SCEC funded research under this project in 1997 saw the completion and publication of two studies, and the initiation and submission of one other. I abstract these below:
Ward, S. N., 1997. Dogtails versus Rainbows: Synthetic earthquake rupture models as an aid in interpreting geological data, Bull. Seism. Soc. Am., To appear in the December Issue.
Geologists have been collecting, for decades, information from historical and paleoearthquakes that could contribute to the formulation of a "big picture" of the earthquake engine. Observations of large earthquake ruptures, unfortunately, are always going to be spotty in space and time and I believe that the extent to which such information succeeds in contributing to a grander view of earthquakes is going to be borne not only by the quantity and quality of data collected, but also by the means by which it is interpreted. This paper addresses the need to more fully understand geological data through carefully tailored computer simulations of fault system ruptures. Dogtails and rainbows are two types of fault rupture terminations that can be recognized in the field and can be interpreted through these models. Rainbows are concave down ruptures that indicate complete stress drop and characteristic slip. Rainbow terminations usually coincide with fault ends or strong segment boundaries. Dogtails are concave up ruptures that indicate incomplete stress drop or stress increase and non-characteristic slip. Dogtail terminations can happen anywhere along a fault or fault segment. The surface slip pattern of the 1979 Imperial Valley earthquake show dogtail and rainbow terminations to the north and south respectively (Figure 3). The rainbow confirms the presence of a strong fault segment boundary six km north of the international border that had been suggested by Sieh (1996). The dogtail implies that the displacement observed in the 1979 quake is not characteristic. By combining information from the 1940 and 1979 surface slip patterns, paleoseismic data, and seismologically determined stress drop estimates, a quantitative Imperial fault model was developed with northern, central, and southern segments possessing 50, 110 and 50 bar strength and 28(, 13 and 22( km length respectively. Both the 1940 and 1979 events showed 1-meter amplitude dogtailed ruptures of the northern segment; however, characteristic slip of the segment is more likely to be about 3 meters. To illustrate the full spectrum of potential rupture modes, models were run forward in time to generate 2000 year rupture "encyclopedia". Although the segmentation and strength of the Imperial fault are well constrained, modest changes in two friction law parameters produce several plausible histories. Further discrimination awaits analysis of the extensive paleoseismic record that geologists believe exists in the shore deposits of the intermittent lakes of the Salton Trough.
Ward, S. N., 1997. More on Mmax, Bull. Seism. Soc. Am., 87, 1199-1208.
Mmax, the maximum magnitude earthquake that a fault is likely to suffer, plays an important role in earthquake hazard estimation. Although observational evidence summarized in plots of characteristic earthquake magnitude (Mchar) versus fault length indicate that smaller faults produce lower magnitude events, an argument has been made that any fault regardless of its length should have Mmax near magnitude eight. The rationale for this argument charges that the contrary observational evidence stems from historical catalogs of limited extent, and that it largely excludes non-conventional earthquakes in which several short and apparently disconnected fault segments fail simultaneously. This paper addresses Mmax using computer models of rupture on faults of various strengths and configurations. Computer models have advantages in that: (a) Mmax quakes always can be generated by forcing complete stress drop on fully stressed faults, thus avoiding the limitations of short historical catalogs; and, (b) that the circumstances necessary for the failure of several segments to contribute to a large Mmax can be investigated quantitatively. I find that for a strike slip California environment, it is physically unlikely for a M8 event to break less than 300-400 km of fault. Were this M8 rupture to occur on as few as five independent segments, shear strength of the participating faults would have to be raised to implausible levels. If the fault segments are not independent and their coseismic stress fields interact, then amplifications in slip are possible without drastic increase in strength. The range of fault geometries where strong interactions and amplifications of stress occur however, is very restricted and discontinuous faults separated by even 5% of their length act more or less independently. Mmax earthquakes breaking realistic-looking distributions of discontinuous faults rarely are more than 0.1 magnitude unit bigger than would be predicted from a moment summation based on the characteristic magnitude Mchar of each of the individual faults (Figure 4). A prudent course in hazard analysis differentiates Mmax from Mchar, allowing Mmax to be 0.2 to 0.3 units larger than Mchar, but not automatically equal to 8.
Ward, S. N., 1997. On the Consistency of Earthquake Moment Rates, Geological Fault Data, and Space Geodetic Strain: The United States,(Geophysical Journal Int., Submitted.
New and dense space geodetic data can now map strain rates over continental-wide areas with a useful degree of precision. Stable strain indicators open the door for space geodesy to join with geology and seismology in formulating improved estimates of global earthquake recurrence. In this paper, 174 GPS/VLBI velocities map United States' strain rates of <0.03 to >30.0 x10-8/y with regional uncertainties of 5 to 50%. Kostrov's formula translates these strain values into regional geodetic moment rates. Two other moment rates, seismic and geologic extracted from historical earthquake and geological fault catalogs, contrast the geodetic rate. Because geologic, seismic and geodetic derive from different views of the earthquake engine, each illuminates different features. In California, ratios of geodetic to geologic are 0.93 to 1.0. The consistency points to the completeness of the region's geological fault data and to the reliability of geodetic measurements there. In the Basin and Range, Northwest and Central United States, both geodetic and seismic greatly exceed geologic. Of possible causes, high incidences of understated and unrecognized faults most likely drive the inconsistency. The ratio of seismic to geodetic is everywhere less than one. The ratio runs systematically from 70-80% in the fastest straining regions to 2% in the slowest. Although aseismic deformation may contribute to this shortfall, I argue that the existing seismic catalogs fail to reflect the long term situation. Impelled by the systematic variation of seismic to geodetic moment rates and by the uniform strain drop observed in all earthquakes regardless of magnitude, I propose that the completeness of any seismic catalog hinges on the product of observation duration and regional strain rate. Slowly straining regions require a proportionally longer period of observation. Characterized by this product, gamma distributions model statistical properties of catalog completeness as proxied by the ratio of observed seismic moment to geodetic moment. I find that adequate levels of completeness should exist in median catalogs of 200 to 300 year duration in regions straining 10-7/y (comparable to southern California). Similar levels of completeness will take more than 20,000 years of earthquake data in regions straining 10-9/y (comparable to southeastern United States). Predictions from this completeness statistic closely mimic the observed seismic to geodetic ratios and allow quantitative responses to previously unanswerable questions such as: "What is the likelihood that the seismic moment extracted from a earthquake catalog of X years falls within Y% of the true long term rate?" The combination of historical seismicity, fault geology and space geodesy offers a powerful tripartite attack on earthquake hazard. Few obstacles block similar analyses in any region of the world.
Figure 1. A dogtail/rainbow fault simulation. Strengths and initial stress were altered so that the final rupture magnitude and extent closely matched the observed slip distribution of the 1979 Imperial Valley earthquake (line and squares, bottom). With a physical model now arguing in support, the likelihood of a hard segment boundary at the southern terminus of the 1979 rupture seems very high, even based on a single rupture sample. The height and dimension of the rainbow termination fix the strength of the northern section of the fault at 40 bars or more. The hard segment boundary must be a least twice as strong to stop the rupture so quickly.
Figure 2. Mmax calculated for distributions of fault segments that resemble actual southern California faults. In each instance, the total length of rupture is 400 km and all of the fault segments experience a uniform 10 bar stress drop. The two numbers in parentheses are two expected magnitudes, and . None of the modeled faults produced an Mmax earthquake greater than would be expected from a sum of the moments of the individual segment failures. By and large, coseismic stress amplifications and reductions cancel in realistic-looking fault geometries.
Figure 3. Space geodetic sites whose velocities are employed in this paper. Filled circles are VLBI sites from NASA/GSFC model Global 1014j. Empty circles are GPS/VLBI sites from the SCEC velocity model. White boundaries mark a seven member regionalization over which strain and moment rates will be averaged.
Figure 4. Maximum geodetic strain rates in units of 10-8/y as determined from the space geodetic data of Figure 3. Strain rates in the United States vary by over a factor of 1000 from <0.03 x10-8/y in the Central/Southeast to >30.0x10-8/y in southern California.
Figure 5. Plots of 10% to 90% percentile outcomes of the ratio of observed moment rate to geodetic moment rate versus geodetic strain rates for 150 (left) and 300 (right) year earthquake catalogs. The circles are data taken as median values. Stability of catalog moment estimates increases with strain rate. In fast straining areas like California, half of 150 year catalogs should estimate mean moment rate within 50%. In slower straining regions, 150-300 year catalogs will likely understate long term moment rates drastically. A seismic moment rate to geodetic moment rate deficit in areas of low strain rate is not indicative of aseismic deformation, but rather of insufficient earthquake sampling. The stars mark conditions in the Southeast region. The high ratio suggests that events as large as 1886 the Charleston earthquake are uncommon in 300 year catalogs.
1997 SCEC Funded Publications.
Ward, S. N., 1997a. More on Mmax, Bull. Seism. Soc. Am., 87, 1199-1208.
Ward, S. N., 1997b. Dogtails versus Rainbows: Synthetic earthquake rupture models as an aid in interpreting geological data, Bull. Seism. Soc. Am., Accepted for December Issue.
Ward, S. N., 1997c. On the consistency of earthquake rates, geological fault data, and space geodetic strain: The United States, Geophys. Jour. Int., submitted.
