# USGS Combined (2004)

This Attenuation Relationship averages the rock-site results over four attenuation relationships and then applies the Borcherdt (1994) nonlinear amplification factors (details below). This relationship is intended to represent the averaging done for the California component of the 2002 USGS National Seismic Hazard Maps (with the added option of including site effects). The four Attenuation Relationships used are:

- Abrahamson & Silva (1997) with site type
**Rock/Shallow-Soil** - Boore, Joyner, & Fumal (1997) with V
_{s}30 = 760 m/sec - Campbell & Bozorgnia (2003) with site type
**BC_Boundary** - Sadigh et al. (1997) with site type
**Rock**

See model details below for more information.

Abrahamson, N. A., and W. J. Silva (1997), Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes, *Seismological Research Letters*, *68*(1), 94-127.

Boore, D. M., W. B. Joyner, and T. E. Fumal (1997), Equations for estimating horizontal response spectra and peak acceleration from western North American earthquakes: A summary of recent work, *Seismological Research Letters*, *68*(1), 128-153.

Borcherdt, R. D. (1994), Estimates of site-dependent response spectra for design (methodology and justification), *Earthquake Spectra*, *10*(4), 617 -653.

Campbell, K. W. and Y. Bozorgnia (2003), Updated near-source ground motion (attenuation) relations for the horizontal and vertical components of peak ground acceleration and acceleration response spectra, *Bulletin of the Seismological Society of America*, *93*(1), 314 -33l.

Sadigh, K., C. -Y. Chang, J. A. Egan, F. Makdisi, and R. R. Youngs (1997), Attenuation relationships for shallow crustal earthquakes based on California strong motion data, *Seismological Research Letters*, *68*(1), 180-189.

- Magnitude (M
_{W}) - all those used by the four attenuation relationships

- all those used by the four attenuation relationships

- Component: [Average Horizontal, Greater of Two Horizontal]
- Standard Deviation Type: [Total, Zero]
- Sigma Truncation Type
- Sigma Truncation Level

**Implementation notes:** The nonlinear amplification factors of Borcherdt (1994) are applied as given in appendix-equations 7a or 7b (for periods %le;0.5 and >0.5 seconds, respectively) using a reference velocity of 760 m/sec (and with the mv and ma coefficients linearly interpolated at intermediate input ground motions). Applying the mid-period amplification factors above 2.0 seconds for SA may not be legitimate.

For the one relationship that has a site-type dependent standard deviation (Sadigh et al., 1997) only the rock-site value is used (the difference is minor).

The Boore, Joyner & Fumal (1997) relationship is not included in the average for SA periods above 2.0 seconds.

For Boore, Joyner & Fumal (1997) the component is set as **Random Horizontal** (rather than **Average Horizontal**) to be consistent with how this was set in the 2002 USGS National Seismic Hazard Maps. All others are set as **Average Horizontal**.

For Campbell and Bozorgnia (2003) the magnitude dependent standard deviation is used.

This class supports a **Greater of Two Horizontal** component by multiplying the average horizontal component median by a factor of 1.15. This value was taken directly from the official USGS ShakeMap documentation. The standard deviation for this component is set the same as the average horizontal, which may not be correct.

Only median IMLs can be computed for Modified Mercalli Intensity (MMI) because the probability distribution for the latter is undifined.

**Developer notes:** Several methods for this class have been overridden to throw Runtime Exceptions, either because it was not clear what to return or because the info is complicated and not necessarily useful. For example, it's not clear what to return from getStdDev(); one could return the average of the std. dev. of the four relationships, but nothing actually uses such an average (the probability of exceedance calculation uses the mean/stdDev for each relationship separately). Another example is what to return from the getPropagationEffectParamsIterator - all of the three distance measures used by the four relationships? - this would lead to confusion and possible inconsistencies in the AttenuationRelationshipApplet. The bottom line is we've maintained the IntensityMeasureRelationshipAPI, but not the ScalarIntensityMeasureRelationshipAPI (so this relationship cannot be added to the AttenuationRelationshipApplet). This class could simply be a subclass of IntensityMeasureRelationship. however, it's not because it uses some of the private methods of AttenuationRelationship.