ISSN:
1365-246X
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Geosciences
Notes:
Subspace projection is an algorithm to calculate synthetic long-period seismograms from weakly coupled free oscillations. The algorithm exploits the fact that seismic motion on a slowly rotating, slightly aspherical earth can be represented by a sum of hybrid multiplets that are quasi-isolated in the frequency domain. This method incorporates the coupling interactions between multiplets to first order, and incorporates coupling interaction within each hybrid multiplet with a Galerkin formalism. Subspace projection does not linearize the response of the seismic waveform itself, but rather linearizes the perturbations to the free oscillations that comprise the seismic waveform. The subspace projection method enjoys a computational advantage over full coupled-mode calculations because eigenvalue-eigenvector decompositions are calculated using much smaller matrices. It is valid for times long after the seismic source onset. Subspace projection can be represented by a power series whose speed of convergence depends on the coupling strength parameter εrms. The estimated root-mean-square (rms) relative waveform perturbation caused by intermultiplet coupling is √2εrms. We tested the accuracy of the algorithm with a series of numerical experiments using rotation, hydrostatic ellipticity and upper mantle lateral structure model M84A. Waveforms were constructed from the modes 0Sl, l= 2,…, 56. We found that the subspace projection seismograms, averaged over 300 source-receiver pairs within frequency bands where coupling was significant, represented 92–99 per cent of the waveform variance caused by coupling among nearest neighbours along the 0Sl dispersion branch. If two multiplets are close in frequency, subspace projection may represent the coupled-mode waveform poorly. Closely spaced multiplets dominate the interaction between different free-oscillation dispersion branches, especially spheroidal-toroidal coupling. Numerical tests suggest that problems occur for Δf≳ 0.020 mHz, even for weakly coupled multiplets. These problems can be overcome by combining closely spaced multiplets into a single ‘augmented’ hybrid subspace. Interactions with modes outside the subspace are represented by subspace projection, while interactions within the augmented subspace are calculated using quasi-degenerate coupling. Synthetic vertical-component seismograms for 0Sl, l= 2,…, 60, and 0Tl, l= 2,…, 54, show mixed-mode coupling effects principally at source azimuths near the Love-wave radiation maximum. Perturbations to the free-oscillation spectrum are large for f≲ 4.2 mHz on polar propagation paths due to rotational coupling. However, the smooth lateral structure in M84A generates a smaller amount of spheroidal-toroidal coupling, and causes only modest distortion in the spectrum for f≳ 4.5 mHz.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1365-246X.1990.tb00761.x
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