Effects of causal absorption on seismic body waves

Červený, Vlastislav; Frangié, Antoine B.; Vaněk, J.

doi:10.1007/bf01635033

Cited by 8 publications

(1 citation statement)

References 16 publications

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“…Real p values have also been used by others for weakly absorbing materials and to avoid computational and conceptual difficulties (see e.g. Červený & Frangié 1982; Moczo et al 1987; Gajewski & Pšenčík 1992). In addition, reflection and transmission coefficients computed using real p values do not contain the above‐mentioned phase discrepancies and jump discontinuities, even if both media are anelastic.…”

Section: Introductionmentioning

confidence: 99%

Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Krebes¹,

Daley²

2007

Geophysical Journal International

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S U M M A R YConsider a plane homogeneous wave incident upon an interface between two anelastic halfspaces. Computing the plane-wave displacement reflection and transmission coefficients requires determining the proper signs of the vertical slownesses of all the reflected and transmitted waves. In certain cases, this is not straightforward. Previous work has shown that choosing the signs by applying the elastic radiation condition results in certain vertical slownesses, and hence coefficients, varying discontinuously and unphysically with the angle of incidence, and that choosing the signs so that the vertical slownesses vary continuously can also produce errors. We suggest three approaches for treating these cases. In the first approach, the signs are chosen so that the vertical slownesses vary continuously up to a certain angle of incidence (close to the elastic critical angle), with the elastic radiation condition being applied beyond that. We show that this is actually just an extension of the elastic radiation condition to complex-valued squared slownesses. In the spherical wave case in which a point source lies in the upper half-space, the approach also agrees with the results obtained by applying the saddle point method to approximate the integral for the reflected wavefield. This approximation is just geometrical ray theory. The first approach also produces coefficients with unphysical aspects, but these are confined to the critical zone, where geometrical ray theory is not valid anyway. Outside of this zone, the coefficients compare quite well with the elastic ones. In the second approach, real values of the horizontal slowness are used to compute the coefficients. This results in coefficients which are continuous and have no unphysical aspects, but do not compare as well with the elastic ones. The third approach involves using other paths in the complex plane (of horizontal slowness) to evaluate the coefficients. We show two examples. The first example is an approximation which involves replacing certain vertical slownesses with their complex conjugates before the coefficients are computed. This is equivalent to evaluating the horizontal slowness along a curve just above the real axis. The second example involves using a path which yields coefficients that are almost identical to the elastic ones. The third approach also results in continuous coefficients with no unphysical aspects, which compare well with the elastic ones.The errors mentioned above suggest to us that the problem of how to correctly compute plane-wave anelastic reflection and transmission coefficients, even in the apparently simple case of a homogeneous incident plane wave, still requires further study.

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Section: Introductionmentioning

confidence: 99%

Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Krebes¹,

Daley²

2007

Geophysical Journal International

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Seismic Wave Fields in Media with Causal Absorption

Červený

Frangié

1983

European Seismological Commission

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Effect of a simple mountain range on underground seismic motion

Zahradnı́k

Urban

1984

Geophysical Journal International

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The influence of a simple mountain range on seismic ground motion is studied. A two-dimensional model of the medium and vertically incident plane SH-waves are considered. Attention is devoted not only l o the wavefield along the Earth's surface, but also within the medium. The wavefield is computed in two steps: ( I ) the computation of the impulse response by the finite-difference method, (2) the computation of the response t o a time variation of the incident wave. approximately corresponding t o a 'hundred-yeai-' local earthquake a ( the sitc. Numerical results (the impulse 1-esponse. the transfer function, the accelerograms, and their spectra) indicate strong spatial variability of the wavefield due to the topographical anomaly. The differences as large as 100 per cent in the peak amplitudes of the accelerograms, and of the order of 5 Hz in their predominant frequencies, at closely (-200 m) spaccd internal points of the medium have been found. Attention is focused also on the effect of causal absorption. Even unrealistically strong absorption seems to be unable t o reduce significantly the spatial variability of the ground niotion. caused by the topography. A variability like this. implying the occurrence of underground differential strains, might be of engineering inipoi-lance in the antiseismic desigti of underground structures (tunnels, for example) in mountainous seismic I-egions. The groundmotion variability along the surface of the mountain is considerably smaller than within the medium.

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Effects of causal absorption on seismic body waves

Cited by 8 publications

References 16 publications

Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Seismic Wave Fields in Media with Causal Absorption

Effect of a simple mountain range on underground seismic motion

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