dist = a_AS_dist[i]
dist = dist[dist>0]
mag = a_MS_mag[i]
# plot the histogram
HD_bins = np.arange(np.amin(np.log10(dist)), np.amax(np.log10(dist)), dPar['HD_binsize'])
HD_dist, HD_bins = np.histogram(np.log10(dist), HD_bins)
HD_bins = 10**HD_bins
HD_dist, HD_bins = np.array(list(zip(*zip(HD_dist, HD_bins))))
aBinSize = [bin*10**dPar['HD_binsize'] - bin for bin in HD_bins]
HD_dist /= aBinSize
HD_dist /= len(dist)
ax.loglog(HD_bins[HD_dist>0], HD_dist[HD_dist>0], '-',c=cols[i], mfc = 'none', mew = .2, label='Histogram')
# plot the rate
HD_bins, HD_rate = seis_utils.eqRate(dist, 24)
HD_rate /= len(dist)
#ax.loglog(HD_bins, HD_rate, 'r-',c=cols[i], lw=1, label='<m>=%.2f' % a_MS_mag[i])##TODO: nullify this line
# plot the smoothed rate
HD_bin_s, HD_rate_smoothed = seis_utils.eqlgRate(np.log10(dist),65)
HD_bin_s, HD_rate_smoothed=HD_bin_s[HD_rate_smoothed > 0], HD_rate_smoothed[HD_rate_smoothed > 0]
HD_rate_smoothed = scipy.signal.savgol_filter(HD_rate_smoothed,3,1)
##ax.loglog(HD_bin_s[HD_rate_smoothed>0],HD_rate_smoothed[HD_rate_smoothed>0],\
## 'b-', c=cols[i],lw=1.5, label='<m>=%.2f'% a_MS_mag[i]) ##TODO: use this line
"""
# plot Emily's fit
L = HD_bins[np.argmax(HD_dist)]
sel = HD_bins >= L
#C# create time vector --> use obspy UTCDateTime or mx.DateTime
a_t_decYr = np.zeros(m_EvInRmax[0].shape[0])
a_t_decYr2 = np.zeros(m_EvInRmax[0].shape[0])
for i in range(m_EvInRmax[0].shape[0]):
a_t_decYr[i] = seis_utils.dateTime2decYr([
m_EvInRmax[0, i], m_EvInRmax[1, i], m_EvInRmax[2, i], m_EvInRmax[3, i],
m_EvInRmax[4, i], m_EvInRmax[5, i]
])
#==================================3================================================
# power-law fitting (AS decay rate)
#===================================================================================
# subtract t MS from aftershock times - new vector has only AS with time relative to MS in days
a_tAS_day = (a_t_decYr[i_MS_ID + 1::] - a_t_decYr[i_MS_ID]) * 365.25
# compute rates
at_bin_AS, aN_bin_AS = seis_utils.eqRate(a_tAS_day, dPar['k'])
####A##### power law fit - least squares
sel_t = np.logical_and(at_bin_AS >= dPar['tmin'], at_bin_AS <= dPar['tmax'])
# only events within tmin and tmax, do log-transformation
f_p_LS, f_K_LS, __, __, __ = scipy.stats.linregress(np.log10(at_bin_AS[sel_t]),
np.log10(aN_bin_AS[sel_t]))
f_K_LS = 10**f_K_LS
print('Omori p-value (least-squares): ', round(f_p_LS, 1), 'K',
round(f_K_LS, 1))
####A##### power law fit - least squares
# for dN/dt = K*t**(-p); remember that we're solving a problem analogous to:
# y_hat = alpha * t**beta, with alpha = 10**a and beta = b
####B##### power law fit - maximum likelihood
dOm = omori.fit_omoriMLE(a_tAS_day[a_tAS_day > 0],
bounds=dPar['a_limit'],
par0=dPar['a_par0'],
a_MS_mag = asSets['a_MS_mag']
a_AS_dist = asSets['a_AS_dist']
i = 0
for f_MSmag, dist in zip(a_MS_mag, a_AS_dist):
# ==================================3=============================================
# plot distance decay
# ================================================================================
name = '<m>=%.2f' % f_MSmag
fig1 = plt.figure(1)
ax1 = plt.subplot(111)
ax1.set_title(name)
for k in [20, 50, 100, 200]:
a_r_bin, a_dens = seis_utils.eqRate(dist, k)
ax1.loglog(a_r_bin, a_dens, 'o', label=str(k), mew=0)
#--------- plot -1.4 slope from felzer and Brodsky for comparison-----------------
gamma = -1.4
selPeak = a_dens == a_dens.max()
preFac = a_dens[selPeak] / (a_r_bin[selPeak]**gamma)
ax1.plot(a_r_bin, preFac * a_r_bin**gamma, 'w-', lw=2.5)
ax1.plot(a_r_bin,
preFac * a_r_bin**gamma,
'k--',
label='Dens ~ r ^ %.1f' % (gamma))
# ==================================4=============================================
# highlight mainshock rupture dimension
# ================================================================================
l0, sigma = 0.01, 0.44
f_L1 = l0 * 10**(sigma * f_MSmag) # Hainzl , Moradpour et al.
catChild.copy(eqCatMc)
catParent.copy(eqCatMc)
# catChild, catPar = create_parent_child_cat( projCat, dNND)
catChild.selEventsFromID(dNND['aEqID_c'], repeats=True)
catParent.selEventsFromID(dNND['aEqID_p'], repeats=True)
print('size of parent catalog', catParent.size(), 'size of offspring cat',
catChild.size())
## l
dsigma = 5e6
Mw = catParent.data['Mag']
M0 = 10**(1.5 * (Mw + 6.03))
l = 0.001 * (7 / 16 * M0 / dsigma)**(1 / 3)
## hd
HD = dNND['aHD']
## Rl
aRl = HD / l
print("haversine distance:", HD)
print("rupture dimension", l)
###histogram
aBins = np.arange(0, 30, dPar['eta_binsize'])
aHist, aBins = np.histogram(aRl, aBins)
aHist, aBins = np.array(list(
zip(*zip(aHist, aBins)))) # cut to same length
aRate_bin, aRate = seis_utils.eqRate(aRl, k)
aHist /= dPar['eta_binsize']
# =================================4==============================================
# plot histogram
# ================================================================================
#myplot.plot_rate_pd(aBins, aHist, aRate_bin, aRate,curr_Mc,'a_hs',dPar['eta_binsize'])
myplot.plot_loglog(aBins, aHist, aRate_bin, aRate, curr_Mc, 'b_hs', k)
'q': 0.35, 'd': 1.2, 'gamma': 0.6,
}
# =================================1==============================================
# load catalog and select
# ================================================================================
eqcat = EqCat()
dCluster = data_utils.loadmat(input_file)
a_MS_mag = dCluster['a_MS_mag']
a_AS_dist = dCluster['a_AS_dist']
a_AS_Rm = np.zeros(len(a_MS_mag)) # maxima of distance distribution
# find the maxima of each set
for i, dist in enumerate(a_AS_dist):
aRateBin_HD, aRate_HD = seis_utils.eqRate(dist, 2 * int(len(dist) / 30)) # ,minK=70
aRate_HD /= len(dist)
sel = aRateBin_HD > 0.1
aRateBin_HD = aRateBin_HD[sel]
aRate_HD = aRate_HD[sel]
iRm = np.argmax(aRate_HD)
a_AS_Rm[i] = aRateBin_HD[iRm]
# =================================3==============================================
# fix single power law
# ================================================================================
print(a_AS_Rm[-1])
sigma, lgC, __, __, __ = scipy.stats.linregress(a_MS_mag, np.log10(a_AS_Rm))
C = 10 ** lgC # unit: km--> m
print("C:%.5f, sigma:%.2f" % (C, sigma))
dsigma = 5e6
Mw = catParent.data['Mag']
M0 = 10**(1.5 * (Mw + 6.03))
l = 0.001 * (7 / 16 * M0 / dsigma)**(1 / 3)
## hd
HD = dNND['aHD']
## Rl
aRl = HD / l
#print("haversine distance:", HD)
#print("rupture dimension", l)
###histogram
aBins = np.arange(0, 30, dPar['eta_binsize'])
aHist, aBins = np.histogram(aRl, aBins)
aHist, aBins = np.array(list(
zip(*zip(aHist, aBins)))) # cut to same length
aRate_bin, aRate = seis_utils.eqRate(aRl, k)
aHist /= dPar['eta_binsize']
# ================================================================================
# bigger parent event pairs
# ================================================================================
# select event pairs with parent event larger than M_pt
sel = catParent.data['Mag'] >= dPar['M_pt']
catChild.selEventsFromID(dNND['aEqID_c'][sel], repeats=True)
catParent.selEventsFromID(dNND['aEqID_p'][sel], repeats=True)
print('after::: size of parent catalog', catParent.size(),
'size of offspring cat', catChild.size())
## l
Mw1 = catParent.data['Mag']
M01 = 10**(1.5 * (Mw1 + 6.03))
l1 = 0.001 * (7 / 16 * M01 / dsigma)**(1 / 3)
## hd
# ================================================================================
# select only the clustering event pairs
sel_cl = np.log10(dNND['aNND']) <= -5 #-4.7
# HD
HD = dNND['aHD'][sel_cl]
print('catalog size: ', len(HD))
# ==================================3=============================================
# plot distance decay
# ================================================================================
fig1 = plt.figure(1)
ax1 = plt.subplot(111)
ax1.set_title(name)
for k in [20, 50, 100, 200]:
a_r_bin, a_dens = seis_utils.eqRate(dNND['aHD'], k)
ax1.loglog(a_r_bin, a_dens, 'o', label=str(k), mew=0)
#--------- plot -1.4 slope from felzer and Brodsky for comparison-----------------
gamma = -1.4
selPeak = a_dens == a_dens.max()
preFac = a_dens[selPeak] / (a_r_bin[selPeak]**gamma)
ax1.plot(a_r_bin, preFac * a_r_bin**gamma, 'w-', lw=2.5)
ax1.plot(a_r_bin,
preFac * a_r_bin**gamma,
'k--',
label='Dens ~ r ^ %.1f' % (gamma))
# ==================================4=============================================
# highlight mainshock rupture dimension
# ================================================================================
# find MS magnitude
print(eqCat.data.keys(), asCat.data.keys())