Solutions of the Equation of Motion with Absorption for some Common Sources
Date
2018-06-06
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Abstract
Different kinds of solutions of the equation of motion (EOM) in a perfectly elastic medium have been derived and also have been widely recognized. However, in fact, we can hardly find an ideal medium without absorption. And, anelasticity of the earth causes physical dispersion of seismic waves. Dispersion resulting from absorption in the propagation medium has been included in the approximations of solutions of the equation of motion for some common sources (a directed point force, double-couple-without-moment forces and a shear-dislocation force) by replacing the velocity or slowness with the complex version. A velocity-frequency relation in the form of 1/v(w)=1/v(w_0r)[1-1/pi/Q*ln(w/w_0r)+i/2Q] has been used, where w is the angular frequency, v(w_0r) is the phase velocity at the reference frequency w_0r. These approximations match very well with the exact numerical results, and the anelastic waveforms have significant differences in amplitude and shape than the elastic ones. Therefore, developing new solutions of the EOM with absorption is a very meaningful thing.
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Keywords
equation of motion, absorption, dispersion
Citation
Sun, Y. (2018). Solutions of the Equation of Motion with Absorption for some Common Sources (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/31982