Source code for openquake.hmtk.seismicity.gcmt_catalogue

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"""
Implements sets of classes for mapping components of the focal mechanism
"""
import datetime
from math import fabs, floor, sqrt, pi
import numpy as np
from openquake.hmtk.seismicity import gcmt_utils as utils
from openquake.hmtk.seismicity.catalogue import Catalogue


[docs]def cmp(a, b): # Python 3 replacement of Python2 cmp return (a > b) - (a < b)
[docs]def cmp_mat(a, b): """ Sorts two matrices returning a positive or zero value """ c = 0 for x, y in zip(a.flat, b.flat): c = cmp(abs(x), abs(y)) if c != 0: return c return c
[docs]class GCMTHypocentre(object): """ Simple representation of the hypocentre """ def __init__(self): """ """ self.source = None self.date = None self.time = None self.longitude = None self.latitude = None self.depth = None self.m_b = None self.m_s = None self.location = None
[docs]class GCMTCentroid(object): """ Representation of a GCMT centroid """ def __init__(self, reference_date, reference_time): """ :param reference_date: Date of hypocentre as instance of :class: datetime.datetime.date :param reference_time: Time of hypocentre as instance of :class: datetime.datetime.time """ self.centroid_type = None self.source = None self.time = reference_time self.time_error = None self.date = reference_date self.longitude = None self.longitude_error = None self.latitude = None self.latitude_error = None self.depth = None self.depth_error = None self.depth_type = None self.centroid_id = None def _get_centroid_time(self, time_diff): """ Calculates the time difference between the date-time classes """ source_time = datetime.datetime.combine(self.date, self.time) second_diff = floor(fabs(time_diff)) microsecond_diff = int(1000. * (time_diff - second_diff)) if time_diff < 0.: source_time = source_time - datetime.timedelta( seconds=int(second_diff), microseconds=microsecond_diff) else: source_time = source_time + datetime.timedelta( seconds=int(second_diff), microseconds=microsecond_diff) self.time = source_time.time() self.date = source_time.date()
[docs]class GCMTPrincipalAxes(object): """ Class to represent the eigensystem of the tensor in terms of T-, B- and P- plunge and azimuth """ def __init__(self): """ """ self.t_axis = None self.b_axis = None self.p_axis = None
[docs] def get_moment_tensor_from_principal_axes(self): """ Retreives the moment tensor from the prinicpal axes """ raise NotImplementedError('Moment tensor from principal axes not yet ' 'implemented!')
[docs] def get_azimuthal_projection(self, height=1.0): """ Returns the azimuthal projection of the tensor according to the method of Frohlich (2001) """ raise NotImplementedError('Get azimuthal projection not yet ' 'implemented!')
[docs]class GCMTMomentTensor(object): """ Class to represent a moment tensor and its associated methods """ def __init__(self, reference_frame=None): """ """ self.tensor = None self.tensor_sigma = None self.exponent = None self.eigenvalues = None self.eigenvectors = None if reference_frame: self.ref_frame = reference_frame else: # Default to USE self.ref_frame = 'USE'
[docs] def normalise_tensor(self): """ Normalise the tensor by dividing it by its norm, defined such that np.sqrt(X:X) """ self.tensor, tensor_norm = utils.normalise_tensor(self.tensor) return self.tensor / tensor_norm, tensor_norm
def _to_ned(self): """ Switches the reference frame to NED """ if self.ref_frame is 'USE': # Rotate return utils.use_to_ned(self.tensor), \ utils.use_to_ned(self.tensor_sigma) elif self.ref_frame is 'NED': # Alreadt NED return self.tensor, self.tensor_sigma else: raise ValueError('Reference frame %s not recognised - cannot ' 'transform to NED!' % self.ref_frame) def _to_use(self): """ Returns a tensor in the USE reference frame """ if self.ref_frame is 'NED': # Rotate return utils.ned_to_use(self.tensor), \ utils.ned_to_use(self.tensor_sigma) elif self.ref_frame is 'USE': # Already USE return self.tensor, self.tensor_sigma else: raise ValueError('Reference frame %s not recognised - cannot ' 'transform to USE!' % self.ref_frame) def _to_6component(self): """ Returns the unique 6-components of the tensor in USE format [Mrr, Mtt, Mpp, Mrt, Mrp, Mtp] """ return utils.tensor_to_6component(self.tensor, self.ref_frame)
[docs] def eigendecompose(self, normalise=False): """ Performs and eigendecomposition of the tensor and orders into descending eigenvalues """ self.eigenvalues, self.eigenvectors = utils.eigendecompose(self.tensor, normalise) return self.eigenvalues, self.eigenvectors
[docs] def get_nodal_planes(self): """ Returns the nodal planes by eigendecomposition of the moment tensor """ # Convert reference frame to NED self.tensor, self.tensor_sigma = self._to_ned() self.ref_frame = 'NED' # Eigenvalue decomposition # Tensor _, evect = utils.eigendecompose(self.tensor) # Rotation matrix _, rot_vec = utils.eigendecompose(np.array([[0., 0., -1], [0., 0., 0.], [-1., 0., 0.]]))
[docs] rotation_matrix = (evect @ rot_vec.T).T if np.linalg.det(rotation_matrix) < 0.: rotation_matrix @= -1. flip_dc = np.array([[0., 0., -1.], [0., -1., 0.], [-1., 0., 0.]]) rotation_matrices = sorted( [rotation_matrix, flip_dc @ rotation_matrix], cmp=cmp_mat) nodal_planes = GCMTNodalPlanes() dip, strike, rake = [(180. / pi) * angle for angle in utils.matrix_to_euler( rotation_matrices[0])] # 1st Nodal Plane nodal_planes.nodal_plane_1 = {'strike': strike % 360, 'dip': dip, 'rake': -rake} # 2nd Nodal Plane dip, strike, rake = [(180. / pi) * angle for angle in utils.matrix_to_euler( rotation_matrices[1])] nodal_planes.nodal_plane_2 = {'strike': strike % 360., 'dip': dip, 'rake': -rake} return nodal_planes
def get_principal_axes(self): """ Uses the eigendecomposition to extract the principal axes from the moment tensor - returning an instance of the GCMTPrincipalAxes class """ # Perform eigendecomposition - returns in order P, B, T _ = self.eigendecompose(normalise=True) principal_axes = GCMTPrincipalAxes() # Eigenvalues principal_axes.p_axis = {'eigenvalue': self.eigenvalues[0]} principal_axes.b_axis = {'eigenvalue': self.eigenvalues[1]} principal_axes.t_axis = {'eigenvalue': self.eigenvalues[2]} # Eigen vectors # 1) P axis azim, plun = utils.get_azimuth_plunge(self.eigenvectors[:, 0], True) principal_axes.p_axis['azimuth'] = azim principal_axes.p_axis['plunge'] = plun # 2) B axis azim, plun = utils.get_azimuth_plunge(self.eigenvectors[:, 1], True) principal_axes.b_axis['azimuth'] = azim principal_axes.b_axis['plunge'] = plun # 3) T axis azim, plun = utils.get_azimuth_plunge(self.eigenvectors[:, 2], True) principal_axes.t_axis['azimuth'] = azim principal_axes.t_axis['plunge'] = plun return principal_axes
[docs]class GCMTEvent(object): """ Class to represent full GCMT moment tensor in ndk format """ def __init__(self): """ """ self.identifier = None self.hypocentre = None self.centroid = None self.magnitude = None self.moment = None self.metadata = {} self.moment_tensor = None self.nodal_planes = None self.principal_axes = None self.f_clvd = None self.e_rel = None
[docs] def get_f_clvd(self): """ Returns the statistic f_clvd: the signed ratio of the sizes of the intermediate and largest principal moments:: f_clvd = -b_axis_eigenvalue / max(|t_axis_eigenvalue|,|p_axis_eigenvalue|) """ if not self.principal_axes: # Principal axes not yet defined for moment tensor - raises error raise ValueError('Principal Axes not defined!') denominator = np.max(np.array([ fabs(self.principal_axes.t_axis['eigenvalue']), fabs(self.principal_axes.p_axis['eigenvalue']) ])) self.f_clvd = -self.principal_axes.b_axis['eigenvalue'] / denominator return self.f_clvd
[docs] def get_relative_error(self): """ Returns the relative error statistic (e_rel), defined by Frohlich & Davis (1999): `e_rel = sqrt((U:U) / (M:M))` where M is the moment tensor, U is the uncertainty tensor and : is the tensor dot product """ if not self.moment_tensor: raise ValueError('Moment tensor not defined!') numer = np.tensordot(self.moment_tensor.tensor_sigma, self.moment_tensor.tensor_sigma) denom = np.tensordot(self.moment_tensor.tensor, self.moment_tensor.tensor) self.e_rel = sqrt(numer / denom) return self.e_rel
[docs]class GCMTNodalPlanes(object): """ Class to represent the nodal plane distribution of the tensor Each nodal plane is represented as a dictionary of the form: {'strike':, 'dip':, 'rake':} """ def __init__(self): """ """ self.nodal_plane_1 = None self.nodal_plane_2 = None
[docs]class GCMTCatalogue(Catalogue): """ Class to hold a catalogue of moment tensors """ FLOAT_ATTRIBUTE_LIST = ['second', 'timeError', 'longitude', 'latitude', 'SemiMajor90', 'SemiMinor90', 'ErrorStrike', 'depth', 'depthError', 'magnitude', 'sigmaMagnitude', 'moment', 'strike1', 'rake1', 'dip1', 'strike2', 'rake2', 'dip2', 'eigenvalue_b', 'azimuth_b', 'plunge_b', 'eigenvalue_p', 'azimuth_p', 'plunge_p', 'eigenvalue_t', 'azimuth_t', 'plunge_t', 'f_clvd', 'e_rel'] INT_ATTRIBUTE_LIST = ['eventID', 'year', 'month', 'day', 'hour', 'minute', 'flag'] STRING_ATTRIBUTE_LIST = ['Agency', 'magnitudeType', 'comment', 'centroidID'] TOTAL_ATTRIBUTE_LIST = list( (set(FLOAT_ATTRIBUTE_LIST).union( set(INT_ATTRIBUTE_LIST))).union( set(STRING_ATTRIBUTE_LIST))) def __init__(self, start_year=None, end_year=None): """ Instantiate catalogue class """ super(GCMTCatalogue, self).__init__() self.gcmts = [] self.number_gcmts = None self.start_year = start_year self.end_year = end_year for attribute in self.TOTAL_ATTRIBUTE_LIST: if attribute in self.FLOAT_ATTRIBUTE_LIST: self.data[attribute] = np.array([], dtype=float) elif attribute in self.INT_ATTRIBUTE_LIST: self.data[attribute] = np.array([], dtype=int)
[docs] def get_number_tensors(self): """ Returns number of CMTs """ return len(self.gcmts)
[docs] def select_catalogue_events(self, id0): ''' Orders the events in the catalogue according to an indexing vector :param np.ndarray id0: Pointer array indicating the locations of selected events ''' for key in self.data.keys(): if isinstance( self.data[key], np.ndarray) and len(self.data[key]) > 0: # Dictionary element is numpy array - use logical indexing self.data[key] = self.data[key][id0] elif isinstance( self.data[key], list) and len(self.data[key]) > 0: # Dictionary element is list self.data[key] = [self.data[key][iloc] for iloc in id0] else: continue if len(self.gcmts) > 0: self.gcmts = [self.gcmts[iloc] for iloc in id0] self.number_gcmts = self.get_number_tensors()
[docs] def gcmt_to_simple_array(self, centroid_location=True): """ Converts the GCMT catalogue to a simple array of [ID, year, month, day, hour, minute, second, long., lat., depth, Mw, strike1, dip1, rake1, strike2, dip2, rake2, b-plunge, b-azimuth, b-eigenvalue, p-plunge, p-azimuth, p-eigenvalue, t-plunge, t-azimuth, t-eigenvalue, moment, f_clvd, erel] """ catalogue = np.zeros([self.get_number_tensors(), 29], dtype=float) for iloc, tensor in enumerate(self.gcmts): catalogue[iloc, 0] = iloc if centroid_location: catalogue[iloc, 1] = float(tensor.centroid.date.year) catalogue[iloc, 2] = float(tensor.centroid.date.month) catalogue[iloc, 3] = float(tensor.centroid.date.day) catalogue[iloc, 4] = float(tensor.centroid.time.hour) catalogue[iloc, 5] = float(tensor.centroid.time.minute) catalogue[iloc, 6] = np.round( np.float(tensor.centroid.time.second) + np.float(tensor.centroid.time.microsecond) / 1000000., 2) catalogue[iloc, 7] = tensor.centroid.longitude catalogue[iloc, 8] = tensor.centroid.latitude catalogue[iloc, 9] = tensor.centroid.depth else: catalogue[iloc, 1] = float(tensor.hypocentre.date.year) catalogue[iloc, 2] = float(tensor.hypocentre.date.month) catalogue[iloc, 3] = float(tensor.hypocentre.date.day) catalogue[iloc, 4] = float(tensor.hypocentre.time.hour) catalogue[iloc, 5] = float(tensor.hypocentre.time.minute) catalogue[iloc, 6] = np.round( np.float(tensor.centroid.time.second) + np.float(tensor.centroid.time.microsecond) / 1000000., 2) catalogue[iloc, 7] = tensor.hypocentre.longitude catalogue[iloc, 8] = tensor.hypocentre.latitude catalogue[iloc, 9] = tensor.hypocentre.depth catalogue[iloc, 10] = tensor.magnitude catalogue[iloc, 11] = tensor.moment catalogue[iloc, 12] = tensor.f_clvd catalogue[iloc, 13] = tensor.e_rel # Nodal planes catalogue[iloc, 14] = tensor.nodal_planes.nodal_plane_1['strike'] catalogue[iloc, 15] = tensor.nodal_planes.nodal_plane_1['dip'] catalogue[iloc, 16] = tensor.nodal_planes.nodal_plane_1['rake'] catalogue[iloc, 17] = tensor.nodal_planes.nodal_plane_2['strike'] catalogue[iloc, 18] = tensor.nodal_planes.nodal_plane_2['dip'] catalogue[iloc, 19] = tensor.nodal_planes.nodal_plane_2['rake'] # Principal axes catalogue[iloc, 20] = tensor.principal_axes.b_axis['eigenvalue'] catalogue[iloc, 21] = tensor.principal_axes.b_axis['azimuth'] catalogue[iloc, 22] = tensor.principal_axes.b_axis['plunge'] catalogue[iloc, 23] = tensor.principal_axes.p_axis['eigenvalue'] catalogue[iloc, 24] = tensor.principal_axes.p_axis['azimuth'] catalogue[iloc, 25] = tensor.principal_axes.p_axis['plunge'] catalogue[iloc, 26] = tensor.principal_axes.t_axis['eigenvalue'] catalogue[iloc, 27] = tensor.principal_axes.t_axis['azimuth'] catalogue[iloc, 28] = tensor.principal_axes.t_axis['plunge'] return catalogue