The Empirical Model
K. R. Felzer
In this appendix I investigate whether there are regions in California that are
currently experiencing lower seismicity rates than their long term average.
Seismicity rates sometimes drop regionally for prolonged periods of time, a
phenomena known as stress shadowing when it is linked casually to a large
earthquake (e.g. Toda and Stein, 2007). Because of recording incompleteness in the
early part of the catalog, we can only robustly search for rate decreases, not rate
increases. We note, however, that most rate increases are clearly linked to
aftershock sequences, swarms, volcanic activity, or anthropogenic activity, and may
be modeled accordingly.
I follow the precedent of the Bay Area Working Group 2002 (Reasenberg et al.,
2003) and UCERF2 (Field et al., 2009) in looking for seismicity rate changes only by
contrasting later and earlier parts of the earthquake catalog; that is, attempts are
not made to compare current seismicity with long term deformation models. Thus
the results must be taken with the caveat that the existing catalog may be too short
to represent true long term seismicity patterns across the state. The earliest
written earthquake data for California comes from the mission era of 1769-1838,
but this data is difficult to associate with precise magnitudes and locations. There is
a data gap from 1838-1849, and then an increase in written information when the
Gold Rush brought population and newspapers to California. Therefore the ``long
term’’ catalog that I use is 1850-2011. I set the ``modern era’’ to 1984-2011, which
corresponds to the well-instrumented era in California. I use M≥5.5 for the 18502011 era, as many earthquakes above this magnitude are present in the catalog.
The statewide catalog is not nearly complete to M 5.5 until the initiation of
statewide instrumental data in 1942 (Felzer and Cao, 2008), but many M≥5.5 that
were near populated regions were recorded. Rate decreases can be documented
even if the early part of the catalog is incomplete, with the caveat that rate decreases
measured are a lower bound – the real change could be more extreme. Rate
increases, on the other hand, cannot be measured robustly when the first part of the
catalog is incomplete and thus we do not attempt to do so here. Limiting the catalog
to its rigorous completeness threshold for the whole state for the 1850-2011 era
would require limiting it to above M 7.4 (Felzer and Cao, 2007), which would leave
too little data for meaningful results. Before calculating rate changes I attempt to
remove aftershocks by using the declustering algorithm of Gardner and Knopoff
(1974), which has been traditionally used in seismic hazard mapping. If aftershocks
are not removed rate decreases will automatically appear wherever active
aftershock sequences are decaying. The Gardner and Knopoff (1974) algorithm has
proved over time to be a reasonable declustering method, but it is important to note
that no declustering algorithm is perfect, and some decreases seen might still be
from aftershock decay.
I smooth the 1850-2011 M≥5.5 earthquakes using the Helmstetter et al. (2007)
protocol with a Gaussian kernel and n=2, meaning that the smoothing constant for
each earthquake is the distance to its nearest neighbor (please see Helmstetter et al.
2007 for details on the method) (Figure 1). Smoothing the seismicity represents a
break from UCERF2 and Working Group 2002; in both of these efforts seismicity
rates were solved for pre-designated regions and applied uniformly to all faults
within the region, even though it was recognized that there could be significant fault
to fault differences (Reasenberg et al., 2003). With the smoothing algorithm used
here we hope to more accurately pinpoint the locations and amplitudes of the rate
changes. For the modern era I use M≥4.7 earthquakes, which gives me the same
total number of earthquakes as the 1850-2011 catalog and thus smoothing that is
on a similar scale. The smoothed 1984-2011 map is given in Figure 2.
The smoothing method does create some potential artifacts, so we inspect both the
raw ratios map (1984-2011 vs. 1850-2011, Figure 3) and the ratios map with
seismicity (Figure 4). There are two areas in which rate decreases are both strong
and clearly associated with a lack of significant 1984-2011 seismicity. These are the
San Francisco Bay Area, as has been previously noted (centered near 37.8N,
122.1W), and the Santa Barbara coastal area (centered near 34.5N and 120.5W).
There also appears to be a rate decrease, although less strong, in the northeast
corner of the state near Susanville and the Nevada border (centered near 40.5N,
120.5W). It can also be seen that a string of old historic earthquakes dots the
Southern San Andreas, which has been relatively quiet since 1932. The measured
ratios between the two smoothed maps, given at 0.1 by 0.1 degree grid points, is
given in the accompanying text file, EmpiricalRatios.txt.
In conclusion, we find empirical support that rates may be currently lower than the
long term average in the San Francisco Bay Area, the Santa Barbara Area, the
Susanville area, and the southern San Andreas fault. The actual rate changes that
should be used for these areas in modeling are best determined by comparing the
smoothed 1984-2011 M≥2.5 seismicity map (Smoothed Seismicity, Appendix ) with
the finalized long term UCERF 3 seismicity rate map.
References
Felzer, K. R., Calculating California seismicity rates, Appendix I, in The Uniform
California Earthquake Rupture Forecast, version 2 (UCERF 2): U.S. Geological
Survey Open File Report 2007-1437I and California Geological Survey Special
Report 203I, 42 pp, (2008).
Field, E. H., T. E. Dawson, K. R. Felzer, A. D. Frankel, V. Gupta, T. H. Jordan, T. Parsons,
M. D. Petersen, R. S. Stein, R. J. Weldon II and C. J. Wills (2009). Uniform
California Earthquake Rupture Forecast, Version 2 (UCERF 2), Bull. Seis. Soc. Am.,
99, 2053-2107.
Gardner, J. K. and L. Knopoff, Is the sequence of earthquakes in southern California,
with aftershocks removed, Poissonian? (1974). Bull. Seis. Soc. Am., 64, 1363—
1367.
Helmstetter, Agnes and Yan Y. Kagan and David D. Jackson (2007). High-resolution
time-indepent grid-based forecast for M≥5 earthquakes in California, Seis. Res.
Lett.., 78, 78-86.
Reasenberg, P. A., T. C. Hanks, and W. H. Bakun (2003). An empirical model for
earthquake probabilities in the San Francisco Bay Region, California, 2002-2031,
Bull. Seis. Soc. Am., 93, 1-13.
Toda, S. and R. Stein, Toggling of seismicity by the 1997 Kagoshima earthquake
couplet: a demonstration of time-dependent stress transfer (2003). J. Geophys.
Res., 108, 2567, doi:10.1029/2003JB002527.
Figure 1 Smoothed M≥5.5 seismicity from 1850-2011 with the earthquake
locations given in black dots.
Figure 2 Smoothed M≥4.7 seismicity from 1984-2011 with the earthquake locations
given in black dots.
Figure 3: Ratio of smoothed seismicity from 1984-2011 to 1850-2011. The color
bar gives the ratio of the average number of earthquakes/year.
Figure 4: Ratio of 1984-2011 to 1850-2011 seismicity, with earthquakes plotted on
the map. 1850-1932 earthquakes are given by black dots, 1932-1984 earthquakes
by orange triangles, and 1984-2011 earthquakes by red squares.