# Source code for openquake.hazardlib.correlation

```
# The Hazard Library
# Copyright (C) 2012-2014, 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
[docs]class BaseCorrelationModel(object):
"""
Base class for correlation models for spatially-distributed ground-shaking
intensities.
"""
__metaclass__ = abc.ABCMeta
@abc.abstractmethod
[docs] 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.
"""
# 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.
corma = self.get_lower_triangle_correlation_matrix(sites, imt)
return numpy.dot(corma, 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
super(JB2009CorrelationModel, self).__init__()
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))
```