RE: EARTHQUAKE SURFACE SLIP DISTRIBUTION

TO: SEISMO GROUP -- Are you interested? Feel free to forward this to 
anyone.

I wanted to discuss this problem a few days ago during the informal
seismo seminar 2004/11/9, but then decided that a written communication
would be a better tool. The problem is the distribution of earthquakes
rupturing Earth's surface and the distribution of earthquake slip. I
feel that suffucient data and technical tools now exist that make the
solution or at least significant progress toward the solution a
relatively easy task. In particular: 

1. High accuracy local earthquake catalogs are available in California
(Richards-Dinger and Shearer, 2000; Shearer et al., 2003; Parkfield)
and perhaps in Japan. 

2. FORTRAN programs to process earthquake datasets and determine both
the b-value and the maximum or corner magnitude are available on the
WEB: 
http://scec.ess.ucla.edu/~ykagan/programs_moms_index.html ;
http://moho.ess.ucla.edu/~kagan/dzmm2.for (FORTRAN program to evaluate
\beta and corner moment M_c) 
ftp://element.ess.ucla.edu/2003107-esupp/ (Peter Bird adaptation of
maximum likelihood map program: use BetaCorner.f90,
Adobe_Illustrator.f90, AI7frame.ai:) 

We need to know the depth distribution of earthquakes and their size
distribution to infer the probability that an earthquake would rupture
the surface. Two effects need to be accounted for: (1) the general
decrease of earthquake numbers when approaching the surface; (2)
dependence of earthquake size distribution on depth. The first issue is
well-known. The second effect has been studied recently by Mori and
Abercrombie (1997) and Gerstenberger et al. (2001). They found that the
b-value decreases with depth. However, they used the classical
Gutenberg-Richter relation which does not take into account the maximum
magnitude. If the maximum earthquake size is taken into consideration,
a more reasonable explanation for the apparent b-value change would be
an increase of the maximum earthquake size with depth [Kagan, 2002,
p.538]. Centroid depth for a large earthquake on a vertical fault
cannot be smaller than a half of the rupture width; inspection of
seismic maps suggests that hypocenters of larger events are on average
deeper than those for small earthquakes. 

It seems likely that only large earthquakes rupture the Earth surface.
Since the total displacement of seismogenic crust at any depth interval
over long time intervals should be uniform, this would mean that slip
of large earthquakes should "catch up" on slip deficit at the Earth
crust left by smaller events, i.e., slip of large earthquakes at the
surface should be on average greater than in the crust middle layers.
If this conjecture is true, then the slip distribution in paleo-seismic
studies can be significantly different from the power-law, giving
misleading support to claims of the characteristic earthquake model.
The results of the studies of the surface slip distribution would have
a major implication for the interpretation of the paleo-seismic data
and our understanding of why the paleo-seismic earthquake size
distribution looks different from that of the catalog studies (see, for
example, Liu et al., 2004). 

REFERENCES: 

Gerstenberger, M. C., S. Wiemer, and D. Giardini, 2001. A systematic
test of the hypothesis that the b value varies with depth in
California, Geophys. Res. Lett., 28(1), 57-60. 

Kagan, Y. Y., 2002. Seismic moment distribution revisited: I.
Statistical results, Geophys. J. Int., 148, 521-542. 

Liu, J., Y. Klinger, K. Sieh and C. Rubin, 2004. Six similar sequential
ruptures of the San Andreas fault, Carrizo Plain, California, Geology,
32(8), 649-652. 

Mori, J., and R. E. Abercrombie, 1997. Depth dependence of earthquake
frequency-magnitude distributions in California: implications for
rupture initiation, J. Geophys. Res., 102, 15081-90. 

Richards-Dinger, K. B., and Shearer, P. M., 2000. Earthquake locations
in southern California obtained using source-specific station terms, J.
Geophys. Res., 105, 10939-10960. 

Shearer, P., E. Hauksson, G. Lin and D. Kilb, 2003. Comprehensive
waveform cross-correlation of southern California seismograms: Part 2.
Event locations obtained using cluster analysis, Eos Trans. AGU,
84(46), Fall Meet. Suppl., Abstract S21D-0326. 

SURFACE_SLIP.TXT;3                         9/9       26-NOV-2004 16:21:35.77