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1. Introduction

Automatically generated moment tensor solutions have recently been added to the suite of real-time products produced by the Southern California Seismic Network (SCSN/CISN). The moment magnitude, Mw, and the moment tensor are both available within minutes for all regional earthquakes that trigger the network with Ml > 4.0, and in many cases for events between Ml3.5−4.0. The method uses the 1-D Time-Domain INVerse Code (TDMT INVC) software package developed by Doug Dreger, which is routinely used in real-time by the UC Berkeley Seismological Laboratory. Green’s Functions are determined for various velocity profiles in Southern California, which are used in the inversion of observed three component broadband waveforms (10s−100s) for a number of stations. Automatic solutions have an assigned quality factor dependent on the number of stations in the inversion, and the goodness of fit between synthetic and observed data. Dependent on the quality, the Mw and moment tensor may be automatically distributed to the general community through e-mail, USGS Simpson’s Maps, and CISNDisplay. The duty seismologists can review the automatically generated solution and re-distribute the solution. A web-interface has been developed to evaluate the quality of the automatic solution, and determine whether it meets the minimum requirements for an immediate distribution. Simple modifications to the stations selected for the inversion are possible, and the inversion can be re-run to optimize the solution. If a minimum quality factor is attained, if the event is in the Southern California reporting regions, the Mw will be the official SCSN/CISN magnitude. The real-time algorithm has been applied to all regional events with Ml > 3.5, and local events with Ml > 3.0 from SCSN catalog stored at the SCEDC. The results show the ability of the method to reliably reproduce, for local events, Mw with Ml > 3.5, and Moment Tensors for Ml > 4.0. Further, the method provides excellent backup solutions for larger events at larger distances, such as in Northern California or Baja California. Comparisons of the moment tensors determined using this model are made with Harvard Centroid Moment Tensors generated for larger earthquakes in the California region, and recent 3-D models for events in the LA region, with excellent correlation.

Fig 4.

2. The Automatic Inversion Process

TMTS Inversion
The SCSN Moment Tensor Real Time Solution is based on the method developed at Berkeley Seismological Laboratory by Doug Dreger. The underlying code is the same as that used for solutions at the Northern California Seismic Network (NCSN), and F-Net in Japan. The solution uses 3-component, low frequency waveform data to estimate the moment tensor, which is decomposed into a scalar seismic moment and double couple orientation parameters, strike, slip and rake. Synthetics derived from the three fundamental faults are used as the basis functions. These fundamental fault synthetics are combined with various 1-D velocity structures typical to Southern, Central and offshore California to form a library of Green’s Functions which are used to match the observed waveforms. The filtering of the observed data, and the Green’s functions used to match the solutions, is dependent on magnitude of the event [Ml < 3.5 : 10−50s; 3.5 < Ml < 5.0 : 20−50s; Ml > 5.0: 20−100s]. This reflects the increased long period energy of larger events. The quality of a solution is determined by the goodness of the fit of synthetic data to the observed data. The Variance Reduction, VR, is a parametric measure of this fit, defined as :

For each solution, the inversion is run with the point source depth at various levels typical of Southern California events (5,8,11,15,18,21km). Inverting at shallower depths can give erroneous solutions, and deeper events are not realistic for Southern Californian events The optimal solution depth is determined as the solution where the variance reduction is maximized.

Real Time Solution

The automatic solution is set to run on all local events with Ml > 3.0, and regional events with Ml > 3.5, identified by the SCSN real-time system. The Mw and Moment Tensor solutions obtained by the SCSN employ a rigorous algorithm which selects broadband velocity data at optimal distance with good azimuthal coverage to attempt to maximise the VR and the stability of the solution. The station list comprises over 200 sites (all CI, AZ, selected BK), and selected data must be between 40−700km of the epicenter, and below 60% of the clipping level of the broadband instruments (0.6cm/s). Selected stations must be from differing azimuthal sectors defined about the epicenter. The real-time algorithm assigns a Quality Value to the solution:

• Quality A The best solution is Quality A (6 stations, VR > 60%), and represents a solution which
is stable enough for both Moment Tensor and Mw to be distributed without further review. The initial
solution searches for a VR>85% for each station in order to obtain the best solution possible (example:
FIGURE 1).
• Quality B If a Quality A solution cannot be obtained, a Quality B solution (4 stations, VR > 40%) is
searched for. Solutions of this nature have a robust Mw fit for immediate distribution, but the Moment
Tensor may not be stable enough for distribution.
• Quality C If no solution can be found which fits Quality B, a Quality C solution is determined using the
3 best stations as determined from the inversions performed in the search for Quality A, B solutions.

A Quality C solution does not have the Mw automatically distributed without review, but does populate the SCEDC database. RealTime and Web-modified solutions (the web interface is shown in FIGURE 2) are distributed by e-mail lists, USGS Simpson’s Maps, CISNDisplay and the SCEDC. The SCEDC hosts a website with permanent archive which queries the SCSN moment tensor database (FIGURE 3).

 

3. The Catalogue : 1999-2004

Entire Dataset

Continuous data has been recorded since Sept. 1999. The solution is run on all events with Ml > 3.0(local) and Ml > 3.5(regional) since this date. All events with solutions (1450 events) are presented in Figure 4. Each focal mechanism is colour-coded for Quality A, B and C. Larger events are typically of Quality A. Figure 5 shows Mw vs. Ml for the dataset. For the approx. 200 Quality A events, the scatter of Ml vs. Mw tends to be small. Though some events differ significantly, it is shown later these appear to be real differences, as other Mw solutions are similar to these here. In Figure 6 the similarity of depths from the Ml solution and the Mw solution are investigated. Clearly there is little correlation between these 2 parameters. Depth is thus ignored in the rest of this investigation.

Individual Years for Southern California Region Events

Figures 7-12 summarize the evolving performance of the solution during the 6 individual years which comprise the catalogue. Only events within the geographical box indicated in Fig. 4 are shown. These include part of the Northern California reporting region, but is included as station density is still relatively good, and 2 large sequences recently
occurred here. The 1999 plots are not complete, only partial time sequences starting from September are available for
a limited number of stations. The Mw7.1 Hector Mine mainshock clips all available stations, so no solution is possible. Nevertheless, the aftershock sequence is so robust there are many more events from these few days than from any other year. Unfortunately, the combination of limited station density at the time, and the occurance of many events very closely spaced means there are a large number of events with Ml > 4 with low quality solutions and many events have inflated magnitudes. 2000, 2001 and 2003 have reduced seismicity. During this period, the SCSN network was growing rapidly, as is the list of available stations. Almost all events within So. Cal. and above Ml3.5 have at least Quality B solutions. ln most all solutions above Ml4.0 with Quality C solutions are associated with aftershock sequences In 2003, the San Simeon sequence at the end of the year dominates the response, and is responsible for all the Quality C solutions with elevated Mw above Ml = 3.5. The Parkfield earthquake is only one of 5 events with Ml > 5 which occurred in 2004. These large events all have good solutions with focal mechanisms similar to other moment tensor solutions, though the aftershock
sequences produce multiple poor solutions for large events. As the density of the network has increased over the course of the catalogue, so have the number of Quality A solutions above Ml4.0

To view the above images, click on the image

 

4. Comparison with other MT Solutions

The Harvard CMT catalogue has solutions for 12 events in the SCSN catalogue. Further, Liu et al (2004) present Moment Tensor solutions from 3-D inversions for 3 Los Angeles region events which also have SCSN and other solutions. Data from these events are compared in Figs. 13 and 14. The SCSN Mw and moment tensors are very similar to other moment tensor solutions over the broad geographical and magnitude ranges of the events in question. The main deviation in magnitude appears to be between the Ml and the other Mw solutions. Thus the deviations observed in the catalogue at large magnitudes (see Figure 4) are likely to true differences, and not a problem with this Mw implementation. The moment tensor is generally found to be stable irrespective of station selection (as long as individual station VR is not very poor) if the overall VR > 60%. Magnitude is similarly stable down to about VR > 40%.

5. Real-Time Mw/MT Challenges

Large Mainshocks, Aftershocks

The Mw7.1 Hector Mine event saturated all the limited number of stations available at the time of the event. A recurrence of this event should not clip the entire network now available, as selected Berkeley stations are now included. The expected M8+ San Andreas event could clip all available broadband events, though the point-source assumption would be violated in this case. We plan to include some IRIS stations from the mid-west in the station list in order to be able to constrain large magnitude events, which would remain on-scale and not violate the point-source approximation. The aftershock sequence of Hector Mine included a large number of events within a few hours of the mainshock. These were assigned Ml solutions with a wide variation in magnitude, most below Ml5. The Moment tensor solution was unable to determine the magnitude of these events - all events within an hour of the mainshock had Mw > 5.0. The first Quality A solution after the event is a Mw5.37 (Ml5.63), 3hours and 15mins after the mainshock. Although the density of stations at the time of this sequence is significantly inferior to the network today, it appears the long period energy from the mainshock prevents solutions for aftershocks being accurately determined. The recent San Simeon and Parkfield events do not exhibit this same lack of resolution in the aftermath of the mainshock, though their aftershock sequences were not as vigorous as those from the significantly larger Hector Mine event. Nevertheless, the increased density of stations may also be a factor in the improved performance.

Teleseisms Tangential Radial Vertical

Teleseisms can introduce significant long period energy into the local reporting region, which can be well above the level produced by moderate local events. This can cause erroneously large Mw with low VR and a poor moment tensor solution. Figs. 17 and 18 show an example from July 15, 2004, where a local Ml3.0 is erroneously assigned a Mw4.45 with VR=39% due to incoming waveforms from a Mw5.7 teleseism at 1944km. This phenomenon is responsible for numerous of the Mw4+ solutions with low VR in Figs. 6-11.

6. Summary

• We have demonstrated the Moment Tensor and Moment Magnitudes can be well-determined in near-real time for almost all local Southern California Events with Ml > 4. Solutions are available within 12 minutes of an event trigger

• A Quality factor is assigned to each solution, based on number of stations, and the overall Variance Reduction of the fit.: A (best, Mw and Moment Tensor automatically released), B (Mw only automatically released, Moment Tensor solution may be unreliable) and C (Mw and Moment Tensor may be unreliable). The automatic solution can be modified using a web interface where the selected stations can be changed.

• For Type A and B events within the SCSN reporting domain, solutions are distributed by e-mail and automatically created links, using QDDS,
on CISNDisplay and the suite of USGS Simpson’s Maps. For all solution types, a text e-mail, plot of VR vs. Depth, and best depth waveform plot
is available through SCSN/SCEDC

• SCEDC houses an searchable archive of all solutions from 1999-2004. It will be available to the public early in the new year.

ACKNOWLEDGMENTS: WE THANK DOUG DREGER, LIND GEE, PEGGY HELLWEG AND PETE LOMBARD FROM THE BERKELEY SEISMOLOGICAL LABORATORY FOR THEIR DISCUSSION AND ADVICE. MOMENT TENSORS ARE COMPUTED USING THE MTPACKAGEV1.1 PACKAGE DEVELOPED BY DOUGLAS DREGER OF THE BERKELEY SEISMOLOGICAL LABORATORY, AND GREEN’S FUNCTIONS WERE COMPUTED USING THE FKRPROG SOFTWARE DEVELOPED BY CHANDAN SAIKIA OF URS. MAPS CREATED WITH GMT. THE SCSN IS FUNDED BY USGS/ANSS AND CALIFORNIA OES