ALBERT

Description: We study the unipotent elements of disconnected algebraic groups of the form $G \langle \tau \rangle$ , where $G$ is a simple algebraic group in characteristic $p$ possessing a graph automorphism $\tau$ of order $p$ . We classify the unipotent classes in the coset $G\tau$ and determine the corresponding centralizers, showing that these bear a close relation to classes in a certain natural connected overgroup of $G \langle \tau \rangle$ . We also obtain a formula for the total number of outer unipotent elements in the finite group $G_ \gamma \langle \tau \rangle$ , where $\gamma$ is a Frobenius morphism, analogous to the well-known Steinberg formula for the number of inner unipotent elements.

Description: The West Tahoe–Dollar Point fault (WTDPF) extends along the western margin of the Lake Tahoe Basin (northern Sierra Nevada, western United States) and is characterized as its most hazardous fault. Fallen Leaf Lake, Cascade Lake, and Emerald Bay are three subbasins of the Lake Tahoe Basin, located south of Lake Tahoe, and provide an opportunity to image primary earthquake deformation along the WTDPF and associated landslide deposits. Here we present results from high-resolution seismic Chirp (compressed high intensity radar pulse) surveys in Fallen Leaf Lake and Cascade Lake, multibeam bathymetry coverage of Fallen Leaf Lake, onshore Lidar (light detection and ranging) data for the southern Lake Tahoe Basin, and radiocarbon dates from piston cores in Fallen Leaf Lake and Emerald Bay. Slide deposits imaged beneath Fallen Leaf Lake appear to be synchronous with slides in Lake Tahoe, Emerald Bay, and Cascade Lake. The temporal correlation of slides between multiple basins suggests triggering by earthquakes on the WTDPF system. If this correlation is correct, we postulate a recurrence interval of ~3–4 k.y. for large earthquakes on the Fallen Leaf Lake segment of the WTDPF, and the time since the most recent event (~4.5 k.y. ago) exceeds this recurrence time. In addition, Chirp data beneath Cascade Lake image strands of the WTDPF offsetting the lake floor as much as ~7.5 m. The Cascade Lake data combined with onshore Lidar allow us to map the WTDPF continuously between Fallen Leaf Lake and Cascade Lake. This improved mapping of the WTDPF reveals the fault geometry and architecture south of Lake Tahoe and improves the geohazard assessment of the region.

Description: Gravity-flow deposits recovered in a suite of sediment cores in Lake Tahoe were examined to determine if the event deposits were triggered by strong shaking from earthquakes on active faults within and in close proximity to the Lake Tahoe Basin. The acoustic character and distribution of individual lacustrine deposits as well as potential source regions were constrained by high-resolution seismic Chirp reflection and multibeam bathymetric data. Between 14 and 17 Holocene event deposits have been identified in Lake Tahoe, and examination of their source areas suggests they originated from different initiation points along the steep margin, with some being synchronous around the basin, as opposed to flood-related deposits. Lithologic characteristics, magnetic susceptibility, carbon and nitrogen isotopic signatures, opal content, and 14 C dating indicate that these event deposits are reworked lacustrine material. Radiocarbon dates indicate that the emplacement of these event deposit sediments correlates well with the late Holocene paleoseismic earthquake record developed for the Tahoe Basin. When taken alone, the causality of these events may appear ambiguous, but when the evidence is examined comprehensively, it suggests that strong shaking may likely have been the primary trigger for many of the event deposits observed in the lake throughout the Holocene. For example, four event deposits are assigned to Tahoe Basin faults. The most recent earthquakes occurred on the Incline Village fault (between 630 and 120 cal. yr B.P.); the southern segment of the West Tahoe fault (between 4510 and 4070 cal. yr B.P.); on the central and northern segments of the West Tahoe fault (5600–5330 cal. yr B.P.); and on the West Tahoe fault (between 7890 and 7190 cal. yr B.P.). The oldest of the four associated Tahoe Basin events coincides with the beginning of an extended period when Lake Tahoe was likely not spilling or spilling intermittently, and this suggests that active faulting and footwall uplift cut off the outlet at this time, exaggerating drought conditions downstream. Likewise, the event between 5600 and 5330 cal. yr B.P. on the West Tahoe fault may have exaggerated a smaller drought reflected downstream in Pyramid Lake. This event may also be the most recent event (MRE) on the largest segment of the West Tahoe fault. If correct, the period since the last rupture is approximately twice the estimated average recurrence interval for the Rubicon segment of the West Tahoe fault. A more complete Holocene record of strong shaking greatly extends the paleoseismic record in the region and indicates a combined recurrence interval of between 750 and 800 yr for all faults in the region.

Description: Stress changes produced by the 1906 San Francisco earthquake had a profound effect on the seismicity of the San Francisco Bay region (SFBR), dramatically reducing it in the twentieth century. Whether the SFBR is still within or has emerged from this seismic quiescence is an issue of debate with implications for earthquake mechanics and seismic hazards. Historically, the SFBR has not experienced one complete earthquake cycle (i.e., the accumulation of stress, its release primarily as coseismic slip during surface-faulting earthquakes, its re-accumulation in the interval following, and its subsequent rerelease). The historical record of earthquake occurrence in the SFBR appears to be complete at about M  5.5 back to 1850 ( Bakun, 1999 ). For large events, the record may be complete back to 1776, which represents about half a cycle. Paleoseismic data provide a more complete view of the most recent pre-1906 SFBR earthquake cycle, extending it back to about 1600. Using these, we have developed estimates of magnitude and seismic moment for alternative sequences of surface-faulting paleoearthquakes occurring between 1600 and 1776 on the region’s major faults. From these we calculate seismic moment and moment release rates for different time intervals between 1600 and 2012. These show the variability in moment release and suggest that, in the SFBR regional plate boundary, stress can be released on a single fault in great earthquakes such as that in 1906 and in multiple ruptures distributed on the regional plate boundary fault system on a decadal time scale.