What Distances are Reported in Seismic Hazard Deaggregations?

By Stephen Harmsen, USGS

The strength of ground motion that will be recorded at a site from a future earthquake is generally modeled as a lognormal random variable whose median monotonically decreases with source-to-site distance, at least when the site is further than some minimum distance from the source. In making this statement, we neglect potential additional information about source, propagation, and site factors. At near-source distances, where median motion is strongest, differences in the construction of ground motion models by investigators of strong motion data yield significant variation of the estimated median for a specific source-to-site distance, R, source magnitude, M, and site conditions (e.g., firm rock, deep soil). Some of this variation is due to the fact that R is defined differently in the various attenuation models (ground-motion prediction models) that are used in the PSHA map calculations and seismic hazard deaggregations.

When additional source factors such as style of slip are modeled, significant effects on median motion are sometimes found. Several of the attenuation models that are used in the 2002-2003 USGS PSHA map updates include a fault geometry term whose effect is to increase median ground motion at rock sites on or near the hanging wall of a thrust or reverse fault - for a given R and M.

Accounting for site conditions can also alter the expected behavior. At soil sites, nonlinear amplification may affect short-period median response differently than that expected for rock sites. For several popular attenuation models, near-source R and larger M yield soil-site median deamplification relative to rock for short period SA (T < 0.3 seconds).

In the interactive deaggregations, we compute source-to-site distances and accumulate ground motion exceedances in bins. In the 1996 edition work, for sites in the western U.S., these are labeled hypocentral distance bins, while in the CEUS they are labeled epicentral distance bins. These labels are not entirely accurate, however, because we use the distance metric of the given attenuation model when we bin exceedance contributions. One of the metrics is the Joyner-Boore distance, or Rjb, which is distance to the vertical projection of the fault to the Earth's surface. Thus, Rjb is zero when the site is over the rupturing portion of a fault. Rjb is not a hypocentral distance. Another metric is Rrup, the nearest distance to the rupture surface. Like Rjb, Rrup is not in general a hypocentral distance. Another distance metric that we use is Rseis, which is the nearest distance to a location on the fault believed to be strong enough to generate strong motion. Rseis only considers parts of the fault that are deeper than a specified depth, usually 5 km, when determining nearest distance to the site. It is unlikely that any of these distance metrics will fortuitously predict a future source hypocentral distance and in general should not be used for this purpose. In the 2002-2003 updates, the distance label on plots has been changed to "Source-to-site distance" in an attempt to respond to criticisms of the "hypocentral distance" label.

Of interest to interpretation of the deaggregation output, the use of different distance metrics can result in the same source contributing to different R bins. The geographic deaggregation can yield a distinctly different site-to-source azimuth (designated back azimuth or BAZ) for the Rjb contribution than that of the other attenuation models. For example, for a site over or nearly over a fault that dips down to the west, BAZ calculated from the Joyner-Boore model may indicate that the source is just west of the site (given that a discrete sampling of points on the fault is used for computing distance), while the other distance metrics may indicate that the source is east of the site. Because the geographic deaggregation inner annulus uses a north-south plane through the site to separate sources into BAZ-dependent bins, contributions from this source may graph at distinctly different locations. You should keep in mind some of the arbitrary programming rules and the details of the attenuation model distance metrics when you attempt to infer where the modal source or other important source is relative to the site from the results of a geographic deaggregation of seismic hazard.

A potentially confusing geographic seismic hazard deaggregation may occur when one active fault is partially or completely above another active fault. Consider, for example, the West Valley fault and the Wasatch fault in the vicinity of Salt Lake City. The surface trace of the east-dipping West Valley fault is 8 to 16 km west of the surface trace of the west-dipping Wasatch. In this case it is possible to find sites for which the entire West Valley contribution plots east of the site, but some of the Wasatch contributions plot west of the site for the reason discussed in the previous paragraph. We would like to thank Dr. James Pechmann of the University of Utah for bringing this example to our attention.

For lower-magnitude random or gridded seismicity in the WUS, the distance that is reported is the slant distance to gridded a-values, which are determined at 0.1 degree intervals in latitude and longitude. The depth of shallow crustal point sources is fixed at 5 km in both the 1996 and 2002 PSHA maps and deaggregations. The depth of deep intraplate sources is 45 km in the 1996 PSHA maps, and is 50 km in the 2002 PSHA maps. Rjb, Rrup, and Rseis are computed as the distances of the site from finite random sources, which occur when M>6.0. When computing source-to-site distances Rrup and Rseis from WUS random-strike finite faults, the top of fault is assumed to be at a depth of 5 km, and when reporting distances in the deaggregation, slant distance (depth =5 km) is used. In this case, the "hypocentral distance" label makes some sense but may be biased.

In the CEUS, epicentral distance is the R label in the 1996-edition deaggregations. At many CEUS sites, most source contributions are from random seismicity. For those sources, source-to-site distance is determined from a grid of "a-values" in the CEUS. Therefore, a more exact distance label might be "distance to grid points" which are defined to occur at 0.2-degree increments in latitude and longitude. In the 1996 PSHA maps, the New Madrid Seismic Zone (NMSZ) sources are modeled as surface-rupturing vertical faults, but the only distance metric used, Rjb, is insensitive to this assumption. Distance is the nearest distance to the fault trace for these sources. Three NMSZ fault traces are used to model uncertainty in fault location. This results in exceedance contributions from the characteristic earthquake in the NMSZ going into two or three distance bins. We cannot predict which if any of these Rjb values would be a reasonable estimate of the epicentral distance for a future NMSZ main shock.

There are a few CEUS faults whose surface traces are in many places visible using low sun-angle photography and whose dips are known to a reasonable level of precision. These include the Meers fault in southwest Oklahoma and the Cheraw fault in southeast Colorado. In these instances, for the 1996 edition PSHA work, Rjb is computed and reported as the source-to-site distance in the interactive deaggregations, and the "epicentral distance" label is likely to be biased. For the 1996 maps, when computing source-to-site distance from CEUS random-strike vertical dip finite faults, the Rjb metric is also used. When reporting these source distances in the deaggregation, the Rjb distance is used and the "epicentral distance" label again may be biased. In the 2002 work, more attenuation models are used than in the 1996 work, some of whose distance metrics are sensitive to focal or fault depth. Fictitious depths, which are dependent on spectral period, are used to insure that Rrup and Rseis are appropriate for random CEUS seismicity. For the NMSZ faults, a source depth of 10 km is used for some of the attenuation models. Because of these added attenuation models, the "epicentral distance" label is no longer appropriate for the 2002 seismic hazard deaggregations. The non-committal "source-to-site distance" is the interim solution to this labeling problem.