Seismic Waves in Laterally Inhomogeneous Media
Part of the series Pageoph Topical Volumes pp 17711789
Scattering of Seismic Waves by Cracks with the Boundary Integral Method
 Kiyoshi YomogidaAffiliated withDivision of Earth and Planetary Sciences, Graduate School of Science, Hokkaido University
 , Rafael BenitesAffiliated withInstitute of Geological and Nuclear Sciences
Abstract
Wedevelop a new scheme to compute 2D SH seismograms for media with many flat cracks, based on the boundary integral method. A dry or tractionfree boundary condition is applied to crack surfaces although other kinds of cracks such as wet or fluidsaturated cracks can be treated simply by assigning different boundary conditions. While body forces are distributed for cavities or inclusions to express scattered wave, dislocations (or displacement discontinuities between the top and the bottom surfaces of each crack) are used as fictitious sources along crack surfaces. With these dislocations as unknown coefficients, the scattered wave is expressed by the normal derivative of Green’s function along the crack surface, which is called “doublelayer potentials” in the boundary integral method, while we used “singlelayer potentials” for cavities or inclusions. These unknowns are determined so that boundary conditions or crack surfaces are satisfied in the leastsquared sense, for example, tractionfree for dry cracks. Seismograms with planewave incidence are synthesized for homogeneous media with many cracks. First, we check the accuracy of our scheme for a medium with one long crack. All the predicted phases such as reflected wave, diffraction from a crack tip and shadow behind the crack are simulated quite accurately, under the same criterion as in the case for cavities or inclusions. Next, we compute seismograms for 50 randomly distributed cracks and compare them with those for circular cavities. When cracks are randomly oriented, waveforms and the strength of scattering attenuation are similar to the cavity case in a frequency range higher thankd≃2 where the size of scatterersd(i.e., crack length or cavity diameter) is comparable with the wavelength considered(kis the wavenumber). On the other hand, the scattering attenuation for cracks becomes much smaller in a lower frequency range(kd <2) because only the volume but not detail geometry of scatterers becomes important with wavelength much longer than each scatterer. When all the cracks are oriented in a fixed direction, the scattering attenuation depends strongly on the incident angle to the crack surface as frequency increases(kd >2): scattering becomes weak for cracks oriented parallel to the direction of the incident wave, while it gets close to the cavity case for cracks aligned perpendicular to the incident wave.
Key words
Scattering crack media attenuation boundary method Title
 Scattering of Seismic Waves by Cracks with the Boundary Integral Method
 Book Title
 Seismic Waves in Laterally Inhomogeneous Media
 Pages
 pp 17711789
 Copyright
 2002
 DOI
 10.1007/9783034881463_20
 Print ISBN
 9783764366773
 Online ISBN
 9783034881463
 Series Title
 Pageoph Topical Volumes
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Basel AG
 Additional Links
 Topics
 Keywords

 Scattering
 crack media
 attenuation
 boundary method
 Industry Sectors
 eBook Packages
 Editors

 Ivan Pšenčík ^{(1)}
 Vlastislav Červený ^{(2)}
 Editor Affiliations

 1. Geophysical Institute, Academy of Sciences of the Czech Republic
 2. Faculty of Mathematics & Physics Dep. of Geophysics, Charles University
 Authors

 Kiyoshi Yomogida ^{(3)}
 Rafael Benites ^{(4)}
 Author Affiliations

 3. Division of Earth and Planetary Sciences, Graduate School of Science, Hokkaido University, Sapporo, 0600810, Japan
 4. Institute of Geological and Nuclear Sciences, Lower Hutt, P.O. Box 30368, New Zealand
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