# Source code for openquake.hazardlib.correlation

```
# The Hazard Library
# Copyright (C) 2012-2017 GEM Foundation
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as
# published by the Free Software Foundation, either version 3 of the
# License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module :mod:`openquake.hazardlib.correlation` defines correlation models for
spatially-distributed ground-shaking intensities.
"""
import abc
import numpy
from openquake.hazardlib.imt import SA, PGA
from openquake.baselib.python3compat import with_metaclass
[docs]class BaseCorrelationModel(with_metaclass(abc.ABCMeta)):
"""
Base class for correlation models for spatially-distributed ground-shaking
intensities.
"""
[docs] @abc.abstractmethod
def get_lower_triangle_correlation_matrix(self, sites, imt):
"""
Get lower-triangle matrix as a result of Cholesky-decomposition
of correlation matrix.
The resulting matrix should have zeros on values above
the main diagonal.
The actual implementations of :class:`BaseCorrelationModel` interface
might calculate the matrix considering site collection and IMT (like
:class:`JB2009CorrelationModel` does) or might have it pre-constructed
for a specific site collection and IMT, in which case they will need
to make sure that parameters to this function match parameters that
were used to pre-calculate decomposed correlation matrix.
:param sites:
:class:`~openquake.hazardlib.site.SiteCollection` to create
correlation matrix for.
:param imt:
Intensity measure type object, see :mod:`openquake.hazardlib.imt`.
"""
[docs] def apply_correlation(self, sites, imt, residuals):
"""
Apply correlation to randomly sampled residuals.
:param sites:
:class:`~openquake.hazardlib.site.SiteCollection` residuals were
sampled for.
:param imt:
Intensity measure type object, see :mod:`openquake.hazardlib.imt`.
:param residuals:
2d numpy array of sampled residuals, where first dimension
represents sites (the length as ``sites`` parameter) and
second one represents different realizations (samples).
:returns:
Array of the same structure and semantics as ``residuals``
but with correlations applied.
NB: the correlation matrix is cached. It is computed only once
per IMT for the complete site collection and then the portion
corresponding to the sites is multiplied by the residuals.
"""
# intra-event residual for a single relization is a product
# of lower-triangle decomposed correlation matrix and vector
# of N random numbers (where N is equal to number of sites).
# we need to do that multiplication once per realization
# with the same matrix and different vectors.
try:
corma = self.cache[imt]
except KeyError:
corma = self.get_lower_triangle_correlation_matrix(
sites.complete, imt)
self.cache[imt] = corma
if len(sites.complete) == len(sites):
return numpy.dot(corma, residuals)
# it is important to allocate little memory, this is why I am
# accumulating below; if S is the length of the complete sites
# the correlation matrix has shape (S, S) and the residuals (N, s),
# where s is the number of samples
return numpy.sum(corma[sites.sids, sid] * res
for sid, res in zip(sites.sids, residuals))
[docs]class JB2009CorrelationModel(BaseCorrelationModel):
"""
"Correlation model for spatially distributed ground-motion intensities"
by Nirmal Jayaram and Jack W. Baker. Published in Earthquake Engineering
and Structural Dynamics 2009; 38, pages 1687-1708.
:param vs30_clustering:
Boolean value to indicate whether "Case 1" or "Case 2" from page 1700
should be applied. ``True`` value means that Vs 30 values show or are
expected to show clustering ("Case 2"), ``False`` means otherwise.
"""
def __init__(self, vs30_clustering):
self.vs30_clustering = vs30_clustering
self.cache = {} # imt -> correlation model
def _get_correlation_matrix(self, sites, imt):
"""
Calculate correlation matrix for a given sites collection.
Correlation depends on spectral period, Vs 30 clustering behaviour
and distance between sites.
Parameters are the same as for
:meth:`BaseCorrelationModel.get_lower_triangle_correlation_matrix`.
"""
distances = sites.mesh.get_distance_matrix()
return self._get_correlation_model(distances, imt)
def _get_correlation_model(self, distances, imt):
"""
Returns the correlation model for a set of distances, given the
appropriate period
:param numpy.ndarray distances:
Distance matrix
:param float period:
Period of spectral acceleration
"""
if isinstance(imt, SA):
period = imt.period
else:
assert isinstance(imt, PGA), imt
period = 0
# formulae are from page 1700
if period < 1:
if not self.vs30_clustering:
# case 1, eq. (17)
b = 8.5 + 17.2 * period
else:
# case 2, eq. (18)
b = 40.7 - 15.0 * period
else:
# both cases, eq. (19)
b = 22.0 + 3.7 * period
# eq. (20)
return numpy.exp((- 3.0 / b) * distances)
[docs] def get_lower_triangle_correlation_matrix(self, sites, imt):
"""
See :meth:`BaseCorrelationModel.get_lower_triangle_correlation_matrix`.
"""
return numpy.linalg.cholesky(self._get_correlation_matrix(sites, imt))
```