Open AccessSeismic waves converted from velocity gradient anomalies in the Earth’s upper mantle
Author(s) -
Bostock M. G.
Publication year - 1999
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1999.00902.x
Subject(s) - slowness , classification of discontinuities , geology , stratification (seeds) , anisotropy , seismic wave , velocity gradient , cholesky decomposition , mathematical analysis , matrix (chemical analysis) , reflection (computer programming) , geometry , wave propagation , homogeneous , geophysics , mathematics , physics , seismology , mechanics , optics , eigenvalues and eigenvectors , statistical physics , materials science , computer science , composite material , biology , germination , quantum mechanics , programming language , seed dormancy , botany , dormancy
Summary Modelling of elastic wave propagation in 1‐D structures is frequently performed using reflectivity techniques in which the Earth’s velocity profile is approximated by stacks of homogeneous layers. The complete reflection/transmission (R/T) response of a zone with arbitrary 1‐D depth variation (including both gradients and discontinuities in material properties) can, however, be calculated using invariant embedding techniques. Results from earlier studies are here extended to derive exact expressions for R/T matrices in arbitrary, 1‐D anisotropic media using a form of Born approxi‐mation valid for thin scatterers and which does not assume small perturbations in material properties. The R/T matrices are solutions to a system of non‐linear, ordinary differential equations of Ricatti type and may be manipulated using standard R/T matrix algebra. In an equivalent description, the wavefield within the heterogeneous zone is considered in terms of depth‐dependent contributions from up‐ and downgoing waves propagating within the embedding reference medium. This leads to efficient calculation of the internal wavefield using R/T matrices of the heterogeneous stratification and portions thereof at minor additional expense. Mode conversion of teleseismic P and S phases from velocity gradients is examined by way of examples and comparison with three‐component data from broad‐band stations of the Yellowknife seismic array. The frequency dependence of such wave interactions depends on the differences in vertical slowness between incident and scattered modes. It is shown that significant energy is converted from transition zones with extent L <λ P /2, a broader interval than will generally produce intramode reflections. A layer structure identified from Ps conversions near 75 km depth below the Slave craton is shown to be compatible with a ~ 10 km thick gradient zone in which anisotropy increases from ambient levels to δ V p = ± 5 per cent, δ V s = ± 2.5 per cent at a discontinuous upper boundary. This characterization supports a previous interpretation as the upper strata of a former oceanic plate juxtaposed against overriding lithosphere during an ancient episode of shallow subduction.