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Summary. A problem in modelling electromagnetic fields used in exploration geophysics is treated mathematically. Analytical expressions are obtained for the electric field due to a harmonic current in a horizontal loop on or above a conducting ground in which is buried a conductive and permeable sphere (ore body). The loop is coaxial with the sphere. For a general time-varying current in the loop, the analysis is carried to the stage where a Fourier inversion can be used to obtain readily the electric field in the time-domain. A new relationship between spherical and cylindrical wave functions is obtained as a transformation of local elements.
Solution of this problem has not been presented before in this form. Lee's solution of 1975 which uses an integral-equation formulation treats a similar problem without taking account of differences in magnetic permeability. The effects of magnetic permeability may have important and useful implications for geophysical explorations.  相似文献   

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This paper examines the impact of DEM resolution on the accuracy of terrain representation and of the gradient determined. The DEMs of three terrain types with diverse complexities were constructed from digitizing contours and then kriging. The accuracy (RMSE) of the DEMs was regressed against contour density (D) and DEM resolution (S) at six resolution levels. It is found that RMSE may be expressed as (7.274 1.666S)D/1000 with an R value of 0.9659. The representation accuracy decreases moderately at an intermediate resolution, but sharply at coarse resolutions for all three terrain types. Resolution reduction profoundly affects the gradient determined from the DEM. While exerting little influence on mean gradient, resolution significantly affects the standard deviation of gradient, especially for a simple terrain. The results obtained in this study may be used to determine the DEM resolution that is appropriate to the accuracy requirements of a particular user.  相似文献   

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We have explored the contemporary spatial relationship between aquatic vegetation and surficial macrofossil and pollen remains in a small, shallow, English lake. A detailed point-based (n = 87) underwater vegetation survey was undertaken in the middle of the plant-growing season in July 2000. Then following plant die-back in November 2000, surface sediment samples (upper 1.5 cm) were collected from 30 of these plant survey points and analysed for plant macro-remains (all 30 samples), and pollen (4 evenly spaced samples). All data were stored as separate layers in a geographical information system and spatial relationships between the aquatic vegetation and plant remains were explored. In contrast to pollen types, plant macrofossils were not evenly dispersed across all parts of the lake and, with the exception of Chara oospores, higher concentrations of remains (particularly for Potamogeton) were found close to areas of source-plant dominance. The spatial pattern of macrophyte–macrofossil relationships revealed that vegetative remains (particularly leaf fragments) were probably deposited at source, whereas seeds were recovered close to the shore suggesting slightly wider dispersal. Overall, however, macro-remains best represented local ‘patch-scale’ vegetation within 20–30 m of the core site. The macro-remains effectively recorded the dominant plants in the lake with 63% of samples containing a combination of remains of Chara, Elodea, and Potamogeton. However, relationships between macrophytes and fossils were complex. Some species were significantly over-represented by macrofossils (e.g., Chara spp., Nitella flexilis agg., and Zannichellia palustris), while others were either under-represented (e.g., Potamogeton spp.), or not represented at all (e.g., Lemna trisulca). Pollen represented macrophyte diversity poorly, but some taxa were found (e.g., Myriophyllum spicatum, Ceratophyllum demersum) that were not recorded by macro-remains. We conclude that macrofossil analysis may be very usefully employed to determine the dominant taxa in past aquatic plant communities of shallow, productive lakes and that the addition of pollen analysis provides further information on former species richness.  相似文献   

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Summary. The slowness-distance ( p, x ) plane is an alternative to the slowness-time intercept ( p, τ ) plane as the intermediate image space in inversion of seismic refraction data. The production of a ( p, x ) image from travel time-distance ( T, x ) data has been presented elsewhere so emphasis here is on ( p, x ) to velocity-depth ( v, z ) transformation. Iterative downward continuation of a ( p, x ) image converges to the correct ( v, z ) image in a manner similar to that in the widely used ( p, τ ) to ( v, z ) process. Application to a real refraction data set from the Imperial Valley of southern California gives a similar ( v, z ) solution via both ( p, x ) and ( p, τ ) images.  相似文献   

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In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a (for cases of   a / R = 0.001  to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r 0 (for cases of   r 0/ R = 0.90  to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a / R , and slightly on   r 0/ R   . For example, in our base-line case,   a / R = 0.03, r 0/ R = 0.96  , the free-surface velocity above the source is 0.26 c , whereas antipodal to the source, the peak free surface velocity is 0.19 c . Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.  相似文献   

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Georges Matheron (1930–2000) and John Tukey (1915–2000) were among the most prominent mathematical statisticians of the 20th century. Both men produced numerous important new theoretical and practical results. This personal appreciation of their work concentrates on contributions to mineral-resources research and describes their influence on my work in mineral-resource evaluation studies at the Geological Survey of Canada (1966–1983).  相似文献   

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