Accession Number : AD1009748


Title :   Traveling Wave Modes of a Plane Layered Anelastic Earth


Descriptive Note : Technical Report,01 Jun 2014,29 Feb 2016


Corporate Author : University of Washington - Applied Physics Laboratory Seattle United States


Personal Author(s) : Odom,Robert I


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/1009748.pdf


Report Date : 20 May 2016


Pagination or Media Count : 22


Abstract : Incorporation of attenuation into the normal mode sum representations of seismic signals is commonlyeffected by applying perturbation theory. This is fine for weak attenuation, but problematic forstronger attenuation. In this work modes of the anelastic medium are represented as complexsuperpositions of elastic eigenfunctions. For the P-SV system a generalized eigenvalue equation for thecomplex eigenwavenumbers and complex coefficients used to construct the anelastic eigenfunctions isderived. The generalized eigenvalue problem for the P-SV problem is exactly linear in theeigenwavenumber at the expense of doubling the dimension. The SH problem is exactly linear in thesquare of the eigenwavenumber. This is in contrast to a similar standing wave problem for the earthfree oscillations (Tromp and Dahlen,1990). Attenuation is commonly incorporated into syntheticseismogram calculations by introduction of complex frequency dependent elastic moduli. The modulidepend nonlinearly on the frequency. The independent variable in the standing wave free oscillationproblem is the frequency, which makes the eigenvalue problem nonlinear. The choice of the wavenumber asthe independent variable for the traveling wave problem leads to a linear problem.


Descriptors :   Seismic waves , attenuation , anisotropy , surface waves , oscillation , seismology , wave propagation , perturbation theory , Eigenfunctions , acoustic signals


Distribution Statement : APPROVED FOR PUBLIC RELEASE