A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys. 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