Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA , SHORT-TERM PROPERTIES OF EARTHQUAKE CATALOGS AND MODELS OF EARTHQUAKE SOURCE

We review the short-term properties of earthquake catalogs, in particular the time and size distributions and the completeness of the early part of aftershock sequences for strong, shallow earthquakes. We determine the parameters of the Omori and Gutenberg-Richter laws for aftershocks close-in-time to a mainshock. Aftershock sequences of large earthquakes in southern California (1952 Kern County, 1992 Joshua Tree--Landers--Big Bear sequence, 1994 Northridge, and 1999 Hector Mine), recorded in the CalTech catalog are analyzed to demonstrate that at the beginning of these series, many small earthquakes are absent from the catalog.

The number of missing earthquakes increases with the magnitude range of a catalog and for some datasets exceeds the number of aftershocks close to a mainshock listed in a catalog. Comparing global earthquake catalogs (Harvard CMT and PDE) with local datasets indicates that the catalogs based on longer period waves miss many early aftershocks even when their magnitudes are well above the stated magnitude threshold.

Such short-term incompleteness may introduce significant biases to the statistical analysis of the seismicity pattern, in particular for branching models of earthquake occurrence incorporating the Omori law, widely employed for short-term seismicity forecasts. Analyzing the source rupture process of several recent large earthquakes suggests that rupture propagation is highly inhomogeneous in space, time, and focal mechanism. These random variations in the rupture process can be viewed as an extension of the aftershock stochastic generating mechanism towards the origin time of a mainshock. Accepted by BSSA, scheduled for August issue

Temporal distribution of earthquakes Omori (1894) found that aftershock rate for the 1891 Nobi earthquake decayed about as 1/time. This decay still continues now in the focal zone of the earthquake. Statistical analysis of earthquake catalogs indicates that the power-law dependence characterizes occurrence of both foreshocks and aftershocks. Mainshock can be considered as an aftershock which happen to be stronger than the previous event.

n(t) = 1/(t+c): c-value does not have physical meaning Positive c-value means that aftershock rate goes to infinity before the mainshock. It is usually interpreted as delay between mainshock rupture end and the start of aftershock activity. Negative c-value means that aftershock rate singularity occurs after the mainshock. This is a more natural assumption. No reliable empirical regularities in c-value behavior have been found.

From Fig. 2 Reasenberg (JGR, 1999): b -- Pairs with foreshock magnitude >= 5.0 and mainshock magnitude >= 5.0, N=1966; d -- Mf >=5.0, Mm >=6.0, N=562.

C > 0 means that aftershock rate goes to infinity at negative time (t<0), i.e., before the mainshock. In log-log scale, when starting at small positive time, the rate increase is shown below.

Reasons for non-zero c-value The overlapping of seismic records in the wake of a strong earthquake. Workforce constraint. Absence or malfunction of seismic stations close to the source zone. Extended spatio-temporal character of earthquake rupture zone -- failure of the point model of earthquake source.

Time interval between end of mainshock and beginning of aftershock sequence End of mainshock rupture is defined by a relative low level of moment release. If the release is still high, this is considered as a continuation of earthquake rupture process. Hence the low level interval is assumed in definition of rupture duration during retrospective interpretation of seismic records.

Time evolution of rupture for the 1999/08/17 Izmit earthquake (Fig. 17 in Delouis et al., BSSA, 92(1), 2002).

Time evolution of rupture for the 1999/10/16 Hector mine earthquake (Fig. 7 in Kaverina et al., BSSA, 92(4), 2002).

H. Houston (JGR, 2001, Fig. 6): 255 events, listed in order of increasing depth. Based on the analysis of Tanioka and Ruff (SRL, 1997) source time functions.

Blue curve -- average of functions truncated at assumed rupture duration. Green and red curves - - averages of 26 and 31 s of the functions (without truncation).

Simulated source-time functions and seismograms for shallow earthquake sources. The upper trace is a synthetic source-time function. The middle plot is a theoretical seismogram, and the lower trace is a convolution of the derivative of source-time function with the theoretical seismogram (Kagan and Knopoff, JGR, 1981).

Conclusions 1. Short-term aftershocks are significantly incomplete in both local and global earthquake catalogs. The incompleteness is more severe for small aftershock events, although even strong aftershocks may be absent closer to the mainshock rupture end. The reasons for this incompleteness are diverse: limitations of the seismographic network, overload of processing facilities in the beginning of aftershock sequences of strong mainshocks, and fundamental difficulties in interpreting complex overlapping seismic records.

2. The number of missing earthquakes in extensive aftershock sequences depends on the magnitude range of a catalog and the seismogram frequency range. For local earthquake catalogs, like the CIT, such a number may be comparable or even exceed the total number of earthquakes in a catalog. Analyzing worldwide earthquake catalogs shows that a significant number of smaller aftershocks are not recorded in the PDE catalog. For the CMT catalog only with its relatively small magnitude range ( ) and use of low-frequency recording, the number of under-reported events is insignificant. 3. These deficiencies in earthquake catalogs, unless fully explored, may introduce substantial biases in the results of statistical analysis.

4. The large non-zero values for the c-coefficient in the Omori law are most likely due to missing aftershocks, especially small ones. Closer to the mainshock origin time, the point model of earthquake source breaks down. Hence, the Omori formula is not expected to reasonably approximate aftershock numbers. 5. For several large mainshocks the recent inversions of slip time-space history exhibit temporal, spatial, and focal mechanism complexity of seismic moment release. We propose that this complexity be represented as an aftershock generating mechanism extended to a mainshock rupture process.

6. Therefore, in a final short-term approximation the earthquake process can be represented as a fractal assemblage of infinitesimal dislocations. What is usually called an individual earthquake is a tightly clustered group of subevents. An earthquake definition truly depends on the properties of the seismographic network and the methods of seismogram interpretation.

Additional recent studies of short- term aftershocks Vidale, J. E., E. S. Cochran, H. Kanamori, and R. W. Clayton, After the lightning and before the thunder; non-Omori behavior of early aftershocks? Eos Trans. AGU 84(46), Fall Meet. Suppl., Abstract S31A-08. Kilb, D., Martynov, V., and Vernon, F., Examination of the Temporal Lag Between the 31 October 2001 Anza, California, M 5.1 Mainshock and the First Aftershocks Recorded by the Anza Seismic Network. (04-149) Poster at the 2004 SSA meeting.