An interpolation method taking into account inequality constraints: I. Methodology

Several kinds of data can provide information about a variable measured on a one- or two-dimensional space; at some points, the value is known to be equal to a certain number. At other points, the only information may be that the variable is greater or smaller than a given value. The theory of splines provides interpolating functions that can take into account both equality and inequality data. These interpolating functions are presented. The parallel between splines and kriging is reviewed, using the formalism of dual kriging. Coefficients of dual kriging can be obtained directly by minimizing a quadratic form. By adding some inequality constraints to this minimization, an interpolating function may be calculated which takes into account inequality data and is more general than a spline. The method is illustrated by some simple one-dimensional examples.Work performed at Sohio Petroleum Company     

The effects of wildfires on the magnetic properties of soils in the Everglades

We present results of a rock‐magnetic study of soils that were affected by wildfires that burned portions of the Everglades in the Spring of 2008. Soils at sites that were extensively burned exhibit a pronounced surface magnetic enhancement effect with magnetizations of surface samples up to 16 times greater than that observed at depth (>7 cm) at these sites. The increase in magnetization results from an increased abundance of a low‐coercivity phase (maghemite) that occurs at the expense of the abundance of a high‐coercivity phase (goethite). These results indicate that fire‐induced heating caused goethite in the surface soils to convert into a more magnetic, low‐coercivity phase, such as maghemite. Goethite is an excellent adsorber of phosphorus, and therefore we hypothesize that the destruction of goethite as a result of burning may have important implications for phosphorus cycling in the Everglades ecosystem. Copyright © 2010 John Wiley & Sons, Ltd.     

Plate kinematics: The Americas,East Africa,and the rest of the world

Euler vectors (relative angular velocity vectors) have been determined for twelve major plates by global inversion of carefully selected sea-floor spreading rates, transform fault trends, and earthquake slip vectors. The rate information comes from marine magnetic anomalies less than 5 m.y. old, so the motions are valid for post-Miocene times. Plate motions in a mean hotspot frame of reference have also been determined, and statistical confidence limits for all the Euler vectors estimated. Among the consequences of the global motion model is the conclusion that fast-spreading ridges (separation rates greater than 3 cm/yr) have plate motion nearly perpendicular to the strike of the ridge and magnetic anomalies. Four more slowly separating ridges have an average obliquity of spreading of almost 20°.For several plate boundaries, results that differ from previous studies are in agreement with geological evidence. The North and South American plates converge slowly about a pole east of the Antilles and near the Mid-Atlantic Ridge. The results for Africa versus Somalia imply slow east-west extension on the East African Rift Valleys. The pole for motion of Eurasia relative to North America is located near Sakhalin, in accordance with evidence from Siberia and Sakhalin.     

Neogene-Quaternary contourite and related deposition on the West Shetland Slope and Faeroe-Shetland Channel revealed by high-resolution seismic studies

The Neogene and Quaternary sediments of the Faeroe-Shetland Channel and West Shetland shelf and slope rest upon a major regional unconformity, the Latest Oligocene Unconformity (LOU), and have been deposited through the interaction of downslope and parallel-to-slope depositional processes. The upper to middle continental slope is dominated by mass-transport deposits (debris flows), which progressively diminish downslope, and were largely generated and deposited during glacial cycles when ice sheets supplied large quantities of terrigeneous sediment to the upper slope and icebergs scoured sea-floor sediments on the outer shelf and uppermost slope. Large-scale sediment failures have also occurred on the upper slope and resulted in deposition of thick, regionally extensive mass-transport deposits on portions of the lower slope and channel floor. In contrast, large fields of migrating sediment waves and drift deposits dominate most of the middle to lower slope below 700 m water depth and represent deposition by strong contour currents of the various water masses moving northeastward and southwestward through the channel. These migrating sediment waves indicate strong northeastward current flow at water depths shallower than 700 m and strong southwestward current flow at water depths from 700 to >1,400 m. These flow directions are consistent with present-day water-mass flow through the Faeroe-Shetland Channel. The Faeroe-Shetland Channel floor is underlain by thin conformable sediments that appear to be predominantly glacial marine and hemipelagic with less common turbidites and debris flows. No evidence is observed in seismic or core data that indicates strong contour-current erosion or redistribution of sediments along the channel floor.     

Paleomagnetic estimate of the emplacement temperature of the long-runout Nevado de Colima volcanic debris avalanche deposit, Mexico

Stoopes and Sheridan have mapped a volcanic debris avalanche of Nevado de Colima which has an exceptionally long runout (120 km) and low fall-height to length ratio (H/L = 0.04). We present paleomagnetic results from this volcanic debris avalanche deposit which provide evidence that this avalanche was emplaced at elevated temperatures. The majority of samples, collected from lithic clasts in the volcanic debris avalanche deposit, exhibit two-component remanent magnetizations with a low-temperature component (25–350°C) which is well grouped about the geomagnetic field direction at Colima and a high-temperature component (350–580°C) which is randomly oriented. Although the temperature of the deposit most likely varied with distance from the volcanic source and the thickness of the deposit, our results suggest an emplacement temperature of approximately 350°C at intermediate distances (18–26 km) from the source. In order for the rock clasts (20–40 cm diameter) to be heated to these temperatures, the avalanche was most likely the results of a magmatic, Bezymianny-type eruption. The mixing of hot, juvenile gases with the clasts provides an explanation for the high degree of fluidization of this material, as evidenced by the long runout of this avalanche deposit.     

Assimilating altimetric data to control the tropical instability waves: an observing system simulation experiment study

Tropical instability waves (TIWs) are not easily simulated by ocean circulation models primarily because such waves are very sensitive to wind forcing. In this study, we investigate the impact of assimilating sea surface height (SSH) observations on the control of TIWs in an observing system simulation experiment (OSSE) context based on a regional model configuration of the tropical Atlantic. A Kalman filtering method with suitable adaptations is found to be successful when altimetric data are assimilated in conjunction with sea surface temperature and some in situ temperature/salinity profiles. In this rather realistic system, the TIW phase is roughly controlled with a single nadir observing satellite. However, a right correction of the TIW structure and amplitude requires at least two nadir observing satellites or a wide swath observing satellite. The significant impact of orbital parameters is also demonstrated: in particular, the Jason or GFO satellite orbits are found to be more suitable than the ENVISAT orbit. More generally, it is found that as soon as adequate sub-sampling exists (with periods of 5–10?days), the length of the repetitivity cycle of orbits does not have a significant impact.     

Tree-ring evidence linking late twentieth century changes in precipitation to slope instability,central New York state,USA

The Burtonsville landslide in central New York, USA, is a kilometer-scale rotational block failure in glacial till that was likely initiated by incision of the adjacent Schoharie Creek. Although the timing of initial failure is unknown, relatively fresh scarps and tilted surfaces suggest that movement is post-glacial and active. The river currently erodes the toe slope and it removed significant material during flooding associated with Hurricane Irene (August 2011). We retrieved tree cores from 111 trees across the landslide to reconstruct modern movement and block tilting as it related to moisture conditions in the region. Our data show that trees across the slide are in sync with respect to the stress response indicated by reaction wood. The magnitude of response to slope instability, as inferred from eccentric growth, has varied considerably across the site. We hypothesize that macropore development during the driest periods, and the differential rate at which water has reached subsurface failure planes, has caused the observed slope instability. The combination of a wetter precipitation regime and slope instability leads to higher sediment loads in the adjacent stream and serves as a useful analogy for similar watersheds in the region.     

Evolution of Hawaiian basalts: a hotspot melting model

Melt generation and extraction along the Hawaiian volcanic chain should be largely controlled by the thermal structure of the Hawaiian swell and the heat source underneath it. We simulate numerically the time- and space-dependent evolution of Hawaiian volcanism in the framework of thermal evolution of the Hawaiian swell, constrained by residual topography, geoid anomalies, and anomalous heat flow along the Hawaiian volcanic chain. The transient heat transfer problem with melting relationships and variable boundary conditions is solved in cylindrical coordinates using a finite difference method. The model requires the lithosphere to be thinned mechanically by mantle plume flow. Melting starts quickly near the base of the plate when the hotspot is encountered. Thermal perturbation and partial melting are largely concentrated in the region where the original lithosphere is thinned and replaced by the mantle flow. The pre-shield Loihi alkalic and tholeiitic basalts are from similar sources, which are a mixture of at least three mantle components: the mantle plume, asthenosphere, and the lower lithosphere. The degree of partial melting averages 10–20%, with a peak value of 30% near the plume center. As a result of continuous compaction, melts are extracted from an active partial melting zone of about 10–20 km thickness, which moves upwards and laterally as the heating and compaction proceed. The rate of melt extraction from the swell increases rapidly to a maximum value of 1 × 10⁵ km³/m.y. over the center of the heat source, corresponding to eruption of large amounts of tholeiitic lavas during the shield-building stage. This volume rate is adequate to account for the observed thickness of the Hawaiian volcanic ridge. Melts from direct partial melting of the mantle plume at depth may be important or even dominant at this stage, although the amount is uncertain. At the waning stage, mixing of melts from the mantle flow pattern with those from low-degree partial melting of the lithosphere may produce postshield alkalic basalts. After the plate moves off the heat source, continuous conductive heating can cause very low degree partial melting (less than 1%) of the lithosphere at shallow depths for about one million years. This process may be responsible for producing post-erosional alkalic basalts. The extraction time for removing such small amount of melts is about 0.4–2 m.y., similar to the time gap between the eruption of post-erosional alkalic lavas and the shield-building stage. Our results show that multi-stage Hawaiian volcanism and the general geochemical characteristics of Hawaiian basalts can be explained by a model of plume-plate interaction.