Particle stirring in turbulent gas disks: Including orbital oscillations

We describe the diffusion and random velocities of solid particles due to stochastic forcing by turbulent gas. We include the orbital dynamics of Keplerian disks, both in-plane epicycles and vertical oscillations. We obtain a new result for the diffusion of solids. The Schmidt number (ratio of gas to particle diffusivity) is Sc≈1+(Ωt_stop)², in terms of the particle stopping time t_stop and the orbital frequency Ω. The standard result, Sc=1+t_stop/t_eddy, in terms of the eddy turnover time, t_eddy, is shown to be incorrect. The main difference is that Sc rises quadratically, not linearly, with stopping time. Consequently, particles larger than 10 cm in protoplanetary disks will suffer less radial diffusion and will settle closer to the midplane. Such a layer of boulders would be more prone to gravitational collapse. Our predictions of RMS speeds, vertical scale height and diffusion coefficients will help interpret numerical simulations. We confirm previous results for the vertical stirring of particles (scale heights and random velocities), and add a correction for arbitrary ratios of eddy to orbital times. The particle layer becomes thinner for t_eddy>1/Ω with the strength of turbulent diffusion held fixed. We use two analytic techniques—the Hinze–Tchen formalism and the Fokker–Planck equation with velocity diffusion—with identical results when the regimes of validity overlap. We include simple physical arguments for the scaling of our results.     

Matrix polynomial representation of the anisotropic magnetotelluric impedance tensor

A formalism based upon the equal penetration depth stratification assumption is extended to a layered anisotropic medium, yielding a recursive algorithm for the computation of the magnetotelluric impedance tensor elements. The development of this new procedure requires an appropriate layer-discretization as well as an extension of the reflection coefficient definition for the anisotropic layered model.This method transfers the differential problem into an algebraic one, and is independent of the electric and magnetic field vectors. The technique is a recursive process which gives a rational matrix polynomial representation for the magnetotelluric impedance tensor.The procedure involves the use of second-order matrices, rather than the fourth-order ones normally used for such a case. Using this representation, a separation of the contribution of the model parameters from that of the frequency is achieved. Consequently the elements of the magnetotelluric impedance tensor are computed, for each frequency, using coefficients which are evaluated just once for a given model.     

HYDRO_GEN: A spatially distributed random field generator for correlated properties

This paper describes a new method for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences. The method is based on two observations: (i) spatially distributed attributes usually display a stationary correlation structure, and (ii) the screening effect of measurements leads to the sufficiency of a small search neighborhood when it comes to projecting measurements and data in space. The algorithm which was developed based on these principles is called HYDRO_GEN, and its features and properties are discussed in depth. HYDRO_GEN is found to be accurate and extremely fast. It is also versatile: it can simulate fields of different nature, starting from weakly stationary fields with a prescribed covariance and ending with fractal fields. The simulated fields can display statistical isotropy or anisotropy.     

Chemical evolution of acid precipitation in the unsaturated zone of the Pennsylvanian siltstones and shale of central Ohio

The North Appalachian Experimental Watershed in Coshocton, Ohio, USA has recorded average pH of precipitation of 4.7 over a 30-year period. The area lies within the Pennsylvanian siltstones and shale, dominated by aluminosilicates and <5% calcite. A study was conducted to determine the evolution of acid deposition through an unsaturated to saturated zone composed of siltstone and shale in an isolated hill, precluding lateral flow and seepage. The results from water–rock chemical reactions modeled using PHREEQM demonstrate the percolating precipitation water is neutralized to pH 7.5 within the top 1.5 m. The model suggests that, along with calcite, dissolution of albite, illite, and kaolinite are the dominant mechanisms of neutralization. The cation exchange capacity of the siltstone and shale, in the range 54.6–386 meq/100 g, appears to be a function of high organic carbon content of 2.0–3.2%. While cation exchange is responsible for some of the Na⁺ in solution, it is not the primary source of Ca²⁺, Mg²⁺, or K⁺ ions. Exchange onto clays is occurring, but is secondary to exchange on organic matter. Chemical composition of groundwater perched within a coal seam is controlled by oxidation and dissolution of pyrite, returning pH to approximately 4.0.     

Climate sensitivity: should the climate tail wag the policy dog?

The small but stubbornly unyielding possibility of a very large long-term response of global temperature to increases in atmospheric carbon dioxide can be termed the fat tail of high climate sensitivity. Recent economic analyses suggest that the fat tail should dominate a rational policy strategy if the damages associated with such high temperatures are large enough. The conclusions of such analyses, however, depend on how economic growth, temperature changes, and climate damages unfold and interact over time. In this paper we focus on the role of two robust physical properties of the climate system: the enormous thermal inertia of the ocean, and the long timescales associated with high climate sensitivity. Economic models that include a climate component, and particularly those that focus on the tails of the probability distributions, should properly represent the physics of this slow response to high climate sensitivity, including the correlated uncertainty between present forcing and climate sensitivity, and the global energetics of the present climate state. If climate sensitivity in fact proves to be high, these considerations prevent the high temperatures in the fat tail from being reached for many centuries. A failure to include these factors risks distorting the resulting economic analyses. For example, we conclude that fat-tail considerations will not strongly influence economic analyses when these analyses follow the common—albeit controversial—practices of assigning large damages only to outcomes with very high temperature changes and of assuming a significant baseline level of economic growth.     

Electromagnetic mapping of electrical conductivity beneath the Columbia basalts1

Sedimentary rocks beneath the Columbia River Basalt Group are recognized as having potential for oil and gas production, but the overlying layered basalts effectively mask seismic reflections from the underlying sediments. Four electromagnetic (EM) methods have been applied on profiles crossing Boylston Ridge, a typical east–west trending anticline of the Yakima Fold Belt, in an attempt to map the resistivity interface between the basalts and the sediments and to map variations in structure and resistivity within the sediments. The EM surveys detected strong variations in resistivity within the basalts, and in particular the continuous magnetotelluric array profiling (EMAP) revealed resistivity lows beneath the surface anticlines. These low resistivity zones probably coincide with fracturing in the core of the anticlines and they appear to correlate well with similar zones of low seismic velocity observed on a nearby seismic profile. The controlled-source EM surveys (in-loop transient, long-offset transient, and variable-offset frequency-domain) were designed in anticipation of relatively uniform high resistivity basalts, and were found to have been seriously distorted by the intrabasalt conductors discovered in the field. In particular, the resistivity sections derived from 1D inversions were found to be inconsistent and misleading. The EMAP survey provided the most information about the subsurface resistivity distribution, and was certainly the most cost-effective. However, both controlled-source and EMAP surveys call for accurate 2D or 3D inversion to accommodate the geological objectives of this project.