Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Slip complexity in dynamic models of earthquake faults.

We summarize recent evidence that models of earthquake faults with dynamically unstable friction laws but no externally imposed heterogeneities can exhibit slip complexity. Two models are described here. The first is a one-dimensional model with velocity-weakening stick-slip friction; the second is a two-dimensional elastodynamic model with slip-weakening friction. Both exhibit small-event complexity and chaotic sequences of large characteristic events. The large events in both models are composed of Heaton pulses. We argue that the key ingredients of these models are reasonably accurate representations of the properties of real faults.

Extraordinary divergence and positive Darwinian selection in a fusagenic protein coating the acrosomal process of abalone spermatozoa.

During fertilization in marine invertebrates, fusion between sperm and egg cell membranes occurs at the tip of the sperm acrosomal process. In abalone sperm the acrosomal process is coated with an 18-kDa protein. In situ, this protein has no effect on the egg vitelline envelope, but in vitro it is a potent fusagen of liposomes. Thus, the 18-kDa protein may mediate membrane fusion between the gametes, a step in gamete recognition known to restrict heterospecific fertilization in other species. The cDNA and deduced amino acid sequences of the 18-kDa protein were determined for five species of California abalone. The deduced amino acid sequences exhibit extraordinary divergence; the percent identity varies from 27% to 87%. Analysis of nucleotide substitution shows extremely high frequencies of amino acid-altering substitution compared to silent substitution, demonstrating that positive Darwinian selection promotes the divergence of this protein. However, amino acid replacement is conservative with respect to size and polarity of residue. The data support the developing idea that in free-spawning marine invertebrates, the proteins mediating fertilization may be subjected to intense, and as yet unknown, selective forces. The extraordinary divergence of fertilization proteins may be related to the establishment of barriers to heterospecific fertilization.