Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

Peak discharge of a Pleistocene lava-dam outburst flood in Grand Canyon, Arizona, USA

The failure of a lava dam 165,000 yr ago produced the largest known flood on the Colorado River in Grand Canyon. The Hyaloclastite Dam was up to 366 m high, and geochemical evidence linked this structure to outburst-flood deposits that occurred for 32 km downstream. Using the Hyaloclastite outburst-flood deposits as paleostage indicators, we used dam-failure and unsteady flow modeling to estimate a peak discharge and flow hydrograph. Failure of the Hyaloclastite Dam released a maximum 11 × 10⁹ m³ of water in 31 h. Peak discharges, estimated from uncertainty in channel geometry, dam height, and hydraulic characteristics, ranged from 2.3 to 5.3 × 10⁵ m³ s⁻¹ for the Hyaloclastite outburst flood. This discharge is an order of magnitude greater than the largest known discharge on the Colorado River (1.4 × 10⁴ m³ s⁻¹) and the largest peak discharge resulting from failure of a constructed dam in the USA (6.5 × 10⁴ m³ s⁻¹). Moreover, the Hyaloclastite outburst flood is the oldest documented Quaternary flood and one of the largest to have occurred in the continental USA. The peak discharge for this flood ranks in the top 30 floods (>10⁵ m³ s⁻¹) known worldwide and in the top ten largest floods in North America.     

The distribution of radiogenic heat production as a function of depth in the Sierra Nevada Batholith, California

Geochemical analyses and geobarometric determinations have been combined to create a depth vs. radiogenic heat production database for the Sierra Nevada batholith, California. This database shows that mean heat production values first increase, then decrease, with increasing depth. Heat production is 2 μW/m³ within the 3-km-thick volcanic pile at the top of the batholith, below which it increases to an average value of 3.5 μW/m³ at 5.5 km depth, then decreases to 0.5–1 μW/m³ at 15 km depth and remains at these values through the entire crust below 15 km. Below the crust, from depths of 40–125 km, the batholith's root and mantle wedge that coevolved beneath the batholith appears to have an average radiogenic heat production rate of 0.14 μW/m³. This is higher than the rates from most published xenolith studies, but reasonable given the presence of crustal components in the arc root assemblages. The pattern of radiogenic heat production interpreted from the depth vs. heat production database is not consistent with the downward-decreasing exponential distribution predicted from modeling of surface heat flow data. The interpreted distribution predicts a reasonable range of geothermal gradients and shows that essentially all of the present day surface heat flow from the Sierra Nevada could be generated within the 35 km thick crust. This requires a very low heat flux from the mantle, which is consistent with a model of cessation of Sierran magmatism during Laramide flat-slab subduction, followed by conductive cooling of the upper mantle for 70 m.y. The heat production variation with depth is principally due to large variations in uranium and thorium concentration; potassium is less variable in concentration within the Sierran crust, and produces relatively little of the heat in high heat production rocks. Because silica content is relatively constant through the upper 30 km of the Sierran batholith, while U, Th, and K concentrations are highly variable, radiogenic heat production does not vary directly with silica content.     

The Mesoproterozoic Midsommersø dolerites and associated high-silica intrusions, North Greenland: crustal melting, contamination and hydrothermal alteration

The Midsommersø dolerites and the flood basalts of the Zig-Zag Dal Basalt Formation, eastern North Greenland, represent a major Mesoproterozoic (∼1,380 Ma) igneous event. The intrusive rocks form large sheets within a succession of feldspathic sandstones which underlie the basalts. The geochemistry of the basalts has recently been re-investigated and reported elsewhere in this Journal; here we present new trace element and Nd-, Sr- and Pb-isotopic data for the intrusive rocks. Unlike the basalts, the intrusions yield evidence of considerable interaction and contamination with upper crustal rocks, especially the sandstones. High-silica rocks (80–90 wt% SiO₂) occur in sheets, up to 60 m thick. They were formed by mobilisation of sandstones, and indicate a very high rate of emplacement of hot basic magma into the sandstones at depth. These mobilised sandstones (‘rheopsammites’) are among the most SiO₂-rich intrusive rocks on earth. Sheets of remobilised granitoid rocks from the crystalline basement (∼70% SiO₂) are also present. Hydrothermal activity, associated with the igneous event, significantly changed the compositions of the silicic rocks as well as that of many dolerites. Sheets of hydrothermally altered (‘red’) dolerites and silicic rocks invariably have borders of dark, fresh dolerite; this is interpreted to be the result of intrusion from zoned magma chambers. Nd isotope data confirm the crustal origin of the silicic rocks as well as the contamination of some dolerites by components derived from crustal sources, while Sr- and Pb-isotopic systems are strongly affected by the hydrothermal alteration, and give little information on the petrogenesis of the rocks. Recent loss of Sr from hydrothermally altered rocks further affected the Sr isotope systems, and earlier age determinations by the Rb–Sr whole-rock isochron method (1,230 Ma) have proved to be in error. The dolerites and the basalts are geochemically very similar, but most dolerites have moderately negative Eu anomalies that are not observed in the basalts. Eu anomalies in the dolerites could be related to contamination by sandstone at depth, but it is not clear why the basalts escaped a similar contamination.     

Shape and distribution analysis of Merensky Reef potholing, Northam Platinum Mine, western Bushveld Complex: implications for pothole formation and growth

Syn-magmatic removal of the cumulate pile during the formation of the Bushveld Complex resulted in “potholes”. Erosion progressed downward in the cumulate pile, resulting in a series of steep, transgressive contacts between locally conformable potholed reefs in the regional pothole sub-facies of the Swartklip Facies in the western limb of the Bushveld Complex. The deepest of these potholes, “third-order” or “FWP2” potholing, occurs where the base of the Merensky Cyclic Unit transgresses the Upper Pseudo-Reef Chromitite marker horizon. The base of a FWP2 pothole on Northam Platinum Mine consists of an unconformable stringer Merensky Chromitite overlain by a medium-grained, poikilitic orthopyroxenite and underlain by either a pegmatitic harzburgite or the medium-grained Lower Pseudo-Reef Anorthosite. Detailed shape and distribution analysis of FWP2 potholes reveals underlying patterns in their shape and distribution which, in turn, suggest a structural control. The ratio between pothole short vs long axes is 0.624 (N=1,385), although the ratio increases from 0.48 to 0.61 in the long axis range 10 to 60 m, then decreases from 0.61 to 0.57 from 61 to 100 m, increasing again from 0.57 to 0.61 from 101 to 400 m, suggesting that there is not a simple relationship between pothole shape and size. Shape (circularity, eccentricity, and dendricity) analysis of a subset of 638 potholes indicates that potholes with long axes <100 m have an elliptical, average normalized shape, elongate on a 120–150° orientation. Potholes with long axis lengths >100 m have an average normalized shape that is bilobate and elongate on a 120° orientation. The average aspect ratio (short axis length divided by long axis length) of potholes is highest for potholes with long axis lengths >100 m and lowest for potholes with long axis lengths between 35 and 60 m. The most common long axis orientation for potholes with long axis lengths <100 m is 150° but 120° for long axis lengths >100 m. Fractal analysis indicates that the distribution of pothole centers is controlled neither by a single nor several interacting fractal dimensions. Autocorrelation (Fry) analysis of the distribution of pothole centers shows recurring pothole distribution trends at 038, 070, and 110° for potholes over the full range of long axis lengths, while the trends of 008 and 152° occur in potholes with long axes lengths between 60 and 100 m. Chi-squared (X ²) analysis of the locations of pothole centers suggests that the distribution of small potholes is highly non-uniform but becomes exponentially more uniform with increasing pothole size. The model which best fits the observed shape and distribution analysis is a combination of protracted independent growth and “nearest neighbor” merging along specific orientations. For instance, the clustered distribution of original pothole centers resulted in merged potholes with long axes lengths of up to 60 m, exhibiting short vs long axes ratios of 0.61, preferred orientations of 150°, and alignment along 010 and 150° trends. Further independent growth allowed for merging of similar-sized (and smaller) neighboring potholes, generating potholes with long axes of up to 100 m in length, a preferred long axis orientation of 150°, and alignment along 010, 040, 075, and 150°. Subsequent preferential merging occurred along a 120° trend, thereby preserving a bilobate form. This implies that while pothole initiation and enlargement may be driven by a “top-down” (i.e., possibly thermomechanical) process, an underlying linear or structural catalyst/control is revealed in changes in pothole shape during enlargement and, furthermore, in the preferred trends along which potholes merged over a considerable period, possibly concomitant with adjustment of major structures in the footwall to the Bushveld Complex and pulses into the magma chamber.     

Flow and form in rehabilitation of large-river ecosystems: An example from the Lower Missouri River

On large, intensively engineered rivers like the Lower Missouri, the template of the physical habitat is determined by the nearly independent interaction of channel form and flow regime. We evaluated the interaction between flow and form by modeling four combinations of modern and historical channel form and modern and historical flow regimes. The analysis used shallow, slow water (shallow-water habitat, SWH, defined as depths between 0 and 1.5 m, and current velocities between 0 and 0.75 m/s) as an indicator of habitat that has been lost on many intensively engineered rivers and one that is thought to be especially important in rearing of young fishes. Two-dimensional hydrodynamic models for modern and historical channels of the Lower Missouri River at Hermann, Missouri, indicate substantial differences between the two channels in total availability and spatial characteristics of SWH. In the modern channel, SWH is maximized at extremely low flows and in overbank flows, whereas the historical channel had substantially more SWH at all discharges and SWH increased with increasing discharge. The historical channel form produced 3–7 times the SWH area of the modern channel regardless of flow regime. The effect of flow regime is evident in increased within-year SWH variability with the natural flow regime, including significant seasonal peaks of SWH associated with spring flooding. Comparison with other reaches along the Lower Missouri River indicates that a) channel form is the dominant control of the availability of habitat even in reaches where the hydrograph is more intensively altered, and b) rehabilitation projects that move toward the historical condition can be successful in increasing topographic diversity and thereby decreasing sensitivity of the availability of habitat to flow regime. The relative efficacy of managing flow and form in creating SWH is useful information toward achieving socially acceptable rehabilitation of the ecosystem in large river systems.     

The Record of an Extreme Flood in the Sediments of Montane Lillooet Lake, British Columbia: Implications for Paleoenvironmental Assessment

Severe rainfall in mid October, 2003 produced the largest floods in almost a century of record on rivers in the Cordillera of southwestern British Columbia. Sediment deposited in Lillooet Lake as a result of this event is clearly distinguished by stratigraphy, colour, texture, magnetic properties, and organic content. Each of these physical properties is related to the lacustrine processes, especially turbid underflow, that distributed the sediment through the lake. The flood, which lasted less than a week, delivered 8–12 times the amount of sediment that accumulates in most entire years in the deepest, central parts of the lake. Recognition of events of this type in the stratigraphic record offers a means of assessing the changing nature of extreme hydroclimatic events, and their relation to more ubiquitous, lower-energy processes.