Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a13 with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109). 相似文献
The Slave craton in northwestern Canada, a relatively small Archean craton (600×400 km), is ideal as a natural laboratory for investigating the formation and evolution of Mesoarchean and Neoarchean sub-continental lithospheric mantle (SCLM). Excellent outcrop and the discovery of economic diamondiferous kimberlite pipes in the centre of the craton during the early 1990s have led to an unparalleled amount of geoscientific information becoming available.
Over the last 5 years deep-probing electromagnetic surveys were conducted on the Slave, using the natural-source magnetotelluric (MT) technique, as part of a variety of programs to study the craton and determine its regional-scale electrical structure. Two of the four types of surveys involved novel MT data acquisition; one through frozen lakes along ice roads during winter, and the second using ocean-bottom MT instrumentation deployed from float planes.
The primary initial objective of the MT surveys was to determine the geometry of the topography of the lithosphere–asthenosphere boundary (LAB) across the Slave craton. However, the MT responses revealed, completely serendipitously, a remarkable anomaly in electrical conductivity in the SCLM of the central Slave craton. This Central Slave Mantle Conductor (CSMC) anomaly is modelled as a localized region of low resistivity (10–15 Ω m) beginning at depths of 80–120 km and striking NE–SW. Where precisely located, it is spatially coincident with the Eocene-aged kimberlite field in the central part of the craton (the so-called “Corridor of Hope”), and also with a geochemically defined ultra-depleted harzburgitic layer interpreted as oceanic or arc-related lithosphere emplaced during early tectonism. The CSMC lies wholly within the NE–SW striking central zone defined by Grütter et al. [Grütter, H.S., Apter, D.B., Kong, J., 1999. Crust–mantle coupling; evidence from mantle-derived xenocrystic garnets. Contributed paper at: The 7th International Kimberlite Conference Proceeding, J.B. Dawson Volume, 1, 307–313] on the basis of garnet geochemistry (G10 vs. G9) populations.
Deep-probing MT data from the lake bottom instruments infer that the conductor has a total depth-integrated conductivity (conductance) of the order of 2000 Siemens, which, given an internal resistivity of 10–15 Ω m, implies a thickness of 20–30 km. Below the CSMC the electrical resistivity of the lithosphere increases by a factor of 3–5 to values of around 50 Ω m. This change occurs at depths consistent with the graphite–diamond transition, which is taken as consistent with a carbon interpretation for the CSMC.
Preliminary three-dimensional MT modelling supports the NE–SW striking geometry for the conductor, and also suggests a NW dip. This geometry is taken as implying that the tectonic processes that emplaced this geophysical–geochemical body are likely related to the subduction of a craton of unknown provenance from the SE (present-day coordinates) during 2630–2620 Ma. It suggests that the lithospheric stacking model of Helmstaedt and Schulze [Helmstaedt, H.H., Schulze, D.J., 1989. Southern African kimberlites and their mantle sample: implications for Archean tectonics and lithosphere evolution. In Ross, J. (Ed.), Kimberlites and Related Rocks, Vol. 1: Their Composition, Occurrence, Origin, and Emplacement. Geological Society of Australia Special Publication, vol. 14, 358–368] is likely correct for the formation of the Slave's current SCLM. 相似文献
With the development of computer graphics, the three-dimensional (3D) visualization brings new technological revolution to the traditional cartography. Therefore, the topographic 3D-map emerges to adapt to this technological revolution, and the applications of topographic 3D-map are spread rapidly to other relevant fields due to its incomparable advantage. The researches on digital map and the construction of map database offer strong technical support and abundant data source for this new technology, so the research and development of topographic 3D-map will receive greater concern. The basic data of the topographic 3D-map are rooted mainly in digital map and its basic model is derived from digital elevation model (DEM) and 3D-models of other DEM-based geographic features. In view of the potential enormous data and the complexity of geographic features, the dynamic representation of geographic information becomes the focus of the research of topographic 3D-map and also the prerequisite condition of 3D query and analysis. In addition to the equipment of hardware that are restraining, to a certain extent, the 3D representation, the data organization structure of geographic information will be the core problem of research on 3D-map. Level of detail (LOD). space partitioning, dynamic object loading (DOL) and object culling are core technologies of the dynamic 3D representation. The objectselection, attribute-query and model-editing are important functions and interaction tools for users with 3D-maps provided by topographic 3D-map system, all of which are based on the data structure of the 3D-model. This paper discusses the basic theories, concepts and cardinal principles of topographic 3I)-map,expounds the basic way to organize the scene hierarchy of topographic 3D-map based on the node mechanism and studies the dynamic representation technologies of topographic 3D-map based on LOD, space partitioning, DOL and object culling. Moreover. such interactive operation functions are explored, in this paper, as spatial query, scene editing and management of topographic 3D-map. Finally, this paper describes briefly the applications of topographic 3D-map in its related fields. 相似文献
As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques
have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K2[6](Al3Mg)[4](Si7Al)O20(OH)4. Values of the atomic exchange interaction parameters Jn used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied
and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral
sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst
we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets
alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the
T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range
order was observed.
Received: 8 August 2002 / Accepted: 14 February 2003
Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed
on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility. 相似文献