Stability and dynamics of the continental tectosphere

Continental cratons overlie thick, high-viscosity, thermal and chemical boundary layers, where the chemical boundary layers are less dense than they would be due to thermal effects alone, perhaps because they are depleted in basaltic constituents. If the continental tectosphere is the same age as the overlying Archaean crust, then the continental tectosphere must be able to survive for several billion years without undergoing a convective instability, despite being both cold and thick. Since platforms and shields correlate only weakly with Earth's gravity and geoid anomalies, acceptable models of the continental tectosphere must also satisfy this gravity constraint. We investigate the long-term stability of the continental tectosphere by carrying out a number of numerical convection experiments within a two-dimensional Cartesian domain. We initiate our experiments with a tectosphere (thermal and chemical boundary layers) immersed in a region of uniform composition, temperature, and viscosity, and consider the effects on the stability of the tectosphere of (1) activation energy (used to define the temperature dependence of viscosity), (2) compositional buoyancy, and (3) linear or non-linear rheology. The large lateral thermal gradients required to match oceanic and tectosphere structures initiate the dominant instability, a “drip” which develops at the side of the tectosphere and moves to beneath its center. High activation energies and high background viscosities restrict the amount and rate of entrainment. Compositional buoyancy does not significantly change the flow pattern. Rather, compositional buoyancy slows the destruction process somewhat and reduces the stress within the tectosphere. With a non-Newtonian rheology, this reduction in stress helps to stiffen the tectosphere. In these experiments, dynamical systems that adequately model the present ocean-continent structures have activation energy E*≥180 kJ mole⁻¹ — a value about one third the estimate of activation energy for olivine, E*≈520 kJ mole⁻¹. Although for E*≈520 kJ mole⁻¹, compositional buoyancy is not required for the tectosphere to survive, the joint application of longevity and gravity constraints allows us to reject all models not containing compositional buoyancy, and to predict that the ratio of compositional to thermal buoyancy within the continental tectosphere is approximately unity.     

Rock-weathering rates as functions of time

The scarcity of documented numerical relations between rock weathering and time has led to a common assumption that rates of weathering are linear. This assumption has been strengthened by studies that have calculated long-term average rates. However, little theoretical or empirical evidence exists to support linear rates for most chemical-weathering processes, with the exception of congruent dissolution processes. The few previous studies of rock-weathering rates that contain quantitative documentation of the relation between chemical weathering and time suggest that the rates of most weathering processes decrease with time. Recent studies of weathering rinds on basaltic and andesitic stones in glacial deposits in the western United States also clearly demonstrate that rock-weathering processes slow with time. Some weathering processes appear to conform to exponential functions of time, such as the square-root time function for hydration of volcanic glass, which conforms to the theoretical predictions of diffusion kinetics. However, weathering of mineralogically heterogeneous rocks involves complex physical and chemical processes that generally can be expressed only empirically, commonly by way of logarithmic time functions. Incongruent dissolution and other weathering processes produce residues, which are commonly used as measures of weathering. These residues appear to slow movement of water to unaltered material and impede chemical transport away from it. If weathering residues impede weathering processes then rates of weathering and rates of residue production are inversely proportional to some function of the residue thickness. This results in simple mathematical analogs for weathering that imply nonlinear time functions. The rate of weathering becomes constant only when an equilibrium thickness of the residue is reached. Because weathering residues are relatively stable chemically, and because physical removal of residues below the ground surface is slight, many weathering features require considerable time to reach constant rates of change. For weathering rinds on volcanic stones in the western United States, this time is at least 0.5 my.     

Spatial representation in the social interaction potential metric: an analysis of scale and parameter sensitivity

The social interaction potential (SIP) metric measures urban structural constraints on social interaction opportunities of a metropolitan region based on the time geographic concept of joint accessibility. Previous implementations of the metric used an interaction surface based on census tracts and the locations of their centroids. This has been shown to be a shortcoming, as the metric strongly depends on the scale of the zoning system in the region, making it difficult to compare the SIP metric between metropolitan regions. This research explores the role of spatial representation in the SIP metric and identifies a suitable grid-based representation that allows for comparison between regions while retaining cost-effectiveness with respect to computational burden. We also report on findings from an extensive sensitivity analysis investigating the SIP metric’s input parameters such as a travel flow congestion factor and the length of the allowable time budget for social activities. The results provide new insights on the role of the modifiable areal unit problem in the computation of time geographic measures of accessibility.     

Present-day oxidative subsidence of organic soils and mitigation in the Sacramento-San Joaquin Delta,California, USA

Subsidence of organic soils in the Sacramento-San Joaquin Delta threatens sustainability of the California (USA) water supply system and agriculture. Land-surface elevation data were collected to assess present-day subsidence rates and evaluate rice as a land use for subsidence mitigation. To depict Delta-wide present-day rates of subsidence, the previously developed SUBCALC model was refined and calibrated using recent data for CO₂ emissions and land-surface elevation changes measured at extensometers. Land-surface elevation change data were evaluated relative to indirect estimates of subsidence and accretion using carbon and nitrogen flux data for rice cultivation. Extensometer and leveling data demonstrate seasonal variations in land-surface elevations associated with groundwater-level fluctuations and inelastic subsidence rates of 0.5–0.8 cm yr^–1. Calibration of the SUBCALC model indicated accuracy of ±0.10 cm yr^–1 where depth to groundwater, soil organic matter content and temperature are known. Regional estimates of subsidence range from <0.3 to >1.8 cm yr^–1. The primary uncertainty is the distribution of soil organic matter content which results in spatial averaging in the mapping of subsidence rates. Analysis of leveling and extensometer data in rice fields resulted in an estimated accretion rate of 0.02–0.8 cm yr^–1. These values generally agreed with indirect estimates based on carbon fluxes and nitrogen mineralization, thus preliminarily demonstrating that rice will stop or greatly reduce subsidence. Areas below elevations of –2 m are candidate areas for implementation of mitigation measures such as rice because there is active subsidence occurring at rates greater than 0.4 cm yr^–1.