On the Acoustic-Electromagnetic Analogy for the Reflection-Refraction Problem

The same mathematical theory can be used to describe physical phenomena of different nature. For instance, the wave equation and the related mathematical developments can be used to describe elastic and electromagnetic wave propagation, and it is also extensively used in quantum mechanics. Fresnel's equations are a classical example of the analogy between shear waves and light waves. George Green in the nineteenth century, used analogies to obtain the reflection coefficients for sound waves and light waves, before the advent of the electromagnetic theory of light.In this work, we investigate the mathematical analogy between elastic waves and electromagentic waves. We obtain a complete parallelism for the reflection and refraction problem, considering the most general situation, that is, the presence of anisotropy and attenuation—viscosity in the elastic case and conductivity in the electromagnetic case. The analogy is illustrated with Fresnel's equations, the Brewster and critical angles, the concept of reflectivity and transmissivity, and the corresponding duals fields. The analysis of the elastic-solid theory of reflection applied by Green to light waves, and a brief historical review of wave propagation through the ether, further illustrate the analogy.     

A 1500-year record of climatic and environmental change in ElkLake, Minnesota I: Varve thickness and gray-scale density

The deepest part (29.5 m) of Elk Lake, ClearwaterCounty, northwestern Minnesota, contains a complete Holocene section that iscontinuously varved. The varve components are predominantly autochthonous(CaCO₃, organic matter, biogenic silica, and several iron andmanganese minerals), but the varves do contain a minor detrital-clastic(aluminosilicate) component that is predominantly wind-borne (eolian) andprovides an important record of atmospheric conditions. Singular spectrumanalysis (SSA) and wavelet analysis of varve thickness recognized significantperiodicities in the multicentennial and multidecadal bands that varied inpower (i.e., variable significance) and position (i.e., variable period) withinthe periodic bands. Persistent periodicities of about 10, 22, 40, and 90 years,and, in particular, multicentennial periodicities in varve thickness and otherproxy variables are similar to those in spectra of radiocarbon production, aproxy for past solar activity. This suggests that there may be a solar control,perhaps through geomagnetic effects on atmospheric circulation. Multicentennialand multidecadal periodicities also occur in wavelet spectra of relativegray-scale density. However, gray-scale density does not appear to correlatewith any of the measured proxy variables, and at this point we do not know whatcontrolled gray scale.     

Using Spatial Statistics to Examine the Pattern of Urban Land Development in Halifax–Dartmouth

This article examines the locational patterns of population and employment and the resultant changes in urban form in the Halifax–Dartmouth region between 1970 and 1996. The article employs the univariate and bivariate K function to measure spatial dependence or clustering within and between the classes of residential and commercial land parcels. The results of the K function estimates suggest that residential land parcels cluster together, commercial land parcels cluster together, and residential and commercial land parcels have become more clustered over time. Evidence of clustering provides insight into the changing urban form of the region and possible multinucleation.     

Wind erosion from military training lands in the Mojave Desert, California, U.S.A.

Military training activities reduce vegetation cover, disturb crusts, and degrade soil aggregates, making the land more vulnerable to wind erosion. The objective of this study was to quantify wind erosion rates for typical conditions at the Marine Corps Air Ground Combat Center, Twentynine Palms, CA, U.S.A. Five Big Spring Number Eight (BSNE) sampler stations were installed at each of five sites. Each BSNE station consisted of five BSNE samplers with the lowest sampler at 0·05 m and the highest sampler at 1·0 m above the soil surface. Once a month, sediment was collected from the samplers for analysis. Occurrence of saltating soil aggregates was recorded every hour using Sensits, one at each site. The site with the most erosion had a sediment discharge of 311 kg m⁻¹ over a period of 17 months. Other sites eroded much less because of significant rock cover or the presence of a crust. Hourly sediment discharge was estimated combining hourly Sensit count and monthly sediment discharge measured using BSNE samplers. More simultaneously measured data are needed to better characterize the relationship between these two and reconstruct a detailed time-series of wind erosion. This measured time-series can then be used for comparison with simulation results from process-based wind erosion models such as the Wind Erosion Prediction System (WEPS), once it has been adapted to the unique aspects of military lands.     

Validation of Landslide Susceptibility Maps; Examples and Applications from a Case Study in Northern Spain

A procedure for validating landslide susceptibility maps wasapplied in a study area in northern Spain and the results obtained compared. Validationwas used to carry out sensitivity analysis for individual variables and combinationsof variables. The validity of different map-making methods was tested, as well as theutility of different types of Favourability Functions. The results obtained show thatvalidation is essential to determine the predictive value of susceptibility maps. Italso helps to better select the most suitable function and significant variables, thus improving the efficiency of the mapping process. Validation based on a temporal strategy makes it possible to derive hazard maps from susceptibility maps.     

Building Web-Based Spatial Information Solutions around Open Specifications and Open Source Software

Geographic Information Systems (GIS) are moving from isolated, standalone, monolithic, proprietary systems working in a client‐server architecture to smaller web‐based applications and components offering specific geo‐processing functionality and transparently exchanging data among them. Interoperability is at the core of this new web services model. Compliance with Open Specifications (OS) enables interoperability. Web‐GIS software's high costs, complexity and special requirements have prevented many organizations from deploying their data and geo‐processing capabilities over the World Wide Web. There are no‐cost Open Source Software (OSS) alternatives to proprietary software for operating systems, web servers, and Relational Database Management Systems. We tested the potential of the combined use of OS and OSS to create web‐based spatial information solutions. We present in detail the steps taken in creating a prototype system to support land use planning in Mexico with web‐based geo‐processing capabilities currently not present in commercial web‐GIS products. We show that the process is straightforward and accessible to a broad audience of geographic information scientists and developers. We conclude that OS and OSS allow the development of web‐based spatial information solutions that are low‐cost, simple to implement, compatible with existing information technology infrastructure, and have the potential of interoperating with other systems and applications in the future.     

Erosion rates of alpine bedrock summit surfaces deduced from in situ Be and Al

We have measured the concentration of in situ produced cosmogenic ¹⁰Be and ²⁶Al from bare bedrock surfaces on summit flats in four western U.S. mountain ranges. The maximum mean bare-bedrock erosion rate from these alpine environments is 7.6 ± 3.9 m My⁻¹. Individual measurements vary between 2 and 19 m My⁻¹. These erosion rates are similar to previous cosmogenic radionuclide (CRN) erosion rates measured in other environments, except for those from extremely arid regions. This indicates that bare bedrock is not weathered into transportable material more rapidly in alpine environments than in other environments, even though frost weathering should be intense in these areas. Our CRN-deduced point measurements of bedrock erosion are slower than typical basin-averaged denudation rates ( 50 m My⁻¹). If our measured CRN erosion rates are accurate indicators of the rate at which summit flats are lowered by erosion, then relief in the mountain ranges examined here is probably increasing.

We develop a model of outcrop erosion to investigate the magnitude of errors associated with applying the steady-state erosion model to episodically eroding outcrops. Our simulations show that interpreting measurements with the steady-state erosion model can yield erosion rates which are either greater or less than the actual long-term mean erosion rate. While errors resulting from episodic erosion are potentially greater than both measurement and production rate errors for single samples, the mean value of many steady-state erosion rate measurements provides a much better estimate of the long-term erosion rate.