Download Modelling of scattered seismic waves at small

Modelling of scattered seismic waves at small-scale structures
K. Essen1 ∗ , W. Friederich1 and T. Bohlen2
1
Ruhr-University Bochum, Institute of Geology, Mineralogy and Geophysics, D-44780 Bochum, Germany
2
TU Bergakademie Freiberg, Institute of Geophysics, Gustav-Zeuner-Str. 12, 09596 Freiberg, Germany
There are several algorithms for the modelling of seismic wave propagation in 3-D
models with vertical as well as lateral variations of elastic parameters today. These algorithms normally make use of grid methods, as for example the finite-difference modelling.
The decomposition of the models into different sub-domains and the usage of modern simultaneous computers allows to considerably reduce run times for large 2-D or 3-D grids.
Nevertheless up to now computations of wave propagation in 2-D and 3-D models require
a high computational effort. Thus it is not possible to calculate numerous models within
a short time, that is necessary for the application of inversion algorithms. To investigate
scattered seismic waves at small-scale structures, we therefore developed an algorithm for
the modelling of wave propagation in 3-D media that applies the Born approximation.
Synthetic seismograms for 1-D reference models are calculated with the Green’s function
method (Friederich & Dalkolmo, 1995). In these 1-D models small-scale scattering volumes with slight pertubations of the elastic parameters compared to the reference model
are added. Different shapes of scattering volumes can be realized by tessellation of the
volumes.
The developed method is to be applied both for technical applications to interpret seismic measurements and for seismological investigations. We used a parallel elastic 2-D/3-D
finite-difference code (Bohlen, 2002) to model the wave propagation in different 2-D and
more realistic 3-D seam models (Essen et al., 2007). The effectiveness of different types
of seam disturbances in producing seam wave reflections was studied. Wave propagation
in a simple 2-D model with an ending seam layer of 2 m thickness was calculated and
compared to results of the Born approximation method (Fig. 1). A fundamental mode
Rayleigh-type seam wave is generated, if the source is located in the seam centre. When
the seam wave reaches the end of the seam layer, the wave is partly reflected with considerably smaller amplitudes. Also a S-wave is generated and radiated into the neighbouring
rock. We found a good correlation between the results of the FD modelling and the Born
approximation method. Phase differences in the scattered waves are caused by the discretisation of the scattering volume when calculating with Born approximation and by
velocity discrepancies when choosing too large grid spacings for the FD-modelling. Amplitude differences can be explained by the different spreading in a 2-D model compared
phone:
bochum.de
∗
+49-234/32-23275; fax:
+49-234/32-14181, E-mail address:
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katja.dietrich@ruhr-uni-
vertical component
synthetics (FD)
synthetics (BORN)
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Figure 1: Comparison of synthetics calculated with Born approximation and with FD
modelling. Fourth-order spatial FD-operators were used. Calculations for a 1-D reference
model showed, that for the FD modellings with a grid spacing of 12 grid points per
minimum wave length velocity discrepancies of about 2 % can occur (Essen et al., 2007).
to a 3-D model.
The developed method will also be used to study the wave propagation at small-scale
structures in the vicinity of the Hellenic subduction zone. Higher-frequency P- and Sbody waves from smaller events will be analysed for reflection at small-scale structures.
Modelling results can help to interpret measured data with respect to expected scattering
bodies. They can be used to test processing and analysis algorithms and are a prerequisite
for inversion techniques.
References
Bohlen, T., 2002. Parallel 3-D viscoelastic finite difference seismic modelling, Computers &
Geoscience, 28, 887–899.
Essen, K., Bohlen, T., Friederich, W. & Meier, T., 2007. Modelling of Rayleigh-type seam waves
in disturbed coal seams and around a coal mine roadway, Geophys. J. Int. (accepted).
Friederich, W. & Dalkolmo, J., 1995. Complete synthetic seismograms for a spherically symmetric earth by a numerical computation of the Green’s function in the frequency domain,
Geophys. J. Int., 122, 537–550.
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