Slip in the 1868 Hayward earthquake from the analysis of historical triangulation data

Despite the importance of the Hayward fault for earthquake hazards in the San Francisco Bay area, neither the rupture length nor the average coseismic slip in the most recent major earthquake, which occurred in 1868 is well known. We estimate slip in the 1868 earthquake by analyzing triangulation data collected between 1853-1860 and 1876-1891. We apply a denuisancing procedure that projects out the dependence of that data on station coordinates, allowing their displacements to be estimated directly. The best fit to the data is obtained with a 52-km-long by 10-km-deep rupture that extends from Warm Springs to near Berkeley, considerably longer than the 30 km of reported surface breakage. The estimated slip for an earthquake of this length is 1.9 +/- 0.4 m, and the seismic moment is M(0) = 3.0 (+/-0.7) x 10(19) N m, corresponding to M(w) 7.0. The data are inconsistent with regionally high strain rate prior to the 1906 earthquake, as had been previously suggested. The triangulation data record northeastward displacement of station Loma Prieta, presumably as a result of the 1865 earthquake. The fault normal displacement is not easily explained by slip on either the San Andreas fault or the 1989 Loma Prieta rupture surface. This observation is, however, consistent with a M(W) similar to 6 3/4 thrust event northeast of the San Andreas fault in the southern Santa Cruz mountains thrust belt.