# Distributed Seismicity

We use the term "distributed seismicity" to indicate earthquakes not clearly attributable to an individual fault source or subduction zone. To model these, we group together seismicity with common characteristics, such as focal mechanism type, strain by the same tectonic forces, rate, or 3D distribution; we then produce source models reflecting these characteristics. Here, we describe two primary source types used to model distributed seismicity.

## Area Sources

Area sources consist of a statistically-determined MFD from
earthquakes occuring in a volume (usually a polygon, defined by the modeler,
with depth limits), with the modelled occurrence rates distributed uniformly
(equal *a*- and *b*-values) over an evenly spaced grid, and paired with a
hypocenter and focal mechanism. In the OpenQuake Engine, the specified
hypocentral depths and focal mechanisms can be probability distributions, or
singular metrics.

## Smoothed Seismicity

Smoothed seismicity is modeled similarly to area sources, but rather than using
a spatially-homogeneous MFD in each source, the *a*-values vary spatially based
on observed seismicity.

GEM has moved away from using traditional area sources, and predominantly models
distributed seismicity with an approach that combines area sources with smoothed
sesimicity, incorporating methods from Frankel (1995). We define a few source
zones with internally consistent tectonics (e.g., up to a few prominent focal
mechanism types, reflecting the same tectonic stresses), solve for the
Gutenberg-Richter *b*-value, and then smooth the occurring seismicity onto a
grid of points. This approach allows us to use larger source zones (and thus
more earthquakes to compute a more robust MFDs) while still capturing spatial
variability in seismicity rate.

We use the declustered crustal sub-catalogue, applying the *Stepp (1971)*
completeness analysis or one based on time-magnitude density plots. Then, from
the earthquakes within each source zone, we compute a double truncated
Gutenberg-Richter MFD from *M*=5 to *M*_{max,obs} + 0.5 (bins of
*M* 0.1), solving for *a*- and *b*-values based on *Weichert (1980)*. We
classify the earthquake probability into weighted depth bins. Lastly, we assign
most-likely nodal planes based on crustal earthquake focal mechanisms within the
source zone based on the GCMT catalogue.

We compute the smoothed seismicity grid by applying a Gaussian filter to the clipped, declustered catalogue for each source zone, and computing the fraction of spatial seismicity rates at each grid node. These are combined with the zone MFD to compute a grid of point-by-point earthquake occurrence rates.

In areas where we also model fault sources, we prevent double counting by
dividing the magnitude occurrence bins between the two source types. If there is
overlap (including a buffer around the surface projection of a fault, we cut the
MFDs for distributed seismicity at *M*_{max}=6.5, and use the same
value as *M*_{min} for fault MFDs (described
here).

## References

Frankel, A. (1995). Mapping seismic hazard in the central and eastern United States. Seismological Research Letters, 66(4), 8-21.

Stepp, J. C. (1971). “An investigation of earthquake risk in the Puget Sound area by the use of the type I distribution of largest extreme”. PhD thesis. Pennsylvania State University (cited on pages 9, 25–27).

Weichert, Dieter H. "Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes." Bulletin of the Seismological Society of America70.4 (1980): 1337-1346.