.zeros(n_groups, dtype='int16')
iq1 = np.zeros(n_groups, dtype='int16')
for k in uind:
ii = [i for i, j in enumerate(group_ind) if j == uind[k]]
iq0[k] = int(np.min(ii))
iq1[k] = int(np.max(ii))
# ---------------------------------------------------------------------
# This is an iterator for each possible combination of traces
# including trace orientations (i.e., flipped).
# ---------------------------------------------------------------------
it_seg = it.product(it.combinations(uind, 2), it.product([0, 1],
[0, 1]))
# Placeholder for the trace pair/orientation that gives the
# largest distance.
dist_save = 0
for k in it_seg:
s0ind = k[0][0]
s1ind = k[0][1]
p0ind = k[1][0]
p1ind = k[1][1]
if p0ind == 0:
P0 = quadlist[iq0[s0ind]][0]
else:
P0 = quadlist[iq1[s0ind]][1]
if p1ind == 0:
P1 = quadlist[iq1[s1ind]][0]
else:
P1 = quadlist[iq0[s1ind]][1]
dist = geodetic.distance(P0.longitude, P0.latitude, 0.0,
P1.longitude, P1.latitude, 0.0)
if dist > dist_save:
dist_save = dist
A0 = P0
A1 = P1
# ---------------------------------------------------------------------
# A0 and A1 are the furthest two segment endpoints, but we still
# need to sort out which one is the "origin".
# ---------------------------------------------------------------------
# This goofy while-loop is to adjust the side of the rupture where the
# origin is located
dummy = -1
while dummy < 0:
A0.depth = 0
A1.depth = 0
p_origin = Vector.fromPoint(A0)
a0 = Vector.fromPoint(A0)
a1 = Vector.fromPoint(A1)
ahat = (a1 - a0).norm()
# Loop over traces
e_j = np.zeros(n_groups)
b_prime = [None] * n_groups
for j in range(n_groups):
P0 = quadlist[iq0[j]][0]
P1 = quadlist[iq1[j]][1]
P0.depth = 0
P1.depth = 0
p0 = Vector.fromPoint(P0)
p1 = Vector.fromPoint(P1)
b_prime[j] = p1 - p0
e_j[j] = ahat.dot(b_prime[j])
E = np.sum(e_j)
# List of discordancy
dc = [np.sign(a) * np.sign(E) for a in e_j]
b = Vector(0, 0, 0)
for j in range(n_groups):
b.x = b.x + b_prime[j].x * dc[j]
b.y = b.y + b_prime[j].y * dc[j]
b.z = b.z + b_prime[j].z * dc[j]
bhat = b.norm()
dummy = bhat.dot(ahat)
if dummy < 0:
tmpA0 = copy.deepcopy(A0)
A0 = copy.deepcopy(A1)
A1 = tmpA0
# ---------------------------------------------------------------------
# To fix discordancy, need to flip quads and rearrange
# the order of quadgc2
# ---------------------------------------------------------------------
# 1) flip quads
for i in range(len(quadgc2)):
if dc[group_ind[i]] < 0:
quadgc2[i] = reverse_quad(quadgc2[i])
# 2) rearrange quadlist order
qind = np.arange(len(quadgc2))
for i in range(n_groups):
qsel = qind[group_ind_np == uind[i]]
if dc[i] < 0:
qrev = qsel[::-1]
qind[group_ind_np == uind[i]] = qrev
quadgc2old = copy.deepcopy(quadgc2)
for i in range(len(qind)):
quadgc2[i] = quadgc2old[qind[i]]
# End of if-statement for adjusting group discordancy
s_i = 0.0
l_i = np.zeros(len(quadgc2))
for i in range(len(quadgc2)):
G0, G1, G2, G3 = quadgc2[i]
# Compute u_i and t_i for this quad
t_i = __calc_t_i(G0, G1, lat, lon, proj)
u_i = __calc_u_i(G0, G1, lat, lon, proj)
# Quad length (top edge)
l_i[i] = get_quad_length(quadgc2[i])
# ---------------------------------------------------------------------
# Weight of segment, three cases
# ---------------------------------------------------------------------
# Case 3: t_i == 0 and 0 <= u_i <= l_i
w_i = np.zeros_like(t_i)
# To avoid division by zero in totweight later on:
ix = (t_i == 0) & (0 <= u_i) & (u_i <= l_i[i])
totweight[ix] = 1.0
# Case 1:
ix = t_i != 0
w_i[ix] = (1.0 / t_i[ix]) * (np.arctan(
(l_i[i] - u_i[ix]) / t_i[ix]) - np.arctan(-u_i[ix] / t_i[ix]))
# Case 2:
ix = (t_i == 0) & ((u_i < 0) | (u_i > l_i[i]))
w_i[ix] = 1 / (u_i[ix] - l_i[i]) - 1 / u_i[ix]
totweight = totweight + w_i
GC2T = GC2T + w_i * t_i
if n_groups == 1:
GC2U = GC2U + w_i * (u_i + s_i)
else:
if i == 0:
qind = np.array(range(len(quadgc2)))
l_kj = 0
s_ij_1 = 0
else:
l_kj = l_i[(group_ind_np == group_ind_np[i]) & (qind < i)]
s_ij_1 = np.sum(l_kj)
# First endpoint in the current 'group' (or 'trace' in GC2 terms)
p1 = Vector.fromPoint(quadgc2[iq0[group_ind[i]]][0])
s_ij_2 = (p1 - p_origin).dot(np.sign(E) * ahat) / 1000.0
# Above is GC2N, for GC2T use:
# s_ij_2 = (p1 - p_origin).dot(bhat) / 1000.0
s_ij = s_ij_1 + s_ij_2
GC2U = GC2U + w_i * (u_i + s_ij)
s_i = s_i + l_i[i]
GC2T = GC2T / totweight
GC2U = GC2U / totweight
# Dictionary for holding the distances
distdict = dict()
distdict['T'] = copy.deepcopy(GC2T).reshape(oldshape)
distdict['U'] = copy.deepcopy(GC2U).reshape(oldshape)
# Take care of Rx
Rx = copy.deepcopy(GC2T) # preserve sign (no absolute value)
Rx = Rx.reshape(oldshape)
distdict['rx'] = Rx
# Ry
Ry = GC2U - s_i / 2.0
Ry = Ry.reshape(oldshape)
distdict['ry'] = Ry
# Ry0
Ry0 = np.zeros_like(GC2U)
ix = GC2U < 0
Ry0[ix] = np.abs(GC2U[ix])
if n_groups > 1:
s_i = s_ij + l_i[-1]
ix = GC2U > s_i
Ry0[ix] = GC2U[ix] - s_i
Ry0 = Ry0.reshape(oldshape)
distdict['ry0'] = Ry0
return distdict
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 _computeGC2(rupture, lon, lat, depth):
"""
Method for computing GC2 from a ShakeMap Rupture instance.
Args:
rupture (Rupture): ShakeMap rupture object.
lon (array): Numpy array of site longitudes.
lat (array): Numpy array of site latitudes.
depth (array): Numpy array of site depths.
Returns:
dict: Dictionary of GC2 distances. Keys include "T", "U", "rx"
"ry", "ry0".
"""
quadlist = rupture.getQuadrilaterals()
quadgc2 = copy.deepcopy(quadlist)
oldshape = lon.shape
if len(oldshape) == 2:
newshape = (oldshape[0] * oldshape[1], 1)
else:
newshape = (oldshape[0], 1)
# -------------------------------------------------------------------------
# Define a projection that spans sites and rupture
# -------------------------------------------------------------------------
all_lat = np.append(lat, rupture.lats)
all_lon = np.append(lon, rupture.lons)
west = np.nanmin(all_lon)
east = np.nanmax(all_lon)
south = np.nanmin(all_lat)
north = np.nanmax(all_lat)
proj = get_orthographic_projection(west, east, north, south)
totweight = np.zeros(newshape, dtype=lon.dtype)
GC2T = np.zeros(newshape, dtype=lon.dtype)
GC2U = np.zeros(newshape, dtype=lon.dtype)
# -------------------------------------------------------------------------
# First sort out strike discordance and nominal strike prior to
# starting the loop if there is more than one group/trace.
# -------------------------------------------------------------------------
group_ind = rupture._getGroupIndex()
# Need group_ind as numpy array for sensible indexing...
group_ind_np = np.array(group_ind)
uind = np.unique(group_ind_np)
n_groups = len(uind)
if n_groups > 1:
# ---------------------------------------------------------------------
# The first thing we need to worry about is finding the coordinate
# shift. U's origin is "selected from the two endpoints most
# distant from each other."
# ---------------------------------------------------------------------
# Need to get index of first and last quad
# for each segment
iq0 = np.zeros(n_groups, dtype='int16')
iq1 = np.zeros(n_groups, dtype='int16')
for k in uind:
ii = [i for i, j in enumerate(group_ind) if j == uind[k]]
iq0[k] = int(np.min(ii))
iq1[k] = int(np.max(ii))
# ---------------------------------------------------------------------
# This is an iterator for each possible combination of traces
# including trace orientations (i.e., flipped).
# ---------------------------------------------------------------------
it_seg = it.product(it.combinations(uind, 2),
it.product([0, 1], [0, 1]))
# Placeholder for the trace pair/orientation that gives the
# largest distance.
dist_save = 0
for k in it_seg:
s0ind = k[0][0]
s1ind = k[0][1]
p0ind = k[1][0]
p1ind = k[1][1]
if p0ind == 0:
P0 = quadlist[iq0[s0ind]][0]
else:
P0 = quadlist[iq1[s0ind]][1]
if p1ind == 0:
P1 = quadlist[iq1[s1ind]][0]
else:
P1 = quadlist[iq0[s1ind]][1]
dist = geodetic.distance(P0.longitude, P0.latitude, 0.0,
P1.longitude, P1.latitude, 0.0)
if dist > dist_save:
dist_save = dist
A0 = P0
A1 = P1
# ---------------------------------------------------------------------
# A0 and A1 are the furthest two segment endpoints, but we still
# need to sort out which one is the "origin".
# ---------------------------------------------------------------------
# This goofy while-loop is to adjust the side of the rupture where the
# origin is located
dummy = -1
while dummy < 0:
A0.depth = 0
A1.depth = 0
p_origin = Vector.fromPoint(A0)
a0 = Vector.fromPoint(A0)
a1 = Vector.fromPoint(A1)
ahat = (a1 - a0).norm()
# Loop over traces
e_j = np.zeros(n_groups)
b_prime = [None] * n_groups
for j in range(n_groups):
P0 = quadlist[iq0[j]][0]
P1 = quadlist[iq1[j]][1]
P0.depth = 0
P1.depth = 0
p0 = Vector.fromPoint(P0)
p1 = Vector.fromPoint(P1)
b_prime[j] = p1 - p0
e_j[j] = ahat.dot(b_prime[j])
E = np.sum(e_j)
# List of discordancy
dc = [np.sign(a) * np.sign(E) for a in e_j]
b = Vector(0, 0, 0)
for j in range(n_groups):
b.x = b.x + b_prime[j].x * dc[j]
b.y = b.y + b_prime[j].y * dc[j]
b.z = b.z + b_prime[j].z * dc[j]
bhat = b.norm()
dummy = bhat.dot(ahat)
if dummy < 0:
tmpA0 = copy.deepcopy(A0)
tmpA1 = copy.deepcopy(A1)
A0 = tmpA1
A1 = tmpA0
# ---------------------------------------------------------------------
# To fix discordancy, need to flip quads and rearrange
# the order of quadgc2
# ---------------------------------------------------------------------
# 1) flip quads
for i in range(len(quadgc2)):
if dc[group_ind[i]] < 0:
quadgc2[i] = reverse_quad(quadgc2[i])
# 2) rearrange quadlist order
qind = np.arange(len(quadgc2))
for i in range(n_groups):
qsel = qind[group_ind_np == uind[i]]
if dc[i] < 0:
qrev = qsel[::-1]
qind[group_ind_np == uind[i]] = qrev
quadgc2old = copy.deepcopy(quadgc2)
for i in range(len(qind)):
quadgc2[i] = quadgc2old[qind[i]]
# End of if-statement for adjusting group discordancy
s_i = 0.0
l_i = np.zeros(len(quadgc2))
for i in range(len(quadgc2)):
G0, G1, G2, G3 = quadgc2[i]
# Compute u_i and t_i for this quad
t_i = __calc_t_i(G0, G1, lat, lon, proj)
u_i = __calc_u_i(G0, G1, lat, lon, proj)
# Quad length (top edge)
l_i[i] = get_quad_length(quadgc2[i])
# ---------------------------------------------------------------------
# Weight of segment, three cases
# ---------------------------------------------------------------------
# Case 3: t_i == 0 and 0 <= u_i <= l_i
w_i = np.zeros_like(t_i)
# Case 1:
ix = t_i != 0
w_i[ix] = (1.0 / t_i[ix]) * (np.arctan((l_i[i] -
u_i[ix]) / t_i[ix]) - np.arctan(-u_i[ix] / t_i[ix]))
# Case 2:
ix = (t_i == 0) & ((u_i < 0) | (u_i > l_i[i]))
w_i[ix] = 1 / (u_i[ix] - l_i[i]) - 1 / u_i[ix]
totweight = totweight + w_i
GC2T = GC2T + w_i * t_i
if n_groups == 1:
GC2U = GC2U + w_i * (u_i + s_i)
else:
if i == 0:
qind = np.array(range(len(quadgc2)))
l_kj = 0
s_ij_1 = 0
else:
l_kj = l_i[(group_ind_np == group_ind_np[i]) & (qind < i)]
s_ij_1 = np.sum(l_kj)
# First endpoint in the current 'group' (or 'trace' in GC2 terms)
p1 = Vector.fromPoint(quadgc2[iq0[group_ind[i]]][0])
s_ij_2 = (p1 - p_origin).dot(np.sign(E) * ahat) / 1000.0
# Above is GC2N, for GC2T use:
# s_ij_2 = (p1 - p_origin).dot(bhat) / 1000.0
s_ij = s_ij_1 + s_ij_2
GC2U = GC2U + w_i * (u_i + s_ij)
s_i = s_i + l_i[i]
GC2T = GC2T / totweight
GC2U = GC2U / totweight
# Dictionary for holding the distances
distdict = dict()
distdict['T'] = copy.deepcopy(GC2T).reshape(oldshape)
distdict['U'] = copy.deepcopy(GC2U).reshape(oldshape)
# Take care of Rx
Rx = copy.deepcopy(GC2T) # preserve sign (no absolute value)
Rx = Rx.reshape(oldshape)
distdict['rx'] = Rx
# Ry
Ry = GC2U - s_i / 2.0
Ry = Ry.reshape(oldshape)
distdict['ry'] = Ry
# Ry0
Ry0 = np.zeros_like(GC2U)
ix = GC2U < 0
Ry0[ix] = np.abs(GC2U[ix])
if n_groups > 1:
s_i = s_ij + l_i[-1]
ix = GC2U > s_i
Ry0[ix] = GC2U[ix] - s_i
Ry0 = Ry0.reshape(oldshape)
distdict['ry0'] = Ry0
return distdict
