Area-magnitude scaling relationships

Package openquake.hazardlib.scalerel contains base classes and implementations of magnitude-area and area-magnitude scaling relationships.

Wells and Coppersmith

Module openquake.hazardlib.scalerel.wc1994 implements WC1994.

class openquake.hazardlib.scalerel.wc1994.WC1994

Wells and Coppersmith magnitude – rupture area relationships, see 1994, Bull. Seism. Soc. Am., pages 974-2002.

Implements both magnitude-area and area-magnitude scaling relationships.

get_median_area(mag, rake)

The values are a function of both magnitude and rake.

Setting the rake to None causes their “All” rupture-types to be applied.

get_median_mag(area, rake)

Return magnitude (Mw) given the area and rake.

Setting the rake to None causes their “All” rupture-types to be applied.

Parameters:

• area – Area in square km.
• rake – Rake angle (the rupture propagation direction) in degrees, from -180 to 180.

get_std_dev_area(mag, rake)

Standard deviation for WC1994. Magnitude is ignored.

get_std_dev_mag(rake)

Standard deviation on the magnitude for the WC1994 area relation.

CEUS SSC

Module openquake.hazardlib.scalerel.ceus2011 implements CEUS2011.

class openquake.hazardlib.scalerel.ceus2011.CEUS2011

Magnitude-Scaling Relationship used for calculations in the CEUS SSC project completed in 2011.

References:

• CEUS SSC Hazard Input Document - Appendix H, page H-3
• CEUS SSC Final Report - Chapter 5, page 5-57

get_median_area(mag, rake)

Calculates median area as 10 ** (mag - 4.366). Rake is ignored.

Peer

Module openquake.hazardlib.scalerel.peer implements PeerMSR.

class openquake.hazardlib.scalerel.peer.PeerMSR

Magnitude-Scaling Relationship defined for PEER PSHA test cases.

See “Verification of Probabilistic Seismic Hazard Analysis Computer Programs”, Patricia Thomas and Ivan Wong, PEER Report 2010/106, May 2010.

get_median_area(mag, rake)

Calculates median area as 10 ** (mag - 4). Rake is ignored.

get_std_dev_area(mag, rake)

Standard deviation for PeerMSR. Mag and rake are ignored.

>>> peer = PeerMSR()
>>> 0.25 == peer.get_std_dev_area(4.0, 50)
True

Point

Module openquake.hazardlib.scalerel.point implements PointMSR.

class openquake.hazardlib.scalerel.point.PointMSR

Implements magnitude-area scaling relationship to mimic point ruptures. Independently of the magnitude value, this scaling relationship returns always a very small value (1e-4 squared km, corresponding to a 10 by 10 m square) for the median area.

NOTE: This scaling-relationship is meant to be used in area and point sources to mimic point ruptures. Is not intended to be used in fault sources, as it would require a fault surface discretization step to small (less than 10 m, using an aspect ratio equal to 1) which is unfeasible for realistic applications.

get_median_area(mag, rake)

Returns a value equal to 1e-4 squared km independently of mag and rake values.

>>> point_msr = PointMSR()
>>> 1e-4 == point_msr.get_median_area(4.0, 50)
True
>>> 1e-4 == point_msr.get_median_area(9.0, 0)
True

Strasser et al. 2010

Module openquake.hazardlib.scalerel.strasser2010 implements StrasserInterface, StrasserIntraslab.

class openquake.hazardlib.scalerel.strasser2010.StrasserInterface

Strasser, Arango and Bommer magnitude – rupture area relationships for interface events.

See F. O. Strasser, M. C. Arango, and J. J. Bommer Scaling of the Source Dimensions of Interface and Intraslab Subduction-zone Earthquakes with Moment Magnitude Seismological Research Letters, November/December 2010, v. 81, p. 941-950, doi:10.1785/gssrl.81.6.941

Implements both magnitude-area and area-magnitude scaling relationships.

get_median_area(mag, rake)

Calculates median areas as 10** (a + b*mag). The values are a function of magnitude. Rake is ignored.

get_median_mag(area, rake)

Return magnitude (Mw) given the area Rake is ignored.

Parameters:area – Area in square km.

get_std_dev_area(mag, rake)

Standard deviation for Strasser et al 2010. Magnitude is ignored.

get_std_dev_mag(rake)

Standard deviation on the magnitude for the Strasser et al. (2010) area relation.

class openquake.hazardlib.scalerel.strasser2010.StrasserIntraslab

Strasser, Arango and Bommer magnitude – rupture area relationships for intraslab events.

See F. O. Strasser, M. C. Arango, and J. J. Bommer Scaling of the Source Dimensions of Interface and Intraslab Subduction-zone Earthquakes with Moment Magnitude Seismological Research Letters, November/December 2010, v. 81, p. 941-950, doi:10.1785/gssrl.81.6.941

Implements both magnitude-area and area-magnitude scaling relationships.

get_median_area(mag, rake)

Calculates median areas as 10** (a + b*mag). The values are a function of magnitude. Rake is ignored.

get_median_mag(area, rake)

Return magnitude (Mw) given the area Rake is ignored.

Parameters:area – Area in square km.

get_std_dev_area(mag, rake)

Standard deviation for Strasser et al 2010. Magnitude is ignored.

get_std_dev_mag(rake)

Standard deviation on the magnitude for the Strasser et al. (2010) area relation.

Abstract base relationship

Module openquake.hazardlib.scalerel.base defines abstract base classes for ASR, MSR, ASRSigma, and MSRSigma

class openquake.hazardlib.scalerel.base.BaseASR

A base class for Area-Magnitude Scaling Relationship. Allows calculation of rupture magnitude from area.

get_median_mag(area, rake)

Return median magnitude (Mw) given the area and rake.

Parameters:

• area – Area in square km.
• rake – Rake angle (the rupture propagation direction) in degrees, from -180 to 180.

class openquake.hazardlib.scalerel.base.BaseASRSigma

Extend BaseASR and allows to include uncertainties (sigma) in rupture magnitude estimation.

get_std_dev_mag(rake)

Return the standard deviation on the magnitude.

Parameters:rake – Rake angle (the rupture propagation direction) in degrees, from -180 to 180.

class openquake.hazardlib.scalerel.base.BaseMSR

A base class for Magnitude-Area Scaling Relationship. Allows calculation of rupture area from magnitude.

get_median_area(mag, rake)

Return median area (in square km) from magnitude mag and rake.

To be overridden by subclasses.

Parameters:

• mag – Moment magnitude (Mw).
• rake – Rake angle (the rupture propagation direction) in degrees, from -180 to 180.

class openquake.hazardlib.scalerel.base.BaseMSRSigma

Extends BaseMSR and allows to include uncertainties (sigma) in rupture area estimation.

get_std_dev_area(mag, rake)

Return the standard deviation of the area distribution given magnitude mag and rake.

To be overridden by subclasses.

Parameters:

• mag – Moment magnitude (Mw).
• rake – Rake angle (the rupture propagation direction) in degrees, from -180 to 180.