def setUp(self):
self.model = IsotropicGaussian()
# Setup simple grid
[gx, gy] = np.meshgrid(np.arange(35.5, 40., 0.5),
np.arange(40.5, 45., 0.5))
ngp = np.shape(gx)[0] * np.shape(gx)[1]
gx = np.reshape(gx, [ngp, 1])
gy = np.reshape(gy, [ngp, 1])
depths = 10. * np.ones(ngp)
self.data = np.column_stack(
[gx, gy, depths, np.zeros(ngp, dtype=float)])
def test_analysis_Frankel_comparison(self):
'''
To test the run_analysis function we compare test results with those
from Frankel's fortran implementation, under the same conditions
'''
self.grid_limits = [-128., -113.0, 0.2, 30., 43.0, 0.2, 0., 100., 100.]
comp_table = np.array([[1933., 4.0], [1900., 5.0], [1850., 6.0],
[1850., 7.0]])
config = {'Length_Limit': 3., 'BandWidth': 50., 'increment': 0.1}
self.model = SmoothedSeismicity(self.grid_limits, bvalue=0.8)
self.catalogue = Catalogue()
frankel_catalogue = np.genfromtxt(
os.path.join(BASE_PATH, FRANKEL_TEST_CATALOGUE))
self.catalogue.data['magnitude'] = frankel_catalogue[:, 0]
self.catalogue.data['longitude'] = frankel_catalogue[:, 1]
self.catalogue.data['latitude'] = frankel_catalogue[:, 2]
self.catalogue.data['depth'] = frankel_catalogue[:, 3]
self.catalogue.data['year'] = frankel_catalogue[:, 4]
self.catalogue.end_year = 2006
frankel_results = np.genfromtxt(
os.path.join(BASE_PATH, FRANKEL_OUTPUT_FILE))
# Run analysis
output_data = self.model.run_analysis(
self.catalogue,
config,
completeness_table=comp_table,
smoothing_kernel=IsotropicGaussian())
self.assertTrue(
fabs(np.sum(output_data[:, -1]) -
np.sum(output_data[:, -2])) < 1.0)
self.assertTrue(fabs(np.sum(output_data[:, -1]) - 390.) < 1.0)
def setUp(self):
self.model = IsotropicGaussian()
# Setup simple grid
[gx, gy] = np.meshgrid(np.arange(35.5, 40., 0.5),
np.arange(40.5, 45., 0.5))
ngp = np.shape(gx)[0] * np.shape(gx)[1]
gx = np.reshape(gx, [ngp, 1])
gy = np.reshape(gy, [ngp, 1])
depths = 10. * np.ones(ngp)
self.data = np.column_stack([gx, gy, depths,
np.zeros(ngp, dtype=float)])
def run_analysis(self,
catalogue,
config,
completeness_table=None,
smoothing_kernel=None):
'''
Runs an analysis of smoothed seismicity in the manner
originally implemented by Frankel (1995)
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param dict config:
Configuration settings of the algorithm:
* 'Length_Limit' - Maximum number of bandwidths for use in
smoothing (Float)
* 'BandWidth' - Bandwidth (km) of the Smoothing Kernel (Float)
* 'increment' - Output incremental (True) or cumulative a-value
(False)
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param smoothing_kernel:
Smoothing kernel as instance of :class:
`openquake.hmtk.seismicity.smoothing.kernels.base.BaseSmoothingKernel`
:returns:
Full smoothed seismicity data as np.ndarray, of the form
[Longitude, Latitude, Depth, Observed, Smoothed]
'''
self.catalogue = catalogue
if smoothing_kernel:
self.kernel = smoothing_kernel
else:
self.kernel = IsotropicGaussian()
# If no grid limits are specified then take from catalogue
if isinstance(self.grid_limits, list):
self.grid_limits = Grid.make_from_list(self.grid_limits)
assert self.grid_limits['xmax'] >= self.grid_limits['xmin']
assert self.grid_limits['xspc'] > 0.0
assert self.grid_limits['ymax'] >= self.grid_limits['ymin']
assert self.grid_limits['yspc'] > 0.0
elif isinstance(self.grid_limits, float):
self.grid_limits = Grid.make_from_catalogue(
self.catalogue, self.grid_limits,
config['Length_Limit'] * config['BandWidth'])
completeness_table, mag_inc = utils.get_even_magnitude_completeness(
completeness_table, self.catalogue)
end_year = self.catalogue.end_year
# Get Weichert factor
t_f, _ = utils.get_weichert_factor(self.beta, completeness_table[:, 1],
completeness_table[:, 0], end_year)
# Get the grid
self.create_3D_grid(self.catalogue, completeness_table, t_f, mag_inc)
if config['increment']:
# Get Hermann adjustment factors
fval, fival = utils.hermann_adjustment_factors(
self.bval, completeness_table[0, 1], config['increment'])
self.data[:, -1] = fval * fival * self.data[:, -1]
# Apply smoothing
smoothed_data, sum_data, sum_smooth = self.kernel.smooth_data(
self.data, config, self.use_3d)
print('Smoothing Total Rate Comparison - '
'Observed: %.6g, Smoothed: %.6g' % (sum_data, sum_smooth))
self.data = np.column_stack([self.data, smoothed_data])
return self.data
class SmoothedSeismicity(object):
'''
Class to implement an analysis of Smoothed Seismicity, including the
grid counting of data and the smoothing.
:param np.ndarray grid:
Observed count in each cell [Long., Lat., Depth., Count]
:param catalogue:
Valid instance of the :class: openquake.hmtk.seismicity.catalogue.Catalogue
:param bool use_3d:
Decide if analysis is 2-D (False) or 3-D (True). If 3-D then distances
will use hypocentral distance, otherwise epicentral distance
:param float bval:
b-value
:param float beta:
Beta value for exponential form (beta = bval * log(10.))
:param np.ndarray data:
Smoothed seismicity output
:param dict grid_limits:
Limits ot the grid used for defining the cells
'''
def __init__(self, grid_limits, use_3d=False, bvalue=None):
'''
Instatiate class with a set of grid limits
:param grid_limits:
It could be a float (in that case the grid is computed from the
catalogue with the given spacing).
Or an array of the form:
[xmin, xmax, spcx, ymin, ymax, spcy, zmin, spcz]
:param bool use_3d:
Choose whether to use hypocentral distances for smoothing or only
epicentral
:param float bval:
b-value for analysis
'''
self.grid = None
self.catalogue = None
self.use_3d = use_3d
self.bval = bvalue
if self.bval:
self.beta = self.bval * log(10.)
else:
self.beta = None
self.data = None
self.grid_limits = grid_limits
self.kernel = None
def run_analysis(self,
catalogue,
config,
completeness_table=None,
smoothing_kernel=None):
'''
Runs an analysis of smoothed seismicity in the manner
originally implemented by Frankel (1995)
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param dict config:
Configuration settings of the algorithm:
* 'Length_Limit' - Maximum number of bandwidths for use in
smoothing (Float)
* 'BandWidth' - Bandwidth (km) of the Smoothing Kernel (Float)
* 'increment' - Output incremental (True) or cumulative a-value
(False)
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param smoothing_kernel:
Smoothing kernel as instance of :class:
`openquake.hmtk.seismicity.smoothing.kernels.base.BaseSmoothingKernel`
:returns:
Full smoothed seismicity data as np.ndarray, of the form
[Longitude, Latitude, Depth, Observed, Smoothed]
'''
self.catalogue = catalogue
if smoothing_kernel:
self.kernel = smoothing_kernel
else:
self.kernel = IsotropicGaussian()
# If no grid limits are specified then take from catalogue
if isinstance(self.grid_limits, list):
self.grid_limits = Grid.make_from_list(self.grid_limits)
assert self.grid_limits['xmax'] >= self.grid_limits['xmin']
assert self.grid_limits['xspc'] > 0.0
assert self.grid_limits['ymax'] >= self.grid_limits['ymin']
assert self.grid_limits['yspc'] > 0.0
elif isinstance(self.grid_limits, float):
self.grid_limits = Grid.make_from_catalogue(
self.catalogue, self.grid_limits,
config['Length_Limit'] * config['BandWidth'])
completeness_table, mag_inc = utils.get_even_magnitude_completeness(
completeness_table, self.catalogue)
end_year = self.catalogue.end_year
# Get Weichert factor
t_f, _ = utils.get_weichert_factor(self.beta, completeness_table[:, 1],
completeness_table[:, 0], end_year)
# Get the grid
self.create_3D_grid(self.catalogue, completeness_table, t_f, mag_inc)
if config['increment']:
# Get Hermann adjustment factors
fval, fival = utils.hermann_adjustment_factors(
self.bval, completeness_table[0, 1], config['increment'])
self.data[:, -1] = fval * fival * self.data[:, -1]
# Apply smoothing
smoothed_data, sum_data, sum_smooth = self.kernel.smooth_data(
self.data, config, self.use_3d)
print('Smoothing Total Rate Comparison - '
'Observed: %.6g, Smoothed: %.6g' % (sum_data, sum_smooth))
self.data = np.column_stack([self.data, smoothed_data])
return self.data
def create_2D_grid_simple(self,
longitude,
latitude,
year,
magnitude,
completeness_table,
t_f=1.,
mag_inc=0.1):
'''
Generates the grid from the limits using an approach closer to that of
Frankel (1995)
:param numpy.ndarray longitude:
Vector of earthquake longitudes
:param numpy.ndarray latitude:
Vector of earthquake latitudes
:param numpy.ndarray year:
Vector of earthquake years
:param numpy.ndarray magnitude:
Vector of earthquake magnitudes
:param numpy.ndarray completeness_table:
Completeness table
:param float t_f:
Weichert adjustment factor
:returns:
Two-dimensional spatial grid of observed rates
'''
assert mag_inc > 0.
xlim = np.ceil((self.grid_limits['xmax'] - self.grid_limits['xmin']) /
self.grid_limits['xspc'])
ylim = np.ceil((self.grid_limits['ymax'] - self.grid_limits['ymin']) /
self.grid_limits['yspc'])
ncolx = int(xlim)
ncoly = int(ylim)
grid_count = np.zeros(ncolx * ncoly, dtype=float)
for iloc in range(0, len(longitude)):
dlon = (longitude[iloc] - self.grid_limits['xmin']) /\
self.grid_limits['xspc']
if (dlon < 0.) or (dlon > xlim):
# Earthquake outside longitude limits
continue
xcol = int(dlon)
if xcol == ncolx:
# If longitude is directly on upper grid line then retain
xcol = ncolx - 1
dlat = fabs(self.grid_limits['ymax'] - latitude[iloc]) /\
self.grid_limits['yspc']
if (dlat < 0.) or (dlat > ylim):
# Earthquake outside latitude limits
continue
ycol = int(dlat) # Correct for floating precision
if ycol == ncoly:
# If latitude is directly on upper grid line then retain
ycol = ncoly - 1
kmarker = (ycol * int(xlim)) + xcol
adjust = _get_adjustment(magnitude[iloc], year[iloc],
completeness_table[0, 1],
completeness_table[:, 0], t_f, mag_inc)
if adjust:
grid_count[kmarker] = grid_count[kmarker] + adjust
return grid_count
def create_3D_grid(self,
catalogue,
completeness_table,
t_f=1.0,
mag_inc=0.1):
'''
Counts the earthquakes observed in a three dimensional grid
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param float t_f:
Weichert adjustment factor
:param float mag_inc:
Increment of the completeness magnitude (rendered 0.1)
:returns:
Three-dimensional spatial grid of observed rates (or two dimensional
if only one depth layer is considered)
'''
x_bins = np.arange(self.grid_limits['xmin'], self.grid_limits['xmax'],
self.grid_limits['xspc'])
if x_bins[-1] < self.grid_limits['xmax']:
x_bins = np.hstack([x_bins, x_bins[-1] + self.grid_limits['xspc']])
y_bins = np.arange(self.grid_limits['ymin'], self.grid_limits['ymax'],
self.grid_limits['yspc'])
if y_bins[-1] < self.grid_limits['ymax']:
y_bins = np.hstack([y_bins, y_bins[-1] + self.grid_limits['yspc']])
z_bins = np.arange(self.grid_limits['zmin'],
self.grid_limits['zmax'] + self.grid_limits['zspc'],
self.grid_limits['zspc'])
if z_bins[-1] < self.grid_limits['zmax']:
z_bins = np.hstack([z_bins, z_bins[-1] + self.grid_limits['zspc']])
# Define centre points of grid cells
gridx, gridy = np.meshgrid((x_bins[1:] + x_bins[:-1]) / 2.,
(y_bins[1:] + y_bins[:-1]) / 2.)
n_x, n_y = np.shape(gridx)
gridx = np.reshape(gridx, [n_x * n_y, 1])
gridy = np.reshape(np.flipud(gridy), [n_x * n_y, 1])
# Only one depth range
idx = np.logical_and(catalogue.data['depth'] >= z_bins[0],
catalogue.data['depth'] < z_bins[1])
mid_depth = (z_bins[0] + z_bins[1]) / 2.
data_grid = np.column_stack([
gridx, gridy, mid_depth * np.ones(n_x * n_y, dtype=float),
self.create_2D_grid_simple(catalogue.data['longitude'][idx],
catalogue.data['latitude'][idx],
catalogue.data['year'][idx],
catalogue.data['magnitude'][idx],
completeness_table, t_f, mag_inc)
])
if len(z_bins) < 3:
# Only one depth range
self.data = data_grid
return
# Multiple depth layers - append to grid
for iloc in range(1, len(z_bins) - 1):
idx = np.logical_and(catalogue.data['depth'] >= z_bins[iloc],
catalogue.data['depth'] < z_bins[iloc + 1])
mid_depth = (z_bins[iloc] + z_bins[iloc + 1]) / 2.
temp_grid = np.column_stack([
gridx, gridy, mid_depth * np.ones(n_x * n_y, dtype=float),
self.create_2D_grid_simple(catalogue.data['longitude'][idx],
catalogue.data['latitude'][idx],
catalogue.data['year'][idx],
catalogue.data['magnitude'][idx],
completeness_table, t_f, mag_inc)
])
data_grid = np.vstack([data_grid, temp_grid])
self.data = data_grid
def write_to_csv(self, filename):
'''
Exports to simple csv
:param str filename:
Path to file for export
'''
fid = open(filename, 'wt')
# Create header list
header_info = [
'Longitude', 'Latitude', 'Depth', 'Observed Count',
'Smoothed Rate', 'b-value'
]
writer = csv.DictWriter(fid, fieldnames=header_info)
headers = dict((name0, name0) for name0 in header_info)
# Write to file
writer.writerow(headers)
for row in self.data:
# institute crude compression by omitting points with no seismicity
# and taking advantage of the %g format
if row[4] == 0:
continue
row_dict = {
'Longitude': '%g' % row[0],
'Latitude': '%g' % row[1],
'Depth': '%g' % row[2],
'Observed Count': '%d' % row[3],
'Smoothed Rate': '%.6g' % row[4],
'b-value': '%g' % self.bval
}
writer.writerow(row_dict)
fid.close()
class TestIsotropicGaussian(unittest.TestCase):
'''
Simple tests the of Isotropic Gaussian Kernel
(as implemented by Frankel (1995))
'''
def setUp(self):
self.model = IsotropicGaussian()
# Setup simple grid
[gx, gy] = np.meshgrid(np.arange(35.5, 40., 0.5),
np.arange(40.5, 45., 0.5))
ngp = np.shape(gx)[0] * np.shape(gx)[1]
gx = np.reshape(gx, [ngp, 1])
gy = np.reshape(gy, [ngp, 1])
depths = 10. * np.ones(ngp)
self.data = np.column_stack(
[gx, gy, depths, np.zeros(ngp, dtype=float)])
def test_kernel_single_event(self):
# ensure kernel is smoothing values correctly for a single event
self.data[50, 3] = 1.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(
os.path.join(BASE_PATH, TEST_1_VALUE_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 1.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 3 dp
self.assertAlmostEqual(sum_data, sum_smooth, 3)
def test_kernel_multiple_event(self):
# ensure kernel is smoothing values correctly for multiple events
self.data[[5, 30, 65], 3] = 1.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(
os.path.join(BASE_PATH, TEST_3_VALUE_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 3.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 3 dp
self.assertAlmostEqual(sum_data, sum_smooth, 2)
def test_kernel_single_event_3d(self):
# ensure kernel is smoothing values correctly for a single event
self.data[50, 3] = 1.
self.data[50, 2] = 20.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(
os.path.join(BASE_PATH, TEST_1_VALUE_3D_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config, is_3d=True)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 1.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 2 dp
self.assertAlmostEqual(sum_data, sum_smooth, 2)
class TestIsotropicGaussian(unittest.TestCase):
'''
Simple tests the of Isotropic Gaussian Kernel
(as implemented by Frankel (1995))
'''
def setUp(self):
self.model = IsotropicGaussian()
# Setup simple grid
[gx, gy] = np.meshgrid(np.arange(35.5, 40., 0.5),
np.arange(40.5, 45., 0.5))
ngp = np.shape(gx)[0] * np.shape(gx)[1]
gx = np.reshape(gx, [ngp, 1])
gy = np.reshape(gy, [ngp, 1])
depths = 10. * np.ones(ngp)
self.data = np.column_stack([gx, gy, depths,
np.zeros(ngp, dtype=float)])
def test_kernel_single_event(self):
# ensure kernel is smoothing values correctly for a single event
self.data[50, 3] = 1.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(os.path.join(BASE_PATH,
TEST_1_VALUE_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 1.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 3 dp
self.assertAlmostEqual(sum_data, sum_smooth, 3)
def test_kernel_multiple_event(self):
# ensure kernel is smoothing values correctly for multiple events
self.data[[5, 30, 65], 3] = 1.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(os.path.join(BASE_PATH,
TEST_3_VALUE_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 3.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 3 dp
self.assertAlmostEqual(sum_data, sum_smooth, 2)
def test_kernel_single_event_3d(self):
# ensure kernel is smoothing values correctly for a single event
self.data[50, 3] = 1.
self.data[50, 2] = 20.
config = {'Length_Limit': 3.0, 'BandWidth': 30.0}
expected_array = np.genfromtxt(os.path.join(BASE_PATH,
TEST_1_VALUE_3D_FILE))
(smoothed_array, sum_data, sum_smooth) = \
self.model.smooth_data(self.data, config, is_3d=True)
raise unittest.SkipTest('Have Graeme fix this')
np.testing.assert_array_almost_equal(expected_array, smoothed_array)
self.assertAlmostEqual(sum_data, 1.)
# Assert that sum of the smoothing is equal to the sum of the
# data values to 2 dp
self.assertAlmostEqual(sum_data, sum_smooth, 2)
def run_analysis(self, catalogue, config, completeness_table=None,
smoothing_kernel=None):
'''
Runs an analysis of smoothed seismicity in the manner
originally implemented by Frankel (1995)
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param dict config:
Configuration settings of the algorithm:
* 'Length_Limit' - Maximum number of bandwidths for use in
smoothing (Float)
* 'BandWidth' - Bandwidth (km) of the Smoothing Kernel (Float)
* 'increment' - Output incremental (True) or cumulative a-value
(False)
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param smoothing_kernel:
Smoothing kernel as instance of :class:
`openquake.hmtk.seismicity.smoothing.kernels.base.BaseSmoothingKernel`
:returns:
Full smoothed seismicity data as np.ndarray, of the form
[Longitude, Latitude, Depth, Observed, Smoothed]
'''
self.catalogue = catalogue
if smoothing_kernel:
self.kernel = smoothing_kernel
else:
self.kernel = IsotropicGaussian()
# If no grid limits are specified then take from catalogue
if isinstance(self.grid_limits, list):
self.grid_limits = Grid.make_from_list(self.grid_limits)
assert self.grid_limits['xmax'] >= self.grid_limits['xmin']
assert self.grid_limits['xspc'] > 0.0
assert self.grid_limits['ymax'] >= self.grid_limits['ymin']
assert self.grid_limits['yspc'] > 0.0
elif isinstance(self.grid_limits, float):
self.grid_limits = Grid.make_from_catalogue(
self.catalogue, self.grid_limits,
config['Length_Limit'] * config['BandWidth'])
completeness_table, mag_inc = utils.get_even_magnitude_completeness(
completeness_table,
self.catalogue)
end_year = self.catalogue.end_year
# Get Weichert factor
t_f, _ = utils.get_weichert_factor(self.beta,
completeness_table[:, 1],
completeness_table[:, 0],
end_year)
# Get the grid
self.create_3D_grid(self.catalogue, completeness_table, t_f, mag_inc)
if config['increment']:
# Get Hermann adjustment factors
fval, fival = utils.hermann_adjustment_factors(
self.bval,
completeness_table[0, 1], config['increment'])
self.data[:, -1] = fval * fival * self.data[:, -1]
# Apply smoothing
smoothed_data, sum_data, sum_smooth = self.kernel.smooth_data(
self.data, config, self.use_3d)
print('Smoothing Total Rate Comparison - '
'Observed: %.6g, Smoothed: %.6g' % (sum_data, sum_smooth))
self.data = np.column_stack([self.data, smoothed_data])
return self.data
class SmoothedSeismicity(object):
'''
Class to implement an analysis of Smoothed Seismicity, including the
grid counting of data and the smoothing.
:param np.ndarray grid:
Observed count in each cell [Long., Lat., Depth., Count]
:param catalogue:
Valid instance of the :class: openquake.hmtk.seismicity.catalogue.Catalogue
:param bool use_3d:
Decide if analysis is 2-D (False) or 3-D (True). If 3-D then distances
will use hypocentral distance, otherwise epicentral distance
:param float bval:
b-value
:param float beta:
Beta value for exponential form (beta = bval * log(10.))
:param np.ndarray data:
Smoothed seismicity output
:param dict grid_limits:
Limits ot the grid used for defining the cells
'''
def __init__(self, grid_limits, use_3d=False, bvalue=None):
'''
Instatiate class with a set of grid limits
:param grid_limits:
It could be a float (in that case the grid is computed from the
catalogue with the given spacing).
Or an array of the form:
[xmin, xmax, spcx, ymin, ymax, spcy, zmin, spcz]
:param bool use_3d:
Choose whether to use hypocentral distances for smoothing or only
epicentral
:param float bval:
b-value for analysis
'''
self.grid = None
self.catalogue = None
self.use_3d = use_3d
self.bval = bvalue
if self.bval:
self.beta = self.bval * log(10.)
else:
self.beta = None
self.data = None
self.grid_limits = grid_limits
self.kernel = None
def run_analysis(self, catalogue, config, completeness_table=None,
smoothing_kernel=None):
'''
Runs an analysis of smoothed seismicity in the manner
originally implemented by Frankel (1995)
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param dict config:
Configuration settings of the algorithm:
* 'Length_Limit' - Maximum number of bandwidths for use in
smoothing (Float)
* 'BandWidth' - Bandwidth (km) of the Smoothing Kernel (Float)
* 'increment' - Output incremental (True) or cumulative a-value
(False)
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param smoothing_kernel:
Smoothing kernel as instance of :class:
`openquake.hmtk.seismicity.smoothing.kernels.base.BaseSmoothingKernel`
:returns:
Full smoothed seismicity data as np.ndarray, of the form
[Longitude, Latitude, Depth, Observed, Smoothed]
'''
self.catalogue = catalogue
if smoothing_kernel:
self.kernel = smoothing_kernel
else:
self.kernel = IsotropicGaussian()
# If no grid limits are specified then take from catalogue
if isinstance(self.grid_limits, list):
self.grid_limits = Grid.make_from_list(self.grid_limits)
assert self.grid_limits['xmax'] >= self.grid_limits['xmin']
assert self.grid_limits['xspc'] > 0.0
assert self.grid_limits['ymax'] >= self.grid_limits['ymin']
assert self.grid_limits['yspc'] > 0.0
elif isinstance(self.grid_limits, float):
self.grid_limits = Grid.make_from_catalogue(
self.catalogue, self.grid_limits,
config['Length_Limit'] * config['BandWidth'])
completeness_table, mag_inc = utils.get_even_magnitude_completeness(
completeness_table,
self.catalogue)
end_year = self.catalogue.end_year
# Get Weichert factor
t_f, _ = utils.get_weichert_factor(self.beta,
completeness_table[:, 1],
completeness_table[:, 0],
end_year)
# Get the grid
self.create_3D_grid(self.catalogue, completeness_table, t_f, mag_inc)
if config['increment']:
# Get Hermann adjustment factors
fval, fival = utils.hermann_adjustment_factors(
self.bval,
completeness_table[0, 1], config['increment'])
self.data[:, -1] = fval * fival * self.data[:, -1]
# Apply smoothing
smoothed_data, sum_data, sum_smooth = self.kernel.smooth_data(
self.data, config, self.use_3d)
print('Smoothing Total Rate Comparison - '
'Observed: %.6g, Smoothed: %.6g' % (sum_data, sum_smooth))
self.data = np.column_stack([self.data, smoothed_data])
return self.data
def create_2D_grid_simple(self, longitude, latitude, year, magnitude,
completeness_table, t_f=1., mag_inc=0.1):
'''
Generates the grid from the limits using an approach closer to that of
Frankel (1995)
:param numpy.ndarray longitude:
Vector of earthquake longitudes
:param numpy.ndarray latitude:
Vector of earthquake latitudes
:param numpy.ndarray year:
Vector of earthquake years
:param numpy.ndarray magnitude:
Vector of earthquake magnitudes
:param numpy.ndarray completeness_table:
Completeness table
:param float t_f:
Weichert adjustment factor
:returns:
Two-dimensional spatial grid of observed rates
'''
assert mag_inc > 0.
xlim = np.ceil(
(self.grid_limits['xmax'] - self.grid_limits['xmin']) /
self.grid_limits['xspc'])
ylim = np.ceil(
(self.grid_limits['ymax'] - self.grid_limits['ymin']) /
self.grid_limits['yspc'])
ncolx = int(xlim)
ncoly = int(ylim)
grid_count = np.zeros(ncolx * ncoly, dtype=float)
for iloc in range(0, len(longitude)):
dlon = (longitude[iloc] - self.grid_limits['xmin']) /\
self.grid_limits['xspc']
if (dlon < 0.) or (dlon > xlim):
# Earthquake outside longitude limits
continue
xcol = int(dlon)
if xcol == ncolx:
# If longitude is directly on upper grid line then retain
xcol = ncolx - 1
dlat = fabs(self.grid_limits['ymax'] - latitude[iloc]) /\
self.grid_limits['yspc']
if (dlat < 0.) or (dlat > ylim):
# Earthquake outside latitude limits
continue
ycol = int(dlat) # Correct for floating precision
if ycol == ncoly:
# If latitude is directly on upper grid line then retain
ycol = ncoly - 1
kmarker = (ycol * int(xlim)) + xcol
adjust = _get_adjustment(magnitude[iloc],
year[iloc],
completeness_table[0, 1],
completeness_table[:, 0],
t_f,
mag_inc)
if adjust:
grid_count[kmarker] = grid_count[kmarker] + adjust
return grid_count
def create_3D_grid(self, catalogue, completeness_table, t_f=1.0,
mag_inc=0.1):
'''
Counts the earthquakes observed in a three dimensional grid
:param catalogue:
Instance of the openquake.hmtk.seismicity.catalogue.Catalogue class
catalogue.data dictionary containing the following -
'year' - numpy.ndarray vector of years
'longitude' - numpy.ndarray vector of longitudes
'latitude' - numpy.ndarray vector of latitudes
'depth' - numpy.ndarray vector of depths
:param np.ndarray completeness_table:
Completeness of the catalogue assuming evenly spaced magnitudes
from most recent bin to oldest bin [year, magnitude]
:param float t_f:
Weichert adjustment factor
:param float mag_inc:
Increment of the completeness magnitude (rendered 0.1)
:returns:
Three-dimensional spatial grid of observed rates (or two dimensional
if only one depth layer is considered)
'''
x_bins = np.arange(self.grid_limits['xmin'],
self.grid_limits['xmax'],
self.grid_limits['xspc'])
if x_bins[-1] < self.grid_limits['xmax']:
x_bins = np.hstack([x_bins, x_bins[-1] + self.grid_limits['xspc']])
y_bins = np.arange(self.grid_limits['ymin'],
self.grid_limits['ymax'],
self.grid_limits['yspc'])
if y_bins[-1] < self.grid_limits['ymax']:
y_bins = np.hstack([y_bins, y_bins[-1] + self.grid_limits['yspc']])
z_bins = np.arange(self.grid_limits['zmin'],
self.grid_limits['zmax'] + self.grid_limits['zspc'],
self.grid_limits['zspc'])
if z_bins[-1] < self.grid_limits['zmax']:
z_bins = np.hstack([z_bins, z_bins[-1] + self.grid_limits['zspc']])
# Define centre points of grid cells
gridx, gridy = np.meshgrid((x_bins[1:] + x_bins[:-1]) / 2.,
(y_bins[1:] + y_bins[:-1]) / 2.)
n_x, n_y = np.shape(gridx)
gridx = np.reshape(gridx, [n_x * n_y, 1])
gridy = np.reshape(np.flipud(gridy), [n_x * n_y, 1])
# Only one depth range
idx = np.logical_and(catalogue.data['depth'] >= z_bins[0],
catalogue.data['depth'] < z_bins[1])
mid_depth = (z_bins[0] + z_bins[1]) / 2.
data_grid = np.column_stack([
gridx,
gridy,
mid_depth * np.ones(n_x * n_y, dtype=float),
self.create_2D_grid_simple(catalogue.data['longitude'][idx],
catalogue.data['latitude'][idx],
catalogue.data['year'][idx],
catalogue.data['magnitude'][idx],
completeness_table,
t_f,
mag_inc)])
if len(z_bins) < 3:
# Only one depth range
self.data = data_grid
return
# Multiple depth layers - append to grid
for iloc in range(1, len(z_bins) - 1):
idx = np.logical_and(catalogue.data['depth'] >= z_bins[iloc],
catalogue.data['depth'] < z_bins[iloc + 1])
mid_depth = (z_bins[iloc] + z_bins[iloc + 1]) / 2.
temp_grid = np.column_stack([
gridx,
gridy,
mid_depth * np.ones(n_x * n_y, dtype=float),
self.create_2D_grid_simple(catalogue.data['longitude'][idx],
catalogue.data['latitude'][idx],
catalogue.data['year'][idx],
catalogue.data['magnitude'][idx],
completeness_table,
t_f,
mag_inc)])
data_grid = np.vstack([data_grid, temp_grid])
self.data = data_grid
def write_to_csv(self, filename):
'''
Exports to simple csv
:param str filename:
Path to file for export
'''
fid = open(filename, 'wt')
# Create header list
header_info = ['Longitude', 'Latitude', 'Depth', 'Observed Count',
'Smoothed Rate', 'b-value']
writer = csv.DictWriter(fid, fieldnames=header_info)
headers = dict((name0, name0) for name0 in header_info)
# Write to file
writer.writerow(headers)
for row in self.data:
# institute crude compression by omitting points with no seismicity
# and taking advantage of the %g format
if row[4] == 0:
continue
row_dict = {'Longitude': '%g' % row[0],
'Latitude': '%g' % row[1],
'Depth': '%g' % row[2],
'Observed Count': '%d' % row[3],
'Smoothed Rate': '%.6g' % row[4],
'b-value': '%g' % self.bval}
writer.writerow(row_dict)
fid.close()