Computed waveforms in transversely isotropic media II. Horizontal point force

White, J. E.; Tongtaow, Chalermkiat; Monash, C.

doi:10.1190/1.1826871

Cited by 1 publication

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“…If the source is an explosion or a point force along symmetry axis, one branch of the triplication disappears. The vertical force result agrees with the calculation of White (1984) for a line source approximated by a borehole along the symmetry axis. Buchwald (1959) and White (1984) demonstrated the difference in energy fall-off for the quasi-P and quasi-SV waves.…”

Section: S Vb K2 Tbsupporting

confidence: 83%

“…The vertical force result agrees with the calculation of White (1984) for a line source approximated by a borehole along the symmetry axis. Buchwald (1959) and White (1984) demonstrated the difference in energy fall-off for the quasi-P and quasi-SV waves. Amplitude decays as -1 power of distance for the P wave, and as -0.8 for the SV waves near the triplication.…”

Section: S Vb K2 Tbsupporting

confidence: 83%

“…The far-field approximation of these strains was given using a stationary-phase approximation. Other workers (White 1984;White et al 1984;Mandal & Toksoz 1990) employed numerical methods to study the radiated waveforms of line-source, vertical and horizontal point forces, and explosion sources. Kazi-Azoual, Bonnet & Jouanna (1988) devised an algorithm using the Kupradze method (Kupradze 1979) for calculating the dynamic Green's function.…”

Section: Introductionmentioning

confidence: 99%

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Simplified dynamic and static Green's functions in transversely isotropic media

Dong

Schmitt

1994

Geophysical Journal International

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S U M M A R YNumerically feasible dynamic Green's function in an unbounded transversely isotropic (TI) medium is obtained in simple dyadic form by evaluating in general an inverse Laplacian operator involved in a previous dynamic Green's function described by Ben-Menahem & Sena (1990). T h e final dyadic form is close to that of the isotropic dyadic Green's function, therefore, lends itself more easily t o analytical and numerical manipulations. It is expressed through three scalar quantities characterizing the propagation of SH, P-SV, and P-SV-SH waves in a transversely isotropic medium. T h e static Green's function has the same dyadic form as the dynamic Green's function and the three corresponding scalar functions are derived. Using the dynamic Green's function, displacements for three point sources are computed t o compare with known numerical results. T h e singular property of the Green's functions is addressed through the surface integral of the static function in the case of coinciding receiver and source. T h e singular contribution is shown t o be -1/2 of the applied force when the static-stress Green's function is integrated over a half-elliptical surface. Results of this paper are particularly suitable t o wavepropagation problems involving the boundary-element method.

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Section: S Vb K2 Tbsupporting

confidence: 83%

Section: S Vb K2 Tbsupporting

confidence: 83%