Relations Between Earthquake Magnitude and Fault Rupture Dimensions: How Regionally Variable Are They?

Data on subsurface rupture dimensions and seismic moments have been gathered for earthquakes in New Zealand, screened for data quality, and analyzed along with the multiregion rupture area data of Hanks and Bakun (2002). Regression analyses have been carried out for relations among magnitude and rupture length (subsurface), width, area, slip, and aspect ratio. Statistical comparisons show that there are significant differences between the regressions of New Zealand and multiregion data. The New Zealand relations among magnitude, area, and displacement are linear; those among magnitude, subsurface rupture length, and width are bilinear; whereas those between magnitude and rupture aspect ratio L / W are trilinear. The magnitudes predicted from rupture subsurface lengths, widths, or areas by multiregion relations are about 0.4 units smaller than those obtained from relations based on New Zealand data. The multiregion relations predict ruptures that are untenably large for New Zealand on the basis of structural and other evidence. Separate regressions were carried out for the California, China, and Japan subsets of the multiregion data, and it was found that there were statistically significant differences between New Zealand and California, New Zealand and Japan, New Zealand and China, and Japan and California. The respective contributions of rupture area and mean displacement to seismic moment are very different in New Zealand from those in California, Japan, and China, suggesting that rupture styles differ with geological region in a manner yet to be appropriately defined. Thus, multiregion relations are a poor approximation of the New Zealand data and perhaps also of the data of other regions where geological conditions differ substantially from the multiregion average.