Other
Scientific paper
Dec 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufm.s21e..04a&link_type=abstract
American Geophysical Union, Fall Meeting 2001, abstract #S21E-04
Other
7209 Earthquake Dynamics And Mechanics, 7215 Earthquake Parameters
Scientific paper
We select 29 earthquakes well-recorded at 2.5 km depth at Cajon Pass (Abercrombie, 1995), including some colocated events. We compare spectral and time domain inferences of the source dimension to estimate final slip s and static stress drop Δ τ . We measure radiated energy Es by integration of the velocity-squared spectra using simple fits to extend the bandwidth outside the observed range to ensure we do not lose significant energy due to instrumental limits. (The Es estimates of Abercrombie (1995) for earthquakes Mo < 5x 1011 Nm are selectively biased to small stress drops, but otherwise the results are similar.) We compare the CJP results with those from larger California earthquakes including Northridge aftershocks and confirm Abercrombie (1995): for the smallest earthquakes, μ Es/M_o << Δ τ (where μ = rigidity) and Es/M_o increases more rapidly than Δ τ as Mo (and also s) increases. To interpret this we define a quantity G' = [Δ τ - 2μ Es/M_o]s/2 which is the total energy dissipation in friction and fracture minus τ s s, where τ s is the final static stress. If τ s = τ d, the dynamic shear strength during the last increments of seismic slip, then G' = G, the fracture energy in a slip-weakening interpretation of dissipation, with τ d then identified as the residual shear strength of Palmer and Rice (1973). Otherwise G' = G + (τ d - τ s)s. We find that G' increases with s, from ~103 J/m2 at s = 1 mm (M1 events) to 106 to 107 J/m2 at s = 1 m (M6). An increasing rupture velocity with Mo cannot explain these results because it would imply unreasonably high Δ τ for the small earthquakes. We tentatively interpret these results within slip-weakening theory, assuming G' ≈ G (i.e., τ s ≈ τ d). One explanation for these observations within the often assumed linear decrease of strength with slip, up to a slip Dc, is that either Dc, or the peak to residual strength drop τ p - τ d, or more generally (τ p - τ d) Dc, varies in proportion to the final slip s. This can match the observations, but implies the unlikely result that the weakening behavior of the fault depends on the final size of the earthquake. We also find that a single slip-weakening function τ (s) is able to match the observations, requiring no such correlation. Fitting G over s = 1 mm to 0.5 m with G ~ s{1 + n}, we find n ~ 0.1 to 0.2. We show that this implies a strength drop from peak τ p - τ (s) ~ sn. This model also implies that the slip weakening continues beyond the final slip s of typical events smaller than ~M6, and that the total strength drop τ p - τ d for large earthquakes is typically > 20 MPa and notably larger than Δ τ . The latter suggests that on average the fault is initially stressed well below the peak strength, requiring stress concentration at the rupture front to propagate slipping. Other interpretations need to be explored outside the context of slip-weakening and allowing for dynamic over/undershoot.
Abercrombie Rachael E.
Rice James R.
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