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 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 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 Mmax,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 Mmax=6.5, and use the same value as Mmin for fault MFDs (described here).
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.