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 MS 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.

Open-File Report↗

USGS1982

Surface displacement on the Imperial and Superstition Hills faults triggered by the Westmorland, California, earthquake of 26 April 1981

Parts of the Imperial and the Superstition Hills faults moved right-laterally at the ground surface at the time of or shortly following the ML 5.6 Westmorland earthquake of 26 April 1981. The displacements occurred prior to any significant aftershocks on either fault and thus are classed as sympathetic. Although the main shock was located in an exceptionally seismogenic part of Imperial Valley, about 20 km distant from either fault, no clear evidence of surface faulting has yet been found in the epicentral area. Horizontal displacement on the Imperial and Superstition Hills faults, southeast and southwest of the epicenter, respectively, reached maxima of 8 mm and 14 mm, and the discontinuous surface ruptures formed along approximately equal lengths of northern segments of the two structures (16.8 km and 15.7 km, respectively). The maximum vertical component of slip on the Imperial fault, 6 ram, was observed 3.4 km north of the point of largest horizontal slip. Vertical movement on the Superstition Hills fault was less than 1 mm. No new displacement was found along the traces of the Brawley fault zone, the San Andreas fault, or the part of the Coyote Creek fault that slipped during the 1968 Borrego Mountain earthquake. A careful search in the epicentral area of the main shock failed to locate any definite evidence of surface faulting. Concentrations of late aftershocks north and northeast of Calipatria near the southeastward projection of the San Andreas fault occurred mostly after our field check; this area was not investigated.

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