Shallow Seismics

Finished and ongoing projects

Aims:

Inference on one-dimensional lithological properties (seismic velocities, Poisson's ratio) from an easy-to-use field technique (vertical hammer-blow and vertical component geophones).

Method:

The 1D-inversion method, mainly using surface wave characteristics, is performed in two steps (Forbriger 1998, 2001, 2003a, and 2003b). In the first step a spectrum of complex coefficients is calculated, which represents the seismic wavefield in a mathematically exact sense (Henry et al. 1980). Alternatively a modified Hankel transformation can be used to calculate the spectral representation. This first stage reduces the nonlinearity and the numerical costs of the forward problem. In addition it allows easy preparation of a primary model by a manual trial and error approach to start the iterative inversion of the second stage. In the second step we use an iterative least-squares scheme to find an earth model. Synthetic spectra and partial derivatives are calculated using the reflectivity method (Fuchs and Müller 1971, Müller 1985, and Ungerer 1990). A Thomson-Haskell scheme (Wang 1999) may be extended to calculate semianalytical partial derivatives on-the-fly (Teshler 1999). The resulting model can be used to start full-waveform inversion methods (Reimann 1999 and Friederich 1999).

Outcome:

Method: Easy-to-use field techniques (vertical hammer-blow and vertical component geophones) provide strong inference on the Vp and Vs properties and the depth of discontinuities in the decameter range from the surface. This holds also for media with a fast top layer (roads e.g.) which contain a low-velocity-channel.
Data: In most cases we observe significant multiple modes which cannot be seperated in the time domain. Even more intricate: In some cases real data observations may not be uniquely classified in the sense of free normal modes (Forbriger 1996). Phase-difference- and single-mode-methods like the SASW method (Stokoe at al. 1994) therefore break down. This aspect demands for methods that considers the full surface wave field (Tokimatsu et al. 1997). Our method is able to extract independent information from all excited modes, guided waves and, at least in principle, body waves too.

References:

• Forbriger, T., 2003a. Inversion of shallow-seismic wavefields. Part I: Wavefield transformation. Geophys. J. Int., Vol. 153, 719-734.
(postscript, PDF)
• Forbriger, T., 2003b. Inversion of shallow-seismic wavefields. Part II: Inferring subsurface properties from wavefield transforms. Geophys. J. Int., Vol. 153, 735-752.
(postscript, PDF)
• Forbriger, T., 2001. Inversion flachseismischer Wellenfelder. Dissertation, Institut für Geophysik, Universität Stuttgart, Germany. (download)
• Forbriger, T., 1998. Wellenfeldanalyse für die Flachseismik. In DGG-Seminar: Umweltgeophysik. FKPE, DGG, Neustadt/Weinstrasse, Germany. (postscript, PDF)
• Forbriger, T., 1996. Zum Problem der Modenidentifikation in der Flachseismik. In Kolloquium: Seismik im Flachbereich. Bucha/Sachsen. (postscript, PDF)
• Friederich, W., 1999. Propagation of seismic shear and surface waves in a laterally heterogeneous mantle by multiple forward scattering, Geophys. J. Int., 136, 180-204.
• Fuchs, K. and Müller, G., 1971. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J. R. astr. Soc., 23(4), 417-433.
• Henry, M., Orcutt, J. A. & Parker, R. L., 1980. A new method for slant stacking refraction data, Geophys. Res. Lett., 7(12), 1073-1076.
• Müller, G., 1985. The reflectivity method: a tutorial, J. Geophys., 58, 153-174.
• Reimann, G., 1999. Inversion flachseismischer Wellenfelder. Diplomarbeit, Institut für Geophysik, Universität Stuttgart, Germany.
• Stokoe, K., Wright, S., Bay, J. & Roesset, J.M., 1994. Characterization of geotechnical sites by SASW method. In Geophysical Characterization of Sites, ed. R. Woods, pp. 15-25. Balkema, A.A., Rotterdam.
• Teshler, A. J., 1999. Beschleunigtes Inversionsverfahren in der Oberflächenwellenseismik. Diplomarbeit, Universität Stuttgart.
• Tokimatsu, K., Tamura, S. & Kojima, H., 1997. Effects of multiple modes on rayleigh wave dispersion characteristics, J. Geotech. Engineering Div., Proc. A.S.C.E., 118(10), 1529-1543.
• Ungerer, J., 1990. Berechnung von Nahfeldseismogrammen mit der Reflektivitätsmethode. Diplomarbeit, Institut für Geophysik, Universität Stuttgart, Germany.
• Wang, R., 1999. A simple orthonormalization method for stable and efficient computation of Greens's functions, Bull. Seism. Soc. Am., 89(3), 733-741.

Aims:

Refining 1D velocity structure and inference on attenuation properties from an easy-to-use field technique (vertical hammer-blow and vertical component geophones).

Method:

Subsurface models obtained by the inversion of wavefield spectra are suitable to serve as initial models for full-waveform inversion (Forbriger 2001 and 2003). Perturbation theory is used for efficient calculation of partial derivatives. Subsurface models are described by polygons with many nodes to allow for a large class of parameter variations. The source-time function must be inferred together with the subsurface parameters.

Outcome:

Seismic waveforms are remarkably sensitive to attenuation properties of the media. Seismic Q is typically smaller than 10. Without an approriate Q model, the waveform fit remains unsatisfactory (apart from amplitude attenuation). Second order polynomials are not appropriate to represent the variation of seismic velocities with depth. Small deviations from this class of parameter functions are necessary to provide a good fit of waveforms.

References:

• Forbriger, T., 2003. Inversion of shallow-seismic wavefields. Part II: Inferring subsurface properties from wavefield transforms. Geophys. J. Int., Vol. 153, 735-752.
(postscript, PDF)
• Forbriger, T., 2001. Inversion flachseismischer Wellenfelder. Dissertation, Institut für Geophysik, Universität Stuttgart, Germany. (download)

Aims:

Extraction of full information from wavefields recorded on shallow media. Inference on lateral heterogeneity and discontinuities. Full 3D-inversion of seismic wavefields recorded on shallow media with an easy-to-use field technique (vertical hammer-blow and vertical component geophones).

Method:

Subsurface models obtained by the inversion of wavefield spectra are suitable to serve as initial models for full waveform inversion (Forbriger 2001 and 2003). They may be refined by 1D waveform inversion. Forward calculation of full seismic wavefields based on parturbation theory (Friederich 1999) allows the efficient inversion of seismic waveforms in 3D media.

References:

• Forbriger, T., 2003. Inversion of shallow-seismic wavefields. Part II: Inferring subsurface properties from wavefield transforms. Geophys. J. Int., Vol. 153, 735-752.
(postscript, PDF)
• Forbriger, T., 2001. Inversion flachseismischer Wellenfelder. Dissertation, Institut für Geophysik, Universität Stuttgart, Germany. (download)
• Friederich, W., 1999. Propagation of seismic shear and surface waves in a laterally heterogeneous mantle by multiple forward scattering, Geophys. J. Int., 136, 180-204.