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| Titel |
Uniformly Asymptotic Frequency Domain Green's Functions for the Acoustic Equation - Theory and Applications in Two and Three Dimensions |
| VerfasserIn |
Matthew Yedlin, Jean Virieux |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250037737
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| Zusammenfassung |
| As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6].
Central to the sensitivity kernel techniques is the use of an appropriate Green’s function in either two or three dimensions and a background model is assumed for the calculation of the Green’s function. In some situations, the constant velocity Green’s function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green’s function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7].
To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green’s function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green’s function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications.
References
[1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics 64(3), pp. 888-901.
[2] J. R. Ernst, A. G. Green, H. Maurer and K. Holliger. 2007, Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data. Geophysics 72, pp. J53.
[3] H. Marquering, F. Dahlen and G. Nolet. 1999, Three-dimensional sensitivity kernels for finite-frequency traveltimes: The banana-doughnut paradox. Geophysical Journal International 137(3), pp. 805-815.
[4] J. Tromp, C. Tape and Q. Liu. 2005, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International 160(1), pp. 195-216.
[5] M. L. Buursink, T. C. Johnson, P. S. Routh and M. D. Knoll. 2008, Crosshole radar velocity tomography with finite-frequency fresnel volume sensitivities. Geophysical Journal International 172(1), pp. 1-17.
[6] I. Iturbe, P. Roux, J. Virieux and B. Nicolas. 2009, Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water. J. Acoust. Soc. Am. 126(2), pp. 713-720.
[7] E. Zauderer. 1971, Uniform asymptotic solutios of the reduced wave equation. Journal of Mathematical Analysis and Application 30, pp. 157-171.
[8] M. J. Yedlin. 1987, Uniform asymptotic solution for the Green’s function for the two-dimensional acoustic equation. J. Acoust. Soc. Am. 81(2) pp. 238-243. |
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