Propagator matrices in elastic wave and vibration problems     

Freeman Gilbert  George E. Backus 《Studia Geophysica et Geodaetica》1966,10(3):271-271

The boundary value problems most frequently encountered in studies of elastic wave propagation in stratified media can be formulated in terms of a finite number of linear, first order and ordinary differential equations with variable coefficients. Volterra (1887) has shown that solutions to such a system of equations are conveniently represented by the product integral, or propagator, of the matrix of coefficients. In this paper we summarize some of the better known properties of propagators plus numerica methods for their computation. When the dispersion relation is somem ^th order minor of the integral matrix it is possible to deal withm ^th minor propagators so that the dispersion relation is a single element of them ^th minor integral matrix. In this way one of the major sources of loss of numerical accuracy in computing the dispersion relation is avoided. Propagator equations forSH and forP-SV waves are given for both isotropic and transversely isotropic media. In addition, the second minor propagator equations forP-SV waves are given. Matrix polynomial approximations to the propagators, obtained from the method of mean coefficients by the Cayley-Hamilton theorem and the Lagrange-Sylvester, interpolation formula, are derived.  相似文献   

Limitations of the Electrical Resistivity Method in Landfill Investigations   总被引：1，自引：0，他引：1  

Gilbert Klefstad  Lyle V. A. Sendlein  Robert C. Palmquist 《Ground water》1977,15(5):418-427

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The Pyrenees: Subduction and collision?     

Gilbert Boillot  Raymond Capdevila 《Earth and Planetary Science Letters》1977,35(1):151-160

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Ion microprobe isotopic measurements of individual interplanetary dust particles     

Kevin D. Mckeegan  Robert M. Walker  Ernst Zinner 《Geochimica et cosmochimica acta》1985,49(9):1971-1987

Ion microprobe measurements of D/H ratios in individual fragments of eight stratospheric dust particles give δD values ranging from ?386 to +2534‰ relative to SMOW. The δD values in five particles far exceed those in terrestrial samples and prove that the samples are interplanetary dust particles (IDPs). The hydrogen isotopic composition is heterogeneous on a scale of a few microns demonstrating that the dust is unequilibrated. Measurements of D/H ratios in conjunction with elemental and molecular ion signals in different fragments of individual IDPs show that a carbonaceous phase, not water, is the carrier of the D enrichments. Previous infrared transmission measurements have shown that IDPs fall into three main spectral classes. Particles from two of those three IR classes show large D/H ratios. Two particles studied from the third class do not. However, one of these contains solar flare tracks and is extraterrestrial. Thus, most, but not all, IDPs contain hydrogen with a non-terrestrial isotopic composition.Carbon isotopic measurements on fragments of three IDPs give ratios similar to terrestrial values and show a largely uniform isotopic composition for a given particle. Small, but significant, differences in δ¹³C of ~40‰ between particles are seen. No correlations between the hydrogen and carbon isotopic compositions are observed.The magnesium and silicon isotopic compositions of fragments of three IDPs are found to be normal within measurement errors.  相似文献   

Origin of Ross Island basanitoids and limitations upon the heterogeneity of mantle sources for alkali basalts and nephelinites     

Shine Soon Sun  Gilbert N. Hanson 《Contributions to Mineralogy and Petrology》1975,52(2):77-106

Primary basanitoids from Ross Island, Antarctica have REE patterns and Pb isotope ratios similar to those for primary alkali basalts and nephelinites on ocean islands. The lead data from all volcanics on Ross Island have a spread of 4% in the 206/204 ratio and give a two-stage model lead age of 1500 m.y. The age is interpreted to be the time since the development of the chemical heterogeneity of the mantle source, presumably during an earlier melting process. Comparison of REE, K, Rb, Sr, Ba and P₂O₅ concentrations for alkali basalts and nephelinites shows that the chondrite normalized mantle source is enriched in light REE with average La/Sm=3.4, Ce/Sm=2.6, Nd/Sm=1.6. Assuming a mantle source with heavy REE abundances of three times chondrites, nephelinites require 3 to 7% partial melting of the mantle source and alkali basalts require 7 to 15% partial melting. The patterns of K, Cu, V and Ti abundances suggest that phlogopite is a residual mineral for most nephelinite, but not alkali basalt mantle sources, and that a sulfide phase and a titanium-rich mineral are in the residual mantle source for both alkali basalts and nephelinites. Small positive Eu anomalies (2–5%) in near primary alkali basalts and nephelinites suggest that the xxx of the mantle sources is 10^?6 to 10^?9 atm. The progressive enrichment of light REE and incompatible elements in the mantle sources for nephelinites and alkali basalts is proposed to result by intrusion of veins of basaltic melt due to very low percentages of melting 1 000 to 3 000 m.y. ago when this part of the deeper mantle was previously involved in convection and partial melting.  相似文献   

⁴⁰Ar/³⁹Ar spectrum ages for biotite,hornblende and muscovite in a contact metamorphic zone     

Gilbert N. Hanson  Kathleen R. Simmons  A.E. Bence 《Geochimica et cosmochimica acta》1975,39(9):1269-1278

Biotite, hornblende and muscovite from 2700 m.y. old rocks in northeastern Minnesota near the contact of the 1150 m.y. Duluth Complex have been analyzed by ⁴⁰Ar/³⁹Ar technique to determine whether spectrum ages can be used to distinguish partial loss of radiogenic argon due to a reheating event. Biotite and hornblende give plateau ages comparable to the ordinary K-Ar ages for all samples including those with intermediate ages. Muscovite gives plateau ages for the samples with less than 11% argon loss. An intermediate muscovite with a conventional K-Ar age of 1850 m.y. gives progressively older ⁴⁰Ar/³⁹Ar ages for higher temperature fractions.Microprobe analysis reveals no systematic correlation between biotite chemistry and loss of argon in the contact zone. This suggests that the rate-controlling process for the loss of argon from biotite in the contact zone may be volume diffusion or recrystallization without a measurable change in major element composition. Biotites with intermediate ages give plateaus because the rate-controlling processes in the vacuum furnace are related to dehydroxylation and delamination and are unrelated to the process causing loss of argon in the contact zone.The data for the muscovites are not easily interpreted, in part because of the limited number of samples. The hornblende data show a correlation between argon loss and change in major element composition suggesting that recrystallization may be a rate-controlling process for the loss of argon from hornblende in the contact zone. The small number of samples precludes a definitive statement.  相似文献   

Ultrahigh-pressure metamorphism and decompressional P-T paths of eclogites and country rocks from Weihai, eastern China   总被引：6，自引：0，他引：6  

R. Y. Zhang    J. G. Liou  W. G. Ernst 《Island Arc》1995,4(4):293-309

Abstract Altered quartz-rich and nearly quartz-free eclogitic rocks and completely retrograde quartz-rich garnet amphibolites occur as blocks or lenses in gneisses at Weihai, northeastern tip of the Sulu ultrahigh-P belt. Eclogitic rocks with assemblage garnet ± clinopyroxene ± coesite + rutile have experienced three-stage metamorphic events including ultrahigh-pressure eclogite, granulite and amphibolite facies. Granulite metamorphic event is characterized by formation of the hypersthene + salite + plagioclase ± hornblende corona between garnet and quartz + clinopyroxene. P-T conditions for the three-stage recrystallization sequence are 840 ± 50°C, >28 kbar, about 760±50°C, 9 kbar, and ~650°C, <8 kbar respectively. Most country rock gneisses contain dominant amphibolite-facies assemblages; some garnet-bearing clinopyroxene gneisses recrystallized under granulite-facies conditions at about 740±50°C and 8.5 kbar; similar to granulite-facies retrograde metamorphism of the enclosed eclogitic blocks. Minor cale-silicate lenses within gneisses containing an assemblage grossular + salite + titanite + quartz with secondary zoisite and plagioclase may have formed within a large pressure range of 14-35 kbar. Eclogitic boudins and quartzo-feldspathic country rocks may have experienced coeval in situ UHP and subsequent retrograde metamorphism. The established nearly isothermal decompression P-T path suggests that this area may represent the interior portion of a relatively large subducted sialic block. The recognized UHP terrane may extend eastward across the Yellow Sea to the Korean Peninsula.  相似文献   

A tribute to Jacques Touret     

Tom Andersen  Marie-Luce Frezzotti  Ernst A. J. Burke 《Lithos》2001,55(1-4):ix-xi

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Buying environmental insurance: Prospects for trading of global climate-protection services     

Joel N. Swisher  Gilbert M. Masters 《Climatic change》1991,19(1-2):233-240

In order to alleviate the threat of global climate change, coordinated international action is needed. This cooperation should include multilateral agreements and new economic initiatives to help implement measures that will slow the accumulation of carbon dioxide in the Earth's atmosphere due to tropical deforestation and fossil-fuel use. An international market in environmental services can help to safeguard the Earth's climate and foster economic development through a North-South transfer of financial resources.We suggest international carbon-emission offsets (ICEOs) as a means by which international markets, under a policy umbrella such as a multilateral climate-protection treaty, could trade carbon-saving services. Such a market would provide a currency for rewarding actions that reduce global carbon emissions, allowing carbon emitters to seek the least expensive ways to reduce emissions. This currency would transfer cash and/or debt relief from industrialized nations to developing nations, allowing the developing nations to profit from the use of clean energy technologies and the protection, rather than depletion, of tropical forests.  相似文献   

Are topographic data sets fractal?     

Lewis E. Gilbert 《Pure and Applied Geophysics》1989,131(1-2):241-254

The scale invariant properties of fractal sets make them attractive models for topographic profiles because those profiles are the end product of a complex system of physical processes operating over many spatial scales. If topographic data sets are fractal, their power spectra will be well represented by lines in log-log space with slopess such that –3s<–1. The power spectra from a Digital Elevation Model (30 meter sample spacing) of the Sierra Nevada Batholith and from Seabeam center beam depths (425 meter sample spacing) along a flowline in the South Atlantic are curved. Straight sections in the spectra can be identified but the slopes of those sections are strongly dependent upon the particulars of the data analysis. Fractal geometry must be used with caution in the discussion of topographic data sets.  相似文献