Spherical Slepian functions and the polar gap in geodesy   总被引：4，自引：0，他引：4  

Frederik J. Simons  F. A. Dahlen 《Geophysical Journal International》2006,166(3):1039-1061

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.  相似文献   

Multifractal modeling and spatial statistics   总被引：9，自引：0，他引：9  

Qiuming Cheng  Frederik P. Agterberg 《Mathematical Geology》1996,28(1):1-16

In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis.  相似文献   

Dr. Váslav Němec: Krumbein Medalist     

Frederik P. Agterberg 《Mathematical Geology》1994,26(6):753-755

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Appreciation of Contributions by Georges Matheron and John Tukey to a Mineral-Resources Research Project     

Agterberg  Frederik P. 《Natural Resources Research》2001,10(4):287-295

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   

Multifractal modeling and spatial point processes   总被引：8，自引：0，他引：8  

Quiming Cheng  Frederik P. Agterberg 《Mathematical Geology》1995,27(7):831-845

The multifractal model can be applied to spatial point processes. It provides new, approximately power-law type, expressions for their second-order intensity and K (r) functions. The box-counting and cluster dimensions are different but mutually interrelated according to multifractal theory. This approach is used to describe the underlying spatial structure of gold mineral occurrences in the Iskut River area, northwestern British Columbia. The box-counting and cluster dimensions for the example are estimated to be 1.335±0.077 and 1.219±0.037, respectively. The relatively strong clustering of the gold deposits is reflected by the fact that both values are considerably less than the corresponding Euclidean dimension (=2).  相似文献   

Book Review: Stein and M. Wysession, An Introduction to Seismology, Earthquakes and Earth Structure, 2003, Blackwell Publishing, Oxford, 498 pp., ISBN 0-86542- 078-5, £39.99.     

Frederik Tilmann 《Surveys in Geophysics》2006,27(1):109-110

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Effect of Surface Heterogeneity on the Boundary-Layer Height: A Case Study at a Semi-Arid Forest     

Peter Brugger  Tirtha Banerjee  Frederik De Roo  Konstantin Kröniger  Rafat Qubaja  Shani Rohatyn  Eyal Rotenberg  Feodor Tatarinov  Dan Yakir  Fulin Yang  Matthias Mauder 《Boundary-Layer Meteorology》2018,169(2):233-250

We investigate the effects of an isolated meso-\(\gamma \)-scale surface heterogeneity for roughness and albedo on the atmospheric boundary-layer (ABL) height, with a case study at a semi-arid forest surrounded by sparse shrubland (forest area: \(28~\text{ km }^2\), forest length in the main wind direction: 7 km). Doppler lidar and ceilometer measurements at this semi-arid forest show an increase in the ABL height over the forest compared with the shrubland on four out of eight days. The differences in the ABL height between shrubland and forest are explained for all days with a model that assumes a linear growth of the internal boundary layer of the forest through the convective ABL upwind of the forest followed by a square-root growth into the stable free atmosphere. For the environmental conditions that existed during our measurements, the increase in ABL height due to large sensible heat fluxes from the forest (\(600~\text {W~m}^{-2}\) in summer) is subdued by stable stratification in the free atmosphere above the ABL, or reduced by high wind speeds in the mixed layer.  相似文献   

Evolution of anthropogenic and biomass burning emissions of air pollutants at global and regional scales during the 1980�C2010 period     

Claire Granier  Bertrand Bessagnet  Tami Bond  Ariela D��Angiola  Hugo Denier van der Gon  Gregory J. Frost  Angelika Heil  Johannes W. Kaiser  Stefan Kinne  Zbigniew Klimont  Silvia Kloster  Jean-Fran?ois Lamarque  Catherine Liousse  Toshihiko Masui  Frederik Meleux  Aude Mieville  Toshimasa Ohara  Jean-Christophe Raut  Keywan Riahi  Martin G. Schultz  Steven J. Smith  Allison Thompson  John van Aardenne  Guido R. van der Werf  Detlef P. van Vuuren 《Climatic change》2011,109(1-2):163-190

Several different inventories of global and regional anthropogenic and biomass burning emissions are assessed for the 1980?C2010 period. The species considered in this study are carbon monoxide, nitrogen oxides, sulfur dioxide and black carbon. The inventories considered include the ACCMIP historical emissions developed in support of the simulations for the IPCC AR5 assessment. Emissions for 2005 and 2010 from the Representative Concentration Pathways (RCPs) are also included. Large discrepancies between the global and regional emissions are identified, which shows that there is still no consensus on the best estimates for surface emissions of atmospheric compounds. At the global scale, anthropogenic emissions of CO, NO_x and SO₂ show the best agreement for most years, although agreement does not necessarily mean that uncertainty is low. The agreement is low for BC emissions, particularly in the period prior to 2000. The best consensus is for NO_x emissions for all periods and all regions, except for China, where emissions in 1980 and 1990 need to be better defined. Emissions of CO need better quantification in the USA and India for all periods; in Central Europe, the evolution of emissions during the past two decades needs to be better determined. The agreement between the different SO₂ emissions datasets is rather good for the USA, but better quantification is needed elsewhere, particularly for Central Europe, India and China. The comparisons performed in this study show that the use of RCP8.5 for the extension of the ACCMIP inventory beyond 2000 is reasonable, until more global or regional estimates become available. Concerning biomass burning emissions, most inventories agree within 50?C80%, depending on the year and season. The large differences between biomass burning inventories are due to differences in the estimates of burned areas from the different available products, as well as in the amount of biomass burned.  相似文献   

Constraints on crustal and mantle structure of the oceanic plate south of Iceland from ocean bottom recorded Rayleigh waves     

Frederik J. Tilmann  Torsten Dahm 《Tectonophysics》2008,447(1-4):66

From April to July 2002 we carried out a deployment of 6 ocean bottom seismometers and 4 ocean bottom hydrophones in the North Atlantic south of Iceland. During the deployment period we recorded clear Rayleigh waves from 2 regional and 14 teleseismic earthquakes. This corresponds to a Rayleigh wave detection rate of nearly 92% for events with M_W ≥ 6.06.0 and epicentral distance less than 110°, close to detection rate estimates based on noise level variability. We measured Rayleigh wave event-station group dispersion and inter-station phase dispersion for one Mid-Atlantic Ridge event. The group dispersion curve is sensitive to the structure of the North-East Atlantic with an average age of  39 Myr. The phase dispersion curve is sensitive to the structure just south of Iceland (average plate age 33 Myr). Both dispersion curves indicate faster velocities than previously postulated for oceanic plate generated at the Reykjanes Ridge. A grid search approach was used to constrain the range of models fitting the data. The high velocity seismic lid just south of Iceland in the model for the phase dispersion path is slower or thinner than in the group dispersion model, which averages over a larger area and a somewhat older plate age, but the velocities in the low velocity half space are similar. We further consider the residual bathymetry in the experimental area. The residual anomaly decreases by 300–400 m from the Reykjanes Ridge to the  30 Myr old plate south of Iceland. This decrease can be explained by the disappearance of a mantle thermal anomaly associated with the Iceland plume. Both the residual bathymetry and the surface wave data are thus consistent with the notion that the southward spreading of the Icelandic plume is channelised underneath the Reykjanes Ridge and does not spread far outside this channel.Based on the experience from the pilot experiment, we estimate that a minimum recording time of 13–15 months in favourable weather conditions (April–September) is required to record enough data to map the spreading plume with surface waves, and to produce a tomographic image to a depth of 1000 km using body waves. This can be achieved by a continuous deployment of at least  20 months, or by two or three deployments during the spring and summer of consecutive years.  相似文献   

Evaluation of Probe-Induced Flow Distortion of Campbell CSAT3 Sonic Anemometers by Numerical Simulation     

Sadiq Huq  Frederik De Roo  Thomas Foken  Matthias Mauder 《Boundary-Layer Meteorology》2017,165(1):9-28

The Campbell CSAT3 sonic anemometer is one of the most popular instruments for turbulence measurements in basic micrometeorological research and ecological applications. While measurement uncertainty has been characterized by field experiments and wind-tunnel studies in the past, there are conflicting estimates, which motivated us to conduct a numerical experiment using large-eddy simulation to evaluate the probe-induced flow distortion of the CSAT3 anemometer under controlled conditions, and with exact knowledge of the undisturbed flow. As opposed to wind-tunnel studies, we imposed oscillations in both the vertical and horizontal velocity components at the distinct frequencies and amplitudes found in typical turbulence spectra in the surface layer. The resulting flow-distortion errors for the standard deviations of the vertical velocity component range from 3 to 7%, and from 1 to 3% for the horizontal velocity component, depending on the azimuth angle. The magnitude of these errors is almost independent of the frequency of wind speed fluctuations, provided the amplitude is typical for surface-layer turbulence. A comparison of the corrections for transducer shadowing proposed by both Kaimal et al. (Proc Dyn Flow Conf, 551–565, 1978) and Horst et al. (Boundary-Layer Meteorol 155:371–395, 2015) show that both methods compensate for a larger part of the observed error, but do not sufficiently account for the azimuth dependency. Further numerical simulations could be conducted in the future to characterize the flow distortion induced by other existing types of sonic anemometers for the purposes of optimizing their geometry.  相似文献