Finite Fault Model

Updated Result of the Sep 3, 2010 Mw 7.0 Darfield, South Island New Zealand Earthquake

Gavin Hayes, NEIC


DATA Process and Inversion

We used GSN broadband waveforms downloaded from the NEIC waveform server. We analyzed 37 teleseismic broadband P waveforms, 34 broadband SH waveforms, and 61 long period surface waves selected based upon data quality and azimuthal distribution. Waveforms are first converted to displacement by removing the instrument response and then used to constrain the slip history based on a finite fault inverse algorithm (Ji et al, 2002). We supplement this displacement data set with velocity records for all of the selected body waves. We shift the hypocenter of the USGS approximately 10 km to the south-southeast to align with the surface trace of the mapped rupture (Lon.=-43.615 deg.; Lat.=172.049 deg.). The fault planes are defined using the updated NEIC W-phase moment tensor solution.


Result

After comparing the waveform fits based on two planes, we find that the nodal plane (strike=85.1 deg., dip=82.2 deg.) fits the data better. The seismic moment release based upon this plane is 4.3E+026 dyne.cm using a 1D crustal model interpolated from CRUST2.0 (Bassin et al., 2000).

Cross-section of slip distribution

slip

Figure 1. Cross-section of slip distribution. The strike direction of fault plane is indicated by the black arrow and the hypocenter location is denoted by the red star. The slip amplitude are showed in color and motion direction of the hanging wall relative to the footwall is indicated by white arrows. Contours show the rupture initiation time in seconds.


Moment Rate Function

rate of moment release

Figure 2. Source time function, describing the rate of moment release with time after earthquake origin.


Comparison of data and synthetic seismograms

Comparison of teleseismic body waves.

Figure 3.1. Comparison of teleseismic body waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of teleseismic body waves.

Figure 3.2. Comparison of teleseismic body waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of teleseismic body waves.

Figure 3.3. Comparison of teleseismic body waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of teleseismic body waves.

Figure 3.4. Comparison of teleseismic body waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of teleseismic body waves.

Figure 3.5. Comparison of teleseismic body waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of long period surface waves.

Figure 4.1. Comparison of long period surface waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of long period surface waves.

Figure 4.2. Comparison of long period surface waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Comparison of long period surface waves.

Figure 4.3. Comparison of long period surface waves. The data is shown in black and the synthetic seismograms are plotted in red. Both data and synthetic seismograms are aligned on the P or SH arrivals. The number at the end of each trace is the peak amplitude of the observation in micro-meters. The number above the beginning of each trace is the source azimuth and below is the epicentral distance. The shading of each record indicates their relative weighting in the inversion (thin lines/light color means lower weighting).


Cross-section of apparent rupture velocity on the fault plane.

Figure 5. Cross-section of apparent rupture velocity on the fault plane. The strike direction of fault plane is indicated by the black arrow and the hypocenter location is denoted by the red star. The rupture velocity is shown in color and motion direction of the hanging wall relative to the footwall is indicated by arrows. Contours show the rupture velocity in 0.025 km/sec intervals.


Inferred horizontal deformation field

Figure 6. Inferred horizontal deformation field resulting from this earthquake, using Coulomb3.1. Colors represent the magnitude of horizontal deformation resulting from the modeled slip distribution. Red arrows represent the magnitude and direction of this deformation. Contours are spaced every 0.05 m.


Inferred horizontal deformation field

Figure 7. Inferred vertical deformation field resulting from this earthquake, using Coulomb3.1. Colors represent the magnitude of verticall deformation resulting from the modeled slip distribution. Contours are spaced every 0.05 m.


Gavin's Comments:

This update is based on detailed modeling of the rupture process of the Darfield earthquake, after updates to the hypocenter and CMT solution. No other constraints are imposed on the inversion. The origin time of this solution matches the initiation of the main shock (16:35:46) rather than the inferred foreshock 5s earlier.


Slip Distribution


References

Ji, C., D.J. Wald, and D.V. Helmberger, Source description of the 1999 Hector Mine, California earthquake; Part I: Wavelet domain inversion theory and resolution analysis, Bull. Seism. Soc. Am., Vol 92, No. 4. pp. 1192-1207, 2002.

Bassin, C., Laske, G. and Masters, G., The Current Limits of Resolution for Surface Wave Tomography in North America, EOS Trans AGU, 81, F897, 2000.


Acknowledgement and Contact Information

This work is supported by the National Earthquake Information Center (NEIC) of the United States Geological Survey. This web page is built and maintained by Dr. G. Hayes at the NEIC.