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In order to refine correlations of surface-wave magnitude, fault rupture length at the ground surface, and fault displacement at the surface by including the uncertainties in these variables, the existing data were critically reviewed and a new data base was compiled. Earthquake magnitudes were redetermined as necessary to make them as consistent as possible with the Gutenberg methods and results, which necessarily make up much of the data base. Measurement errors were estimated for the three variables for 58 moderate to large shallow-focus earthquakes. Regression analyses were then made utilizing the estimated measurement errors. The regression analysis demonstrates that the relations among the variables magnitude, length, and displacement are stochastic in nature. The stochastic variance, introduced in part by incomplete surface expression of seismogenic faulting, variation in shear modulus, and regional factors, dominates the estimated measurement errors. Thus, it is appropriate to use ordinary least squares for the regression models, rather than regression models based upon an underlying deterministic relation with the variance resulting from measurement errors. Significant differences exist in correlations of certain combinations of length, displacement, and magnitude when events are qrouped by fault type or by region, including attenuation regions delineated by Evernden and others. Subdivision of the data results in too few data for some fault types and regions, and for these only regressions using all of the data as a group are reported. Estimates of the magnitude and the standard deviation of the magnitude of a prehistoric or future earthquake associated with a fault can be made by correlating M with the logarithms of rupture length, fault displacement, or the product of length and displacement. Fault rupture area could be reliably estimated for about 20 of the events in the data set. Regression of M S on rupture area did not result in a marked improvement over regressions that did not involve rupture area. Because no subduction-zone earthquakes are included in this study, the reported results do not apply to such zones. * Inasmuch as fault displacement varies with rupture length, both length and displacement would change by a factor somewhat less than 1.7.

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Landsat satellite image (LE70390372003084EDC00) showing location of surface slip triggered along faults in the greater Salton Trough area. Red bars show the generalized location of 2010 surface slip along faults in the central Salton Trough and many additional faults in the southwestern section of the Salton Trough. Surface slip in the central Salton Trough shown only where verified in the field; slip in the southwestern section of the Salton Trough shown where verified in the field or inferred from UAVSAR images.

▲ Figure 3. Calculating mean recurrence (RI) and error distribution for its uncertainty (ID). Enter these calculations by using the editor in code view. Use the generic model as a guide to formatting.

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