- Introduction
- Method
- Computational setup
- Inversion results and interpretations
- Acknowledgements
- References

Inspired by *Hartzell et al.* (1978), we directly inverted observed seismograms using the linear least-squares method of *Hartzell and Heaton* (1983)
in which the finite-source is discretized with a finite distribution of point sources in both space and time instead of inverting deconvolved moment rate functions. In this method, the point sources are triggered by the passage of a circular rupture front.
The Greens function from each subfault to station is defined by the waveform of a small earthquake, or eGf, located near the hypocenter of each subfault. One advantage of this method is that propagation differences over the fault are better represented for each station. The observed seismogram at location *x*
for the main event, *U*, is expressed by the discrete form of the general representation theorem:

where is the location of subfault. ,, and are subfault area, rigidity, and slip for the

where and represent the data and synthetic time series, respectively. The subscript

We used three-component velocity waveforms recorded at five of the Berkeley Seismological Laboratory's High Resolution borehole Seismic
Network (HRSN) stations to examine the rupture processes of the same 5 repeating earthquakes studied by *Dreger et al.* (2007). We also performed eGf deconvolution inversions using the 5 stations, to allow comparison with our waveform inversion results. Locations of repeating earthquakes and stations are
shown in Figure 2.22. For the inversion, we used the same fault parametrization as *Dreger et al.* (2007), a
fault decomposed into 31 by 31 square subfaults of
. The strike, dip, and rake are 137, 90, and 180, respectively. The records from HRSN are sampled at 250 sps, which gives an effective bandwidth of 100 Hz. The subfault size is consistent with approximately a quarter of the wavelength of S waves assuming a velocity of 2.3 km/s at 2.1 km depth. We used the same 0.68 event (eGf 1) as *Dreger et al.* (2007) for the Greens function. eGf 1 is located about 10 m away from the centroid of the target events (*Dreger et al.*, 2007).
Since the eGf is a real earthquake, the waveforms contain a rise time which can bias the slip model to be more compact than it actually is. To cancel this effect, we convolved an assumed eGf rise time of 0.008 seconds with the data before performing the inversion. (*Dreger et al.* (2007)).

Dreger, D., R. M. Nadeau, and A. Chung (2007), Repeating earthquake finite source models: Strong asperities revealed on the San Andreas Fault, *Geophys. Res. Lett.*, 34, L23302, doi:10.1029/2007GL031353.

Hartzell S. H. (1978), Earthquake aftershocks as Green's function, *Geophys. Res. Lett.* 5, 1-4.

Hickman, S., M. Zoback, and W. Ellsworth (2004), Introduction to special section: Preparing for the San Andreas Fault Observatory at Depth, *Geophys. Res. Lett.*, 31, L12S01, doi:10.1029/2004GL020688.

Imanishi, K., W. L. Ellsworth, and S. G. Prejean (2004), Earthquake source parameters determined by the SAFOD Pilot Hole seismic array,*Geophys. Res. Lett.*, 31, L12S09, doi:10.1029/2004GL019420.

Imanishi, K., and W. L. Ellsworth (2006), Source scaling relationships of microearthquakes at Parkfield, CA, determined using the SAFOD pilot hole seismic array, in Earthquakes: Radiated Energy and the Physics of Earthquake Faulting, R. E. Abercrombie, A. McGarr, H. Kanamori and G. Di Toro (Editors), *American Geophysical Monograph* 170, 81-90.

Lawson, C. L., and R. J. Hanson (1974), Solving Least Squares Problems, Prentice Hall, Englewood Clioes, New Jersey, 340 pp.

Nadeau, R. M., W. Foxall, and T. V. McEvilly (1995), Clustering and periodic recurrence of microearthquakes on the San Andreas Fault at Parkfield, California, *Science*, 267, 503-507.

Nadeau, R. M., and L. R. Johnson (1998), Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes, *Bull. Seismol. Soc. Am.*, 88, 790-814.

Ripperger, J., and P.M. Mai (2004), Fast computation of static stress changes on 2D faults from final slip distributions, *Geophys. Res. Lett.*, 31, L18610.

Thurber, C., H. Zhang, F. Waldhauser, J. Hardebeck, A. Michaels, and D. Eberhart-Phillips (2006), Three-dimensional compressional wavespeed model, earthquake relocations, and focal mechanisms for the Parkfield, California, region, *Bull. Seism. Soc. Am.*, 96, S38-S49.

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