def __computeDT(self, period):
"""
Computes DT -- the distance taper term.
"""
slat = self._lat
slon = self._lon
site_z = np.zeros_like(slat)
ddict = get_distance('rrup', slat, slon, site_z, self._rup)
Rrup = np.reshape(ddict['rrup'], (-1, ))
nsite = len(Rrup)
if self._simpleDT: # eqn 3.10
R1 = 35
R2 = 70
DT = np.ones(nsite)
ix = tuple([(Rrup > R1) & (Rrup < R2)])
DT[ix] = 2 - Rrup[ix] / R1
DT[Rrup >= R2] = 0
else: # eqn 3.9
if period >= 1:
R1 = 20 + 10 * np.log(period)
R2 = 2 * (20 + 10 * np.log(period))
else:
R1 = 20
R2 = 40
DT = np.ones(nsite)
# As written in report:
# DT[(Rrup > R1) & (Rrup < R2)] = \
# 2 - Rrup[(Rrup > R1) & (Rrup < R2)]/(20 + 10 * np.log(period))
# Modification:
DT[(Rrup > R1) & (Rrup < R2)] = 2 - \
Rrup[(Rrup > R1) & (Rrup < R2)] / R1
# Note: it is not clear if the above modification is 'correct'
# but it gives results that make more sense
DT[Rrup >= R2] = 0
DT = np.reshape(DT, slat.shape)
self._DT = DT
def __computeDT(self, period):
"""
Computes DT -- the distance taper term.
"""
slat = self._lat
slon = self._lon
site_z = np.zeros_like(slat)
ddict = get_distance('rrup', slat, slon, site_z, self._rup)
Rrup = np.reshape(ddict['rrup'], (-1, ))
nsite = len(Rrup)
if self._simpleDT: # eqn 3.10
R1 = 35
R2 = 70
DT = np.ones(nsite)
ix = [(Rrup > R1) & (Rrup < R2)]
DT[ix] = 2 - Rrup[ix] / R1
DT[Rrup >= R2] = 0
else: # eqn 3.9
if period >= 1:
R1 = 20 + 10 * np.log(period)
R2 = 2 * (20 + 10 * np.log(period))
else:
R1 = 20
R2 = 40
DT = np.ones(nsite)
# As written in report:
# DT[(Rrup > R1) & (Rrup < R2)] = \
# 2 - Rrup[(Rrup > R1) & (Rrup < R2)]/(20 + 10 * np.log(period))
# Modification:
DT[(Rrup > R1) & (Rrup < R2)] = 2 - \
Rrup[(Rrup > R1) & (Rrup < R2)] / R1
# Note: it is not clear if the above modification is 'correct'
# but it gives results that make more sense
DT[Rrup >= R2] = 0
DT = np.reshape(DT, slat.shape)
self._DT = DT
def __init__(self, origin, rup, lat, lon, depth, T):
"""
Constructor for bayless2013.
Args:
origin: Shakemap Origin object.
rup: Shakemap Rupture object.
lat: Numpy array of latitudes.
lon: Numpy array of longitudes.
depth: Numpy array of depths (km); down is positive.
T: Period; Currently, only acceptable values are
0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 7.5, 10.
"""
self._origin = origin
self._rup = rup
self._rake = origin.rake
self._M = origin.mag
self._hyp = origin.getHypo()
self._lon = lon
self._lat = lat
self._dep = depth
self._T = T
# Lists of widths and lengths for each quad in the rupture
self._W = self._rup.getIndividualWidths()
self._L = self._rup.getIndividualTopLengths()
# Number of quads
self._nq = len(self._W)
# Currently assuming that the rake is the same on all subruptures .
self.__getSlipCategory()
# Rupture weights are supposed to be based on seismic moment.
# Since moment is proportional to area, lets just use area
# for now
area = self._W * self._L
self.weights = area / np.sum(area)
# Put in pseudo-hypocenters for each quad
self.__setPseudoHypocenters()
self._fd = 0
for i in range(self._nq):
self.i = i
# Compute some genral stuff that is required for all mechanisms
dtypes = ['rrup', 'rx', 'ry0']
dists = get_distance(dtypes, self._lat, self._lon, self._dep,
self._rup)
self.__Rrup = np.reshape(dists['rrup'], self._lat.shape)
self.__Rx = np.reshape(dists['rx'], self._lat.shape)
self.__Ry = np.reshape(dists['ry0'], self._lat.shape)
# NOTE: use Rx and Ry to compute Az in 'computeAz'. It is probably
# possible to make this a lot faster by avoiding the
# calculation of these distances each time.
# Az is the NGA definition of source-to-site azimuth for a finite
# rupture. See Kaklamanos et al. (2011) Figure 2 for illustration.
self.__computeAz() # uses Rx and Ry, which are for the i-th quad.
# Magnitude taper (does not depend on mechanism)
if self._M <= 5.0:
self._T_Mw = 0.0
elif (self._M > 5.0) and (self._M < 6.5):
self._T_Mw = 1.0 - (6.5 - self._M) / 1.5
else:
self._T_Mw = 1.0
if self.SlipCategory == 'SS':
self.__computeSS()
self._fd = self._fd + self.weights[i] * self._fd_SS
elif self.SlipCategory == 'DS':
self.__computeDS()
self._fd = self._fd + self.weights[i] * self._fd_DS
else:
# Compute both SS and DS
self.__computeSS()
self.__computeDS()
# Normalize rake to reference angle
sintheta = np.abs(np.sin(np.radians(self._rake)))
costheta = np.abs(np.cos(np.radians(self._rake)))
refrake = np.arctan2(sintheta, costheta)
# Compute weights:
DipWeight = refrake / (np.pi / 2.0)
StrikeWeight = 1.0 - DipWeight
fdcombined = StrikeWeight * self._fd_SS + DipWeight * \
self._fd_DS
self._fd = self._fd + self.weights[i] * fdcombined
def test_multisegment_discordant():
# The one thing that isn't check above is discordancy for segments
# with multiple quads. For this, we need a synthetic example.
x0 = np.array([0, 1, -1, 10, 9, 7])
y0 = np.array([0, 10, 20, 40, 35, 30])
z0 = np.array([0, 0, 0, 0, 0, 0])
x1 = np.array([1, -1, 0, 9, 7, 6])
y1 = np.array([10, 20, 30, 35, 30, 25])
z1 = np.array([0, 0, 0, 0, 0, 0])
x2 = np.array([3, 1, 2, 7, 5, 4])
y2 = np.array([10, 20, 30, 35, 30, 25])
z2 = np.array([10, 10, 10, 10, 10, 10])
x3 = np.array([2, 3, 1, 8, 7, 5])
y3 = np.array([0, 10, 20, 40, 35, 30])
z3 = np.array([10, 10, 10, 10, 10, 10])
epilat = 32.15270
epilon = -115.30500
proj = geo.utils.get_orthographic_projection(
epilon - 1, epilon + 1, epilat + 1, epilat - 1)
lon0, lat0 = proj(x0, y0, reverse=True)
lon1, lat1 = proj(x1, y1, reverse=True)
lon2, lat2 = proj(x2, y2, reverse=True)
lon3, lat3 = proj(x3, y3, reverse=True)
# Make an Origin object; most of the 'event' values don't matter for
# this example
origin = Origin({'lat': 0, 'lon': 0, 'depth': 0, 'mag': 7.2, 'eventsourcecode': ''})
rup = QuadRupture.fromVertices(
lon0, lat0, z0, lon1, lat1, z1, lon2, lat2, z2, lon3, lat3, z3,
origin, group_index=[0, 0, 0, 1, 1, 1])
# Sites
buf = 0.25
lat = np.linspace(np.nanmin(rup.lats) - buf, np.nanmax(rup.lats) + buf, 20)
lon = np.linspace(np.nanmin(rup.lons) - buf, np.nanmax(rup.lons) + buf, 20)
lons, lats = np.meshgrid(lon, lat)
dep = np.zeros_like(lons)
x, y = proj(lon, lat)
rupx, rupy = proj(rup.lons, rup.lats)
# Calculate U and T
dtypes = ['U', 'T']
dists = get_distance(dtypes, lats, lons, dep, rup)
targetU = np.array(
[[-28.53228275, -28.36479713, -28.20139732, -28.0407734,
-27.88135558, -27.72144153, -27.55935946, -27.39362017,
-27.22300147, -27.04653062, -26.86338215, -26.67275638,
-26.47381287, -26.26569449, -26.04762427, -25.81902477,
-25.57961136, -25.32943282, -25.06885791, -24.79852214],
[-23.53750292, -23.3748086, -23.21793537, -23.06521934,
-22.91449689, -22.76331684, -22.60928211, -22.45042208,
-22.28542121, -22.11355532, -21.93435402, -21.74720475,
-21.55115107, -21.34497916, -21.12749377, -20.89781118,
-20.6555466, -20.40086149, -20.13439948, -19.85716145],
[-18.53499939, -18.37689929, -18.22732841, -18.08427516,
-17.94468687, -17.80472632, -17.66045115, -17.50880802,
-17.3484421, -17.17963435, -17.0032098, -16.81921732,
-16.62638972, -16.42258419, -16.20564846, -15.9741218,
-15.72753538, -15.4663671, -15.19180844, -14.9054813],
[-13.52283359, -13.36797542, -13.22589288, -13.09466537,
-12.97028551, -12.84653536, -12.71591089, -12.57212088,
-12.41335561, -12.24319318, -12.06681006, -11.88598424,
-11.69798166, -11.49796348, -11.28169605, -11.04691388,
-10.79343174, -10.52262594, -10.23677602, -9.93851158],
[-8.49936685, -8.34357094, -8.20650964, -8.08786858,
-7.98403171, -7.88628837, -7.78005273, -7.64833307,
-7.48359988, -7.29992491, -7.11862682, -6.94410189,
-6.76618701, -6.5727842, -6.35634881, -6.11465447,
-5.84925708, -5.56369035, -5.26212482, -4.94857454],
[-3.46638168, -3.30047216, -3.15914418, -3.04618465,
-2.96252939, -2.90194067, -2.84436315, -2.75029014,
-2.56983592, -2.33744275, -2.1512136, -1.99833104,
-1.84066354, -1.6541107, -1.43071517, -1.17252753,
-0.88592286, -0.57817222, -0.25582315, 0.07585567],
[1.56416954, 1.75393848, 1.9183586, 2.04909316,
2.13723278, 2.17776584, 2.18272501, 2.20967639,
2.37405656, 2.65073289, 2.80205222, 2.90973407,
3.05124404, 3.2505182, 3.50336116, 3.7967575,
4.11742779, 4.45465822, 4.80070204, 5.15033407],
[6.5633489, 6.78740885, 6.99419348, 7.17551069,
7.31963558, 7.4113505, 7.43666779, 7.40177458,
7.40517136, 7.58520044, 7.62013169, 7.71596777,
7.90558457, 8.17213015, 8.49008681, 8.83763176,
9.19937294, 9.56556659, 9.9305469, 10.29132309],
[11.48996073, 11.74301446, 11.99016964, 12.22782156,
12.44984059, 12.6446727, 12.78798484, 12.82584849,
12.61992833, 12.26579742, 12.32166685, 12.54665462,
12.86628045, 13.23578462, 13.62571822, 14.01882924,
14.40617707, 14.78388296, 15.15089889, 15.5076165],
[16.31383216, 16.57376544, 16.83189511, 17.08626411,
17.33309437, 17.56429108, 17.76005623, 17.85853532,
17.57101025, 17.32637346, 17.45075419, 17.77199513,
18.16933168, 18.58284635, 18.9891851, 19.37985879,
19.75324557, 20.11079653, 20.4549905, 20.78837053],
[21.03975749, 21.28450315, 21.5243142, 21.75603974,
21.97469496, 22.17298057, 22.34310053, 22.49668569,
22.73940191, 22.70030633, 22.95351405, 23.35967832,
23.75891016, 24.14867803, 24.51536915, 24.85878249,
25.18398203, 25.49615514, 25.79932964, 26.09638269],
[25.70484089, 25.92709225, 26.14280395, 26.35119497,
26.55363501, 26.75827099, 26.9915523, 27.31779086,
27.77993211, 27.71070831, 28.13624949, 28.723482,
29.25285078, 29.66404032, 30.00169474, 30.30044315,
30.57916576, 30.84804427, 31.1126134, 31.37586841],
[30.35406633, 30.5585145, 30.75843356, 30.95627127,
31.15811912, 31.3763124, 31.63114968, 31.94156189,
32.23691802, 32.38759301, 32.86915665, 33.83467935,
34.46125278, 34.89905345, 35.25111257, 35.55095664,
35.82150686, 36.07720619, 36.32643896, 36.57385362],
[35.0222379, 35.21734711, 35.41081942, 35.60589495,
35.80774808, 36.02313791, 36.25826988, 36.51619168,
36.81025966, 37.21777129, 37.86674108, 38.66578072,
39.25203723, 39.78060643, 40.20815617, 40.5606039,
40.86634527, 41.14457482, 41.40732554, 41.66197722],
[39.73046099, 39.92514041, 40.12152415, 40.32316112,
40.5350467, 40.76393316, 41.01937758, 41.3172128,
41.68596492, 42.16604148, 42.77622755, 43.447503,
44.03771478, 44.55012468, 45.00551259, 45.40376857,
45.75505135, 46.07204699, 46.36554362, 46.64361367],
[44.4876174, 44.68959464, 44.89710008, 45.11420443,
45.34646809, 45.60143197, 45.88932906, 46.22363997,
46.61975585, 47.0884227, 47.62307543, 48.1913408,
48.74937117, 49.26945799, 49.74327902, 50.17123158,
50.55810895, 50.91098842, 51.23731582, 51.54375617],
[49.29279265, 49.50696882, 49.73006999, 49.96625305,
50.22080319, 50.50022572, 50.81209441, 51.1642666,
51.56290694, 52.00913021, 52.49553006, 53.00565389,
53.51861282, 54.01614414, 54.48672101, 54.9254339,
55.33212663, 55.70951516, 56.06170563, 56.39317058],
[54.13906629, 54.3671694, 54.60643024, 54.86053563,
55.13377911, 55.43088558, 55.75658576, 56.1148189,
56.50752978, 56.93329478, 57.38640012, 57.85715119,
58.33367994, 58.80451404, 59.26065475, 59.69644542,
60.10938419, 60.49940252, 60.86803179, 61.21767916],
[59.01741908, 59.25887491, 59.51248349, 59.78119592,
60.06816694, 60.37651862, 60.70895927, 61.0672529,
61.45160192, 61.86010542, 62.28853397, 62.73062937,
63.17894547, 63.62598375, 64.06523791, 64.49185106,
64.90281064, 65.2967858, 65.67377362, 66.03469546],
[63.9193099, 64.17236414, 64.4376317, 64.71732366,
65.01362255, 65.32847988, 65.66334836, 66.0188704,
66.39457546, 66.7886684, 67.19800022, 67.61828012,
68.04451487, 68.47157851, 68.89476917, 69.31022713,
69.71515194, 70.10782673, 70.4875021, 70.85420436]]
)
np.testing.assert_allclose(targetU, dists['U'], atol=0.01)
targetT = np.array(
[[-2.27427469e+01, -1.97498544e+01, -1.67512900e+01,
-1.37464632e+01, -1.07350712e+01, -7.71715083e+00,
-4.69305811e+00, -1.66336318e+00, 1.37131605e+00,
4.41047613e+00, 7.45381136e+00, 1.05011799e+01,
1.35524779e+01, 1.66074913e+01, 1.96657949e+01,
2.27267294e+01, 2.57894503e+01, 2.88530154e+01,
3.19164798e+01, 3.49789747e+01],
[-2.30778766e+01, -2.00896906e+01, -1.70950973e+01,
-1.40931667e+01, -1.10834219e+01, -8.06600712e+00,
-5.04171582e+00, -2.01179123e+00, 1.02248614e+00,
4.06025218e+00, 7.10129626e+00, 1.01459367e+01,
1.31946312e+01, 1.62475702e+01, 1.93044511e+01,
2.23644788e+01, 2.54265185e+01, 2.84892997e+01,
3.15515954e+01, 3.46123426e+01],
[-2.33971472e+01, -2.04144525e+01, -1.74245193e+01,
-1.44256870e+01, -1.14169177e+01, -8.39830615e+00,
-5.37141115e+00, -2.33902937e+00, 6.95823925e-01,
3.73133431e+00, 6.76769593e+00, 9.80663091e+00,
1.28500821e+01, 1.58991008e+01, 1.89534737e+01,
2.20119662e+01, 2.50728111e+01, 2.81341606e+01,
3.11943854e+01, 3.42522163e+01],
[-2.36965870e+01, -2.07206976e+01, -1.77370901e+01,
-1.47426715e+01, -1.17347885e+01, -8.71247709e+00,
-5.67801094e+00, -2.63761285e+00, 4.00625914e-01,
3.43182302e+00, 6.45782532e+00, 9.48491128e+00,
1.25187545e+01, 1.55616657e+01, 1.86127822e+01,
2.16694756e+01, 2.47286680e+01, 2.77876297e+01,
3.08443066e+01, 3.38973527e+01],
[-2.39698399e+01, -2.10022612e+01, -1.80281475e+01,
-1.50423801e+01, -1.20388157e+01, -9.01204040e+00,
-5.96160398e+00, -2.89867328e+00, 1.52194374e-01,
3.17268218e+00, 6.17334725e+00, 9.17699572e+00,
1.21964990e+01, 1.52330975e+01, 1.82821226e+01,
2.13375815e+01, 2.43943933e+01, 2.74490375e+01,
3.04994435e+01, 3.35446330e+01],
[-2.42070742e+01, -2.12471979e+01, -1.82855675e+01,
-1.53163304e+01, -1.23296744e+01, -9.31127857e+00,
-6.24535210e+00, -3.12882361e+00, -2.24460581e-02,
2.95354485e+00, 5.89215412e+00, 8.86387424e+00,
1.18748249e+01, 1.49128245e+01, 1.79640055e+01,
2.10182501e+01, 2.40696313e+01, 2.71153177e+01,
3.01543919e+01, 3.31869788e+01],
[-2.43971375e+01, -2.14368866e+01, -1.84826148e+01,
-1.55321207e+01, -1.25786621e+01, -9.60654678e+00,
-6.58612151e+00, -3.48118311e+00, -3.16555025e-01,
2.61618307e+00, 5.53740540e+00, 8.52666510e+00,
1.15623361e+01, 1.46149780e+01, 1.76674294e+01,
2.07125025e+01, 2.37483764e+01, 2.67756033e+01,
2.97955606e+01, 3.28097430e+01],
[-2.45384925e+01, -2.15583842e+01, -1.85874288e+01,
-1.56290738e+01, -1.26867853e+01, -9.76140655e+00,
-6.84407754e+00, -3.90089971e+00, -8.41806596e-01,
2.14754495e+00, 5.18583472e+00, 8.26271822e+00,
1.13266091e+01, 1.43684333e+01, 1.73916223e+01,
2.04017469e+01, 2.34034936e+01, 2.64002111e+01,
2.93941282e+01, 3.23866586e+01],
[-2.46576775e+01, -2.16355610e+01, -1.86129545e+01,
-1.55919156e+01, -1.25763765e+01, -9.57306672e+00,
-6.59044329e+00, -3.62352541e+00, -5.92041388e-01,
2.33255341e+00, 5.29498494e+00, 8.24834463e+00,
1.11833819e+01, 1.41167617e+01, 1.70571082e+01,
2.00065102e+01, 2.29645946e+01, 2.59302937e+01,
2.89023967e+01, 3.18797332e+01],
[-2.48161623e+01, -2.17489533e+01, -1.86651328e+01,
-1.55589864e+01, -1.24224388e+01, -9.24466730e+00,
-6.01521475e+00, -2.75148770e+00, 3.89519039e-01,
2.99589525e+00, 5.45696689e+00, 8.01247078e+00,
1.07291540e+01, 1.35565782e+01, 1.64461360e+01,
1.93723515e+01, 2.23222250e+01, 2.52881249e+01,
2.82650171e+01, 3.12494172e+01],
[-2.50857405e+01, -2.20002811e+01, -1.88926336e+01,
-1.57550887e+01, -1.25770789e+01, -9.34497451e+00,
-6.04430316e+00, -2.67290100e+00, 5.40854953e-01,
2.30509492e+00, 3.58183843e+00, 6.23701436e+00,
9.28727128e+00, 1.23205706e+01, 1.53428945e+01,
1.83666035e+01, 2.13934954e+01, 2.44218171e+01,
2.74496472e+01, 3.04757209e+01],
[-2.55082697e+01, -2.24454912e+01, -1.93710045e+01,
-1.62824768e+01, -1.31767102e+01, -1.00469827e+01,
-6.86985653e+00, -3.54681638e+00, 1.07062999e-01,
3.34891657e-01, -1.70694750e-01, 3.57896940e+00,
7.17013928e+00, 1.05232789e+01, 1.37976070e+01,
1.70230221e+01, 2.02076136e+01, 2.33576919e+01,
2.64794914e+01, 2.95785985e+01],
[-2.60778515e+01, -2.30695744e+01, -2.00684150e+01,
-1.70790651e+01, -1.41074315e+01, -1.11587507e+01,
-8.23273307e+00, -5.33306966e+00, -2.80144302e+00,
-1.84760416e+00, -1.05368779e+00, 1.26163211e+00,
4.90086292e+00, 8.53883059e+00, 1.20996577e+01,
1.55589098e+01, 1.89237978e+01, 2.22114952e+01,
2.54390313e+01, 2.86203790e+01],
[-2.67537229e+01, -2.38123298e+01, -2.08964272e+01,
-1.80168638e+01, -1.51896230e+01, -1.24401995e+01,
-9.81536176e+00, -7.41008520e+00, -5.38073414e+00,
-3.78262975e+00, -2.29669890e+00, -3.53057240e-01,
3.13642477e+00, 6.97021789e+00, 1.07026969e+01,
1.42945488e+01, 1.77655640e+01, 2.11406146e+01,
2.44409375e+01, 2.76832489e+01],
[-2.74832153e+01, -2.46028623e+01, -2.17593854e+01,
-1.89653378e+01, -1.62381218e+01, -1.36022404e+01,
-1.10914555e+01, -8.74572618e+00, -6.58963863e+00,
-4.58336507e+00, -2.57607747e+00, -2.67233150e-01,
2.82788692e+00, 6.36737407e+00, 9.93334021e+00,
1.34440609e+01, 1.68846862e+01, 2.02577163e+01,
2.35710668e+01, 2.68337230e+01],
[-2.82199728e+01, -2.53838486e+01, -2.25869234e+01,
-1.98388981e+01, -1.71512612e+01, -1.45365893e+01,
-1.20059297e+01, -9.56220853e+00, -7.18799023e+00,
-4.83006994e+00, -2.39120744e+00, 2.51308627e-01,
3.17331949e+00, 6.33022626e+00, 9.61428455e+00,
1.29426788e+01, 1.62705993e+01, 1.95770961e+01,
2.28539081e+01, 2.60992146e+01],
[-2.89332200e+01, -2.61222251e+01, -2.33461951e+01,
-2.06105222e+01, -1.79200485e+01, -1.52776479e+01,
-1.26817390e+01, -1.01225741e+01, -7.57801870e+00,
-5.01122873e+00, -2.37434916e+00, 3.78303328e-01,
3.27093827e+00, 6.29527723e+00, 9.41912399e+00,
1.26046423e+01, 1.58204753e+01, 1.90448689e+01,
2.22643265e+01, 2.54712657e+01],
[-2.96082809e+01, -2.68067500e+01, -2.40331802e+01,
-2.12894659e+01, -1.85760763e+01, -1.58910124e+01,
-1.32284735e+01, -1.05774862e+01, -7.92111801e+00,
-5.23724922e+00, -2.50179068e+00, 3.05790568e-01,
3.19666197e+00, 6.16975035e+00, 9.21353475e+00,
1.23109519e+01, 1.54443017e+01, 1.85982825e+01,
2.17611016e+01, 2.49243957e+01],
[-3.02420504e+01, -2.74395034e+01, -2.46578094e+01,
-2.18967353e+01, -1.91546206e+01, -1.64278219e+01,
-1.37101816e+01, -1.09927140e+01, -8.26378719e+00,
-5.51007519e+00, -2.71836365e+00, 1.22111758e-01,
3.01754598e+00, 5.96851903e+00, 8.97043180e+00,
1.20150997e+01, 1.50927299e+01, 1.81935916e+01,
2.13090724e+01, 2.44321477e+01],
[-3.08377073e+01, -2.80281994e+01, -2.52335334e+01,
-2.24524366e+01, -1.96825082e+01, -1.69199811e+01,
-1.41595768e+01, -1.13945492e+01, -8.61701306e+00,
-5.81861191e+00, -2.99148017e+00, -1.29317230e-01,
2.77170749e+00, 5.71249079e+00, 8.69110042e+00,
1.17033684e+01, 1.47437429e+01, 1.78061436e+01,
2.08846464e+01, 2.39739290e+01]]
)
np.testing.assert_allclose(targetT, dists['T'], atol=0.01)
def __init__(self, origin, rup, lat, lon, depth, T):
"""
Constructor for bayless2013.
Args:
origin: Shakemap Origin object.
rup: Shakemap Rupture object.
lat: Numpy array of latitudes.
lon: Numpy array of longitudes.
depth: Numpy array of depths (km); down is positive.
T: Period; Currently, only acceptable values are
0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 7.5, 10.
"""
self._origin = origin
self._rup = rup
self._rake = origin.rake
self._M = origin.mag
self._hyp = origin.getHypo()
self._lon = lon
self._lat = lat
self._dep = depth
self._T = T
# Lists of widths and lengths for each quad in the rupture
self._W = self._rup.getIndividualWidths()
self._L = self._rup.getIndividualTopLengths()
# Number of quads
self._nq = len(self._W)
# Currently assuming that the rake is the same on all subruptures .
self.__getSlipCategory()
# Rupture weights are supposed to be based on seismic moment.
# Since moment is proportional to area, lets just use area
# for now
area = self._W * self._L
self.weights = area / np.sum(area)
# Put in pseudo-hypocenters for each quad
self.__setPseudoHypocenters()
self._fd = 0
for i in range(self._nq):
self.i = i
# Compute some genral stuff that is required for all mechanisms
dtypes = ['rrup', 'rx', 'ry0']
dists = get_distance(dtypes, self._lat, self._lon, self._dep,
self._rup)
self.__Rrup = np.reshape(dists['rrup'], self._lat.shape)
self.__Rx = np.reshape(dists['rx'], self._lat.shape)
self.__Ry = np.reshape(dists['ry0'], self._lat.shape)
# NOTE: use Rx and Ry to compute Az in 'computeAz'. It is probably
# possible to make this a lot faster by avoiding the
# calculation of these distances each time.
# Az is the NGA definition of source-to-site azimuth for a finite
# rupture. See Kaklamanos et al. (2011) Figure 2 for illustration.
self.__computeAz() # uses Rx and Ry, which are for the i-th quad.
# Magnitude taper (does not depend on mechanism)
if self._M <= 5.0:
self._T_Mw = 0.0
elif (self._M > 5.0) and (self._M < 6.5):
self._T_Mw = 1.0 - (6.5 - self._M) / 1.5
else:
self._T_Mw = 1.0
if self.SlipCategory == 'SS':
self.__computeSS()
self._fd = self._fd + self.weights[i] * self._fd_SS
elif self.SlipCategory == 'DS':
self.__computeDS()
self._fd = self._fd + self.weights[i] * self._fd_DS
else:
# Compute both SS and DS
self.__computeSS()
self.__computeDS()
# Normalize rake to reference angle
sintheta = np.abs(np.sin(np.radians(self._rake)))
costheta = np.abs(np.cos(np.radians(self._rake)))
refrake = np.arctan2(sintheta, costheta)
# Compute weights:
DipWeight = refrake / (np.pi / 2.0)
StrikeWeight = 1.0 - DipWeight
fdcombined = StrikeWeight * self._fd_SS + DipWeight * \
self._fd_DS
self._fd = self._fd + self.weights[i] * fdcombined
def test_multisegment_discordant():
# The one thing that isn't check above is discordancy for segments
# with multiple quads. For this, we need a synthetic example.
x0 = np.array([0, 1, -1, 10, 9, 7])
y0 = np.array([0, 10, 20, 40, 35, 30])
z0 = np.array([0, 0, 0, 0, 0, 0])
x1 = np.array([1, -1, 0, 9, 7, 6])
y1 = np.array([10, 20, 30, 35, 30, 25])
z1 = np.array([0, 0, 0, 0, 0, 0])
x2 = np.array([3, 1, 2, 7, 5, 4])
y2 = np.array([10, 20, 30, 35, 30, 25])
z2 = np.array([10, 10, 10, 10, 10, 10])
x3 = np.array([2, 3, 1, 8, 7, 5])
y3 = np.array([0, 10, 20, 40, 35, 30])
z3 = np.array([10, 10, 10, 10, 10, 10])
epilat = 32.15270
epilon = -115.30500
proj = geo.utils.get_orthographic_projection(epilon - 1, epilon + 1,
epilat + 1, epilat - 1)
lon0, lat0 = proj(x0, y0, reverse=True)
lon1, lat1 = proj(x1, y1, reverse=True)
lon2, lat2 = proj(x2, y2, reverse=True)
lon3, lat3 = proj(x3, y3, reverse=True)
# Make an Origin object; most of the 'event' values don't matter for
# this example
origin = Origin({
'lat': 0,
'lon': 0,
'depth': 0,
'mag': 7.2,
'eventsourcecode': ''
})
rup = QuadRupture.fromVertices(lon0,
lat0,
z0,
lon1,
lat1,
z1,
lon2,
lat2,
z2,
lon3,
lat3,
z3,
origin,
group_index=[0, 0, 0, 1, 1, 1])
# Sites
buf = 0.25
lat = np.linspace(np.nanmin(rup.lats) - buf, np.nanmax(rup.lats) + buf, 20)
lon = np.linspace(np.nanmin(rup.lons) - buf, np.nanmax(rup.lons) + buf, 20)
lons, lats = np.meshgrid(lon, lat)
dep = np.zeros_like(lons)
x, y = proj(lon, lat)
rupx, rupy = proj(rup.lons, rup.lats)
# Calculate U and T
dtypes = ['U', 'T']
dists = get_distance(dtypes, lats, lons, dep, rup)
targetU = np.array(
[[
-28.53228275, -28.36479713, -28.20139732, -28.0407734,
-27.88135558, -27.72144153, -27.55935946, -27.39362017,
-27.22300147, -27.04653062, -26.86338215, -26.67275638,
-26.47381287, -26.26569449, -26.04762427, -25.81902477,
-25.57961136, -25.32943282, -25.06885791, -24.79852214
],
[
-23.53750292, -23.3748086, -23.21793537, -23.06521934,
-22.91449689, -22.76331684, -22.60928211, -22.45042208,
-22.28542121, -22.11355532, -21.93435402, -21.74720475,
-21.55115107, -21.34497916, -21.12749377, -20.89781118,
-20.6555466, -20.40086149, -20.13439948, -19.85716145
],
[
-18.53499939, -18.37689929, -18.22732841, -18.08427516,
-17.94468687, -17.80472632, -17.66045115, -17.50880802,
-17.3484421, -17.17963435, -17.0032098, -16.81921732,
-16.62638972, -16.42258419, -16.20564846, -15.9741218,
-15.72753538, -15.4663671, -15.19180844, -14.9054813
],
[
-13.52283359, -13.36797542, -13.22589288, -13.09466537,
-12.97028551, -12.84653536, -12.71591089, -12.57212088,
-12.41335561, -12.24319318, -12.06681006, -11.88598424,
-11.69798166, -11.49796348, -11.28169605, -11.04691388,
-10.79343174, -10.52262594, -10.23677602, -9.93851158
],
[
-8.49936685, -8.34357094, -8.20650964, -8.08786858, -7.98403171,
-7.88628837, -7.78005273, -7.64833307, -7.48359988, -7.29992491,
-7.11862682, -6.94410189, -6.76618701, -6.5727842, -6.35634881,
-6.11465447, -5.84925708, -5.56369035, -5.26212482, -4.94857454
],
[
-3.46638168, -3.30047216, -3.15914418, -3.04618465, -2.96252939,
-2.90194067, -2.84436315, -2.75029014, -2.56983592, -2.33744275,
-2.1512136, -1.99833104, -1.84066354, -1.6541107, -1.43071517,
-1.17252753, -0.88592286, -0.57817222, -0.25582315, 0.07585567
],
[
1.56416954, 1.75393848, 1.9183586, 2.04909316, 2.13723278,
2.17776584, 2.18272501, 2.20967639, 2.37405656, 2.65073289,
2.80205222, 2.90973407, 3.05124404, 3.2505182, 3.50336116,
3.7967575, 4.11742779, 4.45465822, 4.80070204, 5.15033407
],
[
6.5633489, 6.78740885, 6.99419348, 7.17551069, 7.31963558,
7.4113505, 7.43666779, 7.40177458, 7.40517136, 7.58520044,
7.62013169, 7.71596777, 7.90558457, 8.17213015, 8.49008681,
8.83763176, 9.19937294, 9.56556659, 9.9305469, 10.29132309
],
[
11.48996073, 11.74301446, 11.99016964, 12.22782156, 12.44984059,
12.6446727, 12.78798484, 12.82584849, 12.61992833, 12.26579742,
12.32166685, 12.54665462, 12.86628045, 13.23578462, 13.62571822,
14.01882924, 14.40617707, 14.78388296, 15.15089889, 15.5076165
],
[
16.31383216, 16.57376544, 16.83189511, 17.08626411, 17.33309437,
17.56429108, 17.76005623, 17.85853532, 17.57101025, 17.32637346,
17.45075419, 17.77199513, 18.16933168, 18.58284635, 18.9891851,
19.37985879, 19.75324557, 20.11079653, 20.4549905, 20.78837053
],
[
21.03975749, 21.28450315, 21.5243142, 21.75603974, 21.97469496,
22.17298057, 22.34310053, 22.49668569, 22.73940191, 22.70030633,
22.95351405, 23.35967832, 23.75891016, 24.14867803, 24.51536915,
24.85878249, 25.18398203, 25.49615514, 25.79932964, 26.09638269
],
[
25.70484089, 25.92709225, 26.14280395, 26.35119497, 26.55363501,
26.75827099, 26.9915523, 27.31779086, 27.77993211, 27.71070831,
28.13624949, 28.723482, 29.25285078, 29.66404032, 30.00169474,
30.30044315, 30.57916576, 30.84804427, 31.1126134, 31.37586841
],
[
30.35406633, 30.5585145, 30.75843356, 30.95627127, 31.15811912,
31.3763124, 31.63114968, 31.94156189, 32.23691802, 32.38759301,
32.86915665, 33.83467935, 34.46125278, 34.89905345, 35.25111257,
35.55095664, 35.82150686, 36.07720619, 36.32643896, 36.57385362
],
[
35.0222379, 35.21734711, 35.41081942, 35.60589495, 35.80774808,
36.02313791, 36.25826988, 36.51619168, 36.81025966, 37.21777129,
37.86674108, 38.66578072, 39.25203723, 39.78060643, 40.20815617,
40.5606039, 40.86634527, 41.14457482, 41.40732554, 41.66197722
],
[
39.73046099, 39.92514041, 40.12152415, 40.32316112, 40.5350467,
40.76393316, 41.01937758, 41.3172128, 41.68596492, 42.16604148,
42.77622755, 43.447503, 44.03771478, 44.55012468, 45.00551259,
45.40376857, 45.75505135, 46.07204699, 46.36554362, 46.64361367
],
[
44.4876174, 44.68959464, 44.89710008, 45.11420443, 45.34646809,
45.60143197, 45.88932906, 46.22363997, 46.61975585, 47.0884227,
47.62307543, 48.1913408, 48.74937117, 49.26945799, 49.74327902,
50.17123158, 50.55810895, 50.91098842, 51.23731582, 51.54375617
],
[
49.29279265, 49.50696882, 49.73006999, 49.96625305, 50.22080319,
50.50022572, 50.81209441, 51.1642666, 51.56290694, 52.00913021,
52.49553006, 53.00565389, 53.51861282, 54.01614414, 54.48672101,
54.9254339, 55.33212663, 55.70951516, 56.06170563, 56.39317058
],
[
54.13906629, 54.3671694, 54.60643024, 54.86053563, 55.13377911,
55.43088558, 55.75658576, 56.1148189, 56.50752978, 56.93329478,
57.38640012, 57.85715119, 58.33367994, 58.80451404, 59.26065475,
59.69644542, 60.10938419, 60.49940252, 60.86803179, 61.21767916
],
[
59.01741908, 59.25887491, 59.51248349, 59.78119592, 60.06816694,
60.37651862, 60.70895927, 61.0672529, 61.45160192, 61.86010542,
62.28853397, 62.73062937, 63.17894547, 63.62598375, 64.06523791,
64.49185106, 64.90281064, 65.2967858, 65.67377362, 66.03469546
],
[
63.9193099, 64.17236414, 64.4376317, 64.71732366, 65.01362255,
65.32847988, 65.66334836, 66.0188704, 66.39457546, 66.7886684,
67.19800022, 67.61828012, 68.04451487, 68.47157851, 68.89476917,
69.31022713, 69.71515194, 70.10782673, 70.4875021, 70.85420436
]])
np.testing.assert_allclose(targetU, dists['U'], atol=0.01)
targetT = np.array([
[
-2.27427469e+01, -1.97498544e+01, -1.67512900e+01, -1.37464632e+01,
-1.07350712e+01, -7.71715083e+00, -4.69305811e+00, -1.66336318e+00,
1.37131605e+00, 4.41047613e+00, 7.45381136e+00, 1.05011799e+01,
1.35524779e+01, 1.66074913e+01, 1.96657949e+01, 2.27267294e+01,
2.57894503e+01, 2.88530154e+01, 3.19164798e+01, 3.49789747e+01
],
[
-2.30778766e+01, -2.00896906e+01, -1.70950973e+01, -1.40931667e+01,
-1.10834219e+01, -8.06600712e+00, -5.04171582e+00, -2.01179123e+00,
1.02248614e+00, 4.06025218e+00, 7.10129626e+00, 1.01459367e+01,
1.31946312e+01, 1.62475702e+01, 1.93044511e+01, 2.23644788e+01,
2.54265185e+01, 2.84892997e+01, 3.15515954e+01, 3.46123426e+01
],
[
-2.33971472e+01, -2.04144525e+01, -1.74245193e+01, -1.44256870e+01,
-1.14169177e+01, -8.39830615e+00, -5.37141115e+00, -2.33902937e+00,
6.95823925e-01, 3.73133431e+00, 6.76769593e+00, 9.80663091e+00,
1.28500821e+01, 1.58991008e+01, 1.89534737e+01, 2.20119662e+01,
2.50728111e+01, 2.81341606e+01, 3.11943854e+01, 3.42522163e+01
],
[
-2.36965870e+01, -2.07206976e+01, -1.77370901e+01, -1.47426715e+01,
-1.17347885e+01, -8.71247709e+00, -5.67801094e+00, -2.63761285e+00,
4.00625914e-01, 3.43182302e+00, 6.45782532e+00, 9.48491128e+00,
1.25187545e+01, 1.55616657e+01, 1.86127822e+01, 2.16694756e+01,
2.47286680e+01, 2.77876297e+01, 3.08443066e+01, 3.38973527e+01
],
[
-2.39698399e+01, -2.10022612e+01, -1.80281475e+01, -1.50423801e+01,
-1.20388157e+01, -9.01204040e+00, -5.96160398e+00, -2.89867328e+00,
1.52194374e-01, 3.17268218e+00, 6.17334725e+00, 9.17699572e+00,
1.21964990e+01, 1.52330975e+01, 1.82821226e+01, 2.13375815e+01,
2.43943933e+01, 2.74490375e+01, 3.04994435e+01, 3.35446330e+01
],
[
-2.42070742e+01, -2.12471979e+01, -1.82855675e+01, -1.53163304e+01,
-1.23296744e+01, -9.31127857e+00, -6.24535210e+00, -3.12882361e+00,
-2.24460581e-02, 2.95354485e+00, 5.89215412e+00, 8.86387424e+00,
1.18748249e+01, 1.49128245e+01, 1.79640055e+01, 2.10182501e+01,
2.40696313e+01, 2.71153177e+01, 3.01543919e+01, 3.31869788e+01
],
[
-2.43971375e+01, -2.14368866e+01, -1.84826148e+01, -1.55321207e+01,
-1.25786621e+01, -9.60654678e+00, -6.58612151e+00, -3.48118311e+00,
-3.16555025e-01, 2.61618307e+00, 5.53740540e+00, 8.52666510e+00,
1.15623361e+01, 1.46149780e+01, 1.76674294e+01, 2.07125025e+01,
2.37483764e+01, 2.67756033e+01, 2.97955606e+01, 3.28097430e+01
],
[
-2.45384925e+01, -2.15583842e+01, -1.85874288e+01, -1.56290738e+01,
-1.26867853e+01, -9.76140655e+00, -6.84407754e+00, -3.90089971e+00,
-8.41806596e-01, 2.14754495e+00, 5.18583472e+00, 8.26271822e+00,
1.13266091e+01, 1.43684333e+01, 1.73916223e+01, 2.04017469e+01,
2.34034936e+01, 2.64002111e+01, 2.93941282e+01, 3.23866586e+01
],
[
-2.46576775e+01, -2.16355610e+01, -1.86129545e+01, -1.55919156e+01,
-1.25763765e+01, -9.57306672e+00, -6.59044329e+00, -3.62352541e+00,
-5.92041388e-01, 2.33255341e+00, 5.29498494e+00, 8.24834463e+00,
1.11833819e+01, 1.41167617e+01, 1.70571082e+01, 2.00065102e+01,
2.29645946e+01, 2.59302937e+01, 2.89023967e+01, 3.18797332e+01
],
[
-2.48161623e+01, -2.17489533e+01, -1.86651328e+01, -1.55589864e+01,
-1.24224388e+01, -9.24466730e+00, -6.01521475e+00, -2.75148770e+00,
3.89519039e-01, 2.99589525e+00, 5.45696689e+00, 8.01247078e+00,
1.07291540e+01, 1.35565782e+01, 1.64461360e+01, 1.93723515e+01,
2.23222250e+01, 2.52881249e+01, 2.82650171e+01, 3.12494172e+01
],
[
-2.50857405e+01, -2.20002811e+01, -1.88926336e+01, -1.57550887e+01,
-1.25770789e+01, -9.34497451e+00, -6.04430316e+00, -2.67290100e+00,
5.40854953e-01, 2.30509492e+00, 3.58183843e+00, 6.23701436e+00,
9.28727128e+00, 1.23205706e+01, 1.53428945e+01, 1.83666035e+01,
2.13934954e+01, 2.44218171e+01, 2.74496472e+01, 3.04757209e+01
],
[
-2.55082697e+01, -2.24454912e+01, -1.93710045e+01, -1.62824768e+01,
-1.31767102e+01, -1.00469827e+01, -6.86985653e+00, -3.54681638e+00,
1.07062999e-01, 3.34891657e-01, -1.70694750e-01, 3.57896940e+00,
7.17013928e+00, 1.05232789e+01, 1.37976070e+01, 1.70230221e+01,
2.02076136e+01, 2.33576919e+01, 2.64794914e+01, 2.95785985e+01
],
[
-2.60778515e+01, -2.30695744e+01, -2.00684150e+01, -1.70790651e+01,
-1.41074315e+01, -1.11587507e+01, -8.23273307e+00, -5.33306966e+00,
-2.80144302e+00, -1.84760416e+00, -1.05368779e+00, 1.26163211e+00,
4.90086292e+00, 8.53883059e+00, 1.20996577e+01, 1.55589098e+01,
1.89237978e+01, 2.22114952e+01, 2.54390313e+01, 2.86203790e+01
],
[
-2.67537229e+01, -2.38123298e+01, -2.08964272e+01, -1.80168638e+01,
-1.51896230e+01, -1.24401995e+01, -9.81536176e+00, -7.41008520e+00,
-5.38073414e+00, -3.78262975e+00, -2.29669890e+00, -3.53057240e-01,
3.13642477e+00, 6.97021789e+00, 1.07026969e+01, 1.42945488e+01,
1.77655640e+01, 2.11406146e+01, 2.44409375e+01, 2.76832489e+01
],
[
-2.74832153e+01, -2.46028623e+01, -2.17593854e+01, -1.89653378e+01,
-1.62381218e+01, -1.36022404e+01, -1.10914555e+01, -8.74572618e+00,
-6.58963863e+00, -4.58336507e+00, -2.57607747e+00, -2.67233150e-01,
2.82788692e+00, 6.36737407e+00, 9.93334021e+00, 1.34440609e+01,
1.68846862e+01, 2.02577163e+01, 2.35710668e+01, 2.68337230e+01
],
[
-2.82199728e+01, -2.53838486e+01, -2.25869234e+01, -1.98388981e+01,
-1.71512612e+01, -1.45365893e+01, -1.20059297e+01, -9.56220853e+00,
-7.18799023e+00, -4.83006994e+00, -2.39120744e+00, 2.51308627e-01,
3.17331949e+00, 6.33022626e+00, 9.61428455e+00, 1.29426788e+01,
1.62705993e+01, 1.95770961e+01, 2.28539081e+01, 2.60992146e+01
],
[
-2.89332200e+01, -2.61222251e+01, -2.33461951e+01, -2.06105222e+01,
-1.79200485e+01, -1.52776479e+01, -1.26817390e+01, -1.01225741e+01,
-7.57801870e+00, -5.01122873e+00, -2.37434916e+00, 3.78303328e-01,
3.27093827e+00, 6.29527723e+00, 9.41912399e+00, 1.26046423e+01,
1.58204753e+01, 1.90448689e+01, 2.22643265e+01, 2.54712657e+01
],
[
-2.96082809e+01, -2.68067500e+01, -2.40331802e+01, -2.12894659e+01,
-1.85760763e+01, -1.58910124e+01, -1.32284735e+01, -1.05774862e+01,
-7.92111801e+00, -5.23724922e+00, -2.50179068e+00, 3.05790568e-01,
3.19666197e+00, 6.16975035e+00, 9.21353475e+00, 1.23109519e+01,
1.54443017e+01, 1.85982825e+01, 2.17611016e+01, 2.49243957e+01
],
[
-3.02420504e+01, -2.74395034e+01, -2.46578094e+01, -2.18967353e+01,
-1.91546206e+01, -1.64278219e+01, -1.37101816e+01, -1.09927140e+01,
-8.26378719e+00, -5.51007519e+00, -2.71836365e+00, 1.22111758e-01,
3.01754598e+00, 5.96851903e+00, 8.97043180e+00, 1.20150997e+01,
1.50927299e+01, 1.81935916e+01, 2.13090724e+01, 2.44321477e+01
],
[
-3.08377073e+01, -2.80281994e+01, -2.52335334e+01, -2.24524366e+01,
-1.96825082e+01, -1.69199811e+01, -1.41595768e+01, -1.13945492e+01,
-8.61701306e+00, -5.81861191e+00, -2.99148017e+00, -1.29317230e-01,
2.77170749e+00, 5.71249079e+00, 8.69110042e+00, 1.17033684e+01,
1.47437429e+01, 1.78061436e+01, 2.08846464e+01, 2.39739290e+01
]
])
np.testing.assert_allclose(targetT, dists['T'], atol=0.01)