def pole_position(start, euler_1, rate_1, euler_2, rate_2, switchpoint, time):
euler_pole_1 = mcplates.EulerPole(euler_1[0], euler_1[1], rate_1)
euler_pole_2 = mcplates.EulerPole(euler_2[0], euler_2[1], rate_2)
start_pole = mcplates.PaleomagneticPole(start[0], start[1], age=time)
if time <= switchpoint:
start_pole.rotate(euler_pole_1, euler_pole_1.rate * time)
else:
start_pole.rotate(euler_pole_1, euler_pole_1.rate * switchpoint)
start_pole.rotate(euler_pole_2,
euler_pole_2.rate * (time - switchpoint))
lon_lat = np.array([start_pole.longitude, start_pole.latitude])
return lon_lat
def plot_trace(trace):
euler_1_directions = trace('euler_1')[:]
rates_1 = trace('rate_1')[:]
euler_2_directions = trace('euler_2')[:]
rates_2 = trace('rate_2')[:]
start_directions = trace('start')[:]
switchpoints = trace('switchpoint')[:]
interval = max([1, int(len(rates_1) / 1000)])
#ax = plt.axes(projection = ccrs.Orthographic(0.,30.))
ax = plt.axes(projection=ccrs.Mollweide(0.))
ax.gridlines()
ax.set_global()
mcplates.plot.plot_distribution(ax, euler_1_directions[:, 0],
euler_1_directions[:, 1])
mcplates.plot.plot_distribution(ax, euler_2_directions[:, 0],
euler_2_directions[:, 1])
age_list = np.linspace(ages[0], ages[-1], 100)
pathlons = np.empty_like(age_list)
pathlats = np.empty_like(age_list)
for start, e1, r1, e2, r2, switch \
in zip(start_directions[::interval],
euler_1_directions[::interval], rates_1[::interval],
euler_2_directions[::interval], rates_2[::interval],
switchpoints[::interval]):
for i, a in enumerate(age_list):
lon_lat = pole_position(start, e1, r1, e2, r2, switch, a)
pathlons[i] = lon_lat[0]
pathlats[i] = lon_lat[1]
ax.plot(pathlons,
pathlats,
color='b',
transform=ccrs.PlateCarree(),
alpha=0.05)
for p in lon_lats:
pole = mcplates.PaleomagneticPole(p[0], p[1], angular_error=10.)
pole.plot(ax)
plt.show()
def plot_result():
ax = plt.axes(projection = ccrs.Orthographic(0.,-30.))
#ax = plt.axes(projection = ccrs.Mollweide(0.))
ax.gridlines()
ax.set_global()
direction_samples = path.euler_directions()
for directions in direction_samples:
mcplates.plot.plot_distribution( ax, directions[:,0], directions[:,1])
pathlons, pathlats = path.compute_synthetic_paths(n=100)
for pathlon,pathlat in zip(pathlons,pathlats):
ax.plot(pathlon,pathlat, transform=ccrs.PlateCarree(), color='b', alpha=0.05 )
for p in lon_lats:
pole = mcplates.PaleomagneticPole( p[0], p[1], angular_error=10. )
pole.plot(ax)
plt.show()
def create_model(n_euler_rotations, use_tpw):
if n_euler_rotations < 0:
raise Exception(
"Number of plate Euler rotations must be greater than or equal to zero"
)
if use_tpw != False and use_tpw != True:
raise Exception("Must enter 'true' or 'false' for whether to use TPW")
if n_euler_rotations == 0 and use_tpw == False:
raise Exception(
"Must use either TPW or plate Euler rotations, or both")
print("Fitting Keweenawan APW track with"\
+("out TPW and " if use_tpw == False else " TPW and ")\
+str(n_euler_rotations)+" Euler rotation"\
+ ("" if n_euler_rotations == 1 else "s") )
data = pd.read_csv("pole_means.csv")
# Give unnamed column an appropriate name
data.rename(columns={'Unnamed: 0': 'Name',\
'Unnamed: 14': 'GaussianOrUniform'},\
inplace=True)
data = data[data.Name !=
'Osler_N'] #Huge error, does not contribute much to the model
data = data[data.PoleName !=
'Abitibi'] # Standstill at the beginning, not realistic to fit
data = data[data.PoleName !=
'Haliburton'] #Much younger, far away pole, difficutlt to fit
data.sort_values('AgeNominal', ascending=False, inplace=True)
poles = []
pole_names = []
pole_colors = []
for i, row in data.iterrows():
pole_lat = row['PLat']
pole_lon = row['PLon'] - lon_shift
a95 = row['A95']
age = row['AgeNominal']
if row['GaussianOrUniform'] == 'gaussian':
sigma_age = row['Gaussian_2sigma'] / 2.
elif row['GaussianOrUniform'] == 'uniform':
sigma_age = (row['AgeLower'], row['AgeUpper'])
else:
raise Exception("Unrecognized age error type")
pole = mcplates.PaleomagneticPole(pole_lon,
pole_lat,
angular_error=a95,
age=age,
sigma_age=sigma_age)
poles.append(pole)
pole_names.append(row['PoleName'])
pole_colors.append(row['color'])
tpw_str = 'true' if use_tpw else 'false'
prefix = 'keweenawan_' + str(n_euler_rotations) + '_' + tpw_str
path = mcplates.APWPath(prefix, poles, n_euler_rotations)
tpw_rate_scale = 2.5 if use_tpw else None
path.create_model(site_lon_lat=(slon, slat), watson_concentration=0.0,\
rate_scale=2.5, tpw_rate_scale=tpw_rate_scale)
return path, poles, pole_names, pole_colors
data.sort_values('HIGHAGE', ascending=False, inplace=True)
# Add poles from Australia pole list
poles = []
pole_names = []
for i, row in data.iterrows():
pole_lat = row['PLAT']
pole_lon = row['PLONG'] - lon_shift
a95 = np.sqrt(row['DP'] * row['DM'])
age = (row['HIGHAGE'] + row['LOWAGE']) / 2.
sigma_age = (row['LOWAGE'], row['HIGHAGE'])
pole = mcplates.PaleomagneticPole(pole_lon,
pole_lat,
angular_error=a95,
age=age,
sigma_age=sigma_age)
poles.append(pole)
pole_names.append(row['ROCKNAME'])
# Add pole with low error for present day pole
poles.append(
mcplates.PaleomagneticPole(0.,
90.,
angular_error=1.,
age=0.,
sigma_age=0.01))
# Reference position on the Australian continent
slat = -25.3 # Uluru lat
start_age = 50.
hidden_start_pole = [0., 90.]
hidden_euler_pole = [40., -20.]
hidden_euler_rate = 1.5
#Make a dummy APW path to create the synthetic data
dummy_pole_position_fn = mcplates.APWPath.generate_pole_position_fn(
n_euler_poles, start_age)
pole_list = []
for a in ages:
lon_lat = dummy_pole_position_fn(hidden_start_pole, a, 0.0, 0.0,
hidden_euler_pole, hidden_euler_rate)
pole_list.append(
mcplates.PaleomagneticPole(lon_lat[0],
lon_lat[1],
angular_error=5.,
age=a,
sigma_age=0.01))
for p in pole_list[1:-1]:
p.plot(ax, color='b')
#Make a plate
times = np.linspace(min(ages), max(ages), 100.)
pb1_lon = np.empty_like(times)
pb1_lat = np.empty_like(times)
pb2_lon = np.empty_like(times)
pb2_lat = np.empty_like(times)
for i, t in enumerate(times):
start1 = (30., 60.)
start2 = (40., 15.)
lon_lat = dummy_pole_position_fn(start1, t, 0.0, 0.0, hidden_euler_pole,
import matplotlib.pyplot as plt import cartopy.crs as ccrs import mcplates pole1 = mcplates.PaleomagneticPole(10., 30., angular_error=30.) pole2 = mcplates.PaleomagneticPole(20., 60., angular_error=20.) pole3 = mcplates.PaleomagneticPole(30., 80., angular_error=10.) ax = plt.axes(projection=ccrs.Orthographic(30., 30.)) ax.set_global() ax.gridlines() pole1.plot(ax, color='r') pole2.plot(ax, color='g') pole3.plot(ax, color='b') plt.show()
import cartopy.crs as ccrs
import pymc
import mcplates
dbname = 'pickles/apw.pickle'
# Generate a synthetic data set
ages =[0.,10.,20.,30.,40]
sigma_ages = [2., 2., 2., 2., [38.,43.]]
lon_lats = [ [300., -20.], [340.,0.], [0.,30.], [20., 0.], [60.,-20.]]
poles = []
for a, s, ll in zip(ages, sigma_ages, lon_lats):
pole = mcplates.PaleomagneticPole( ll[0], ll[1], angular_error=10., age=a, sigma_age=s)
poles.append(pole)
path = mcplates.APWPath( 'apw', poles, 2 )
path.create_model()
def plot_result():
ax = plt.axes(projection = ccrs.Orthographic(0.,-30.))
#ax = plt.axes(projection = ccrs.Mollweide(0.))
ax.gridlines()
ax.set_global()
direction_samples = path.euler_directions()
for directions in direction_samples:
mcplates.plot.plot_distribution( ax, directions[:,0], directions[:,1])
dbname = 'one_euler_pole_b'
n_euler_poles=1
# Generate a synthetic data set
ages = [60., 80., 100., 120.]
start_age = 120.
hidden_start_pole = [30., 90.]
hidden_euler_pole = [0., 0.]
hidden_euler_rate = 1.
#Make a dummy APW path to create the synthetic data
dummy_pole_position_fn = mcplates.APWPath.generate_pole_position_fn( n_euler_poles, start_age)
pole_list = []
for a in ages:
lon_lat = dummy_pole_position_fn(hidden_start_pole, a, 0.0, 0.0, hidden_euler_pole, hidden_euler_rate)
pole_list.append( mcplates.PaleomagneticPole( lon_lat[0], lon_lat[1], angular_error = 10., age=a, sigma_age = 0.01))
path = mcplates.APWPath( dbname, pole_list, n_euler_poles)
path.create_model(watson_concentration=0.0, rate_scale = 2.5)
def plot_result():
fig = plt.figure( figsize=(8,4) )
ax = fig.add_subplot(1,2,1, projection = ccrs.Orthographic(-30.,15.))
ax.gridlines()
ax.set_global()
colors = itertools.cycle([cmap_red, cmap_green])
direction_samples = path.euler_directions()
for directions in direction_samples:
