In order to extract information about the 3-D structure and composition of the crust from seismic observations, it is necessary to be able to predict how seismic wavefields are affected by complex structures. Since exact analytical solutions to the wave equations do not exist for most subsurface configurations, the solutions can be obtained only by numerical methods.

Seismic modelling is helpful for predicting and understanding the kinematic and dynamic properties of seismic waves propagating through models of the crust. With the increased amount of detailed information required from seismic data, seismic modelling has become an essential tool for the evaluation of seismic measurements. It helps in every stage of a seismic investigation. It can help determine optimal recording parameters in data acquisition. Synthetic datasets can be computed to test processing procedures. The comparison of synthetic and field seismograms leads to a better understanding of seismic measurements and thus, finer details can be extracted from seismic field recordings. In seismic inversion procedures, modeling is the kernel of the inversion process.

The seismic working group concentrates on the optimization of 2-D and 3-D time domain finite-difference numerical methods, since these methods are applicable to arbitrary complex media. Domain-decomposition allows to use modern cluster technology. By using the free and portable message passing interface (MPI) the simulations are distributed on our in-house Linux PC cluster. The codes also show good performance on massive parallel supercomputers.

The following finite-difference modelling codes are currently being optimized:

• SOFI3D - 3-D viscoelastic, elastic, and acoustic wave simulations

• SOFI2D - 2-D viscoelastic and elastic wave simulations for P- and SV-waves

• SOFI2D_sh - 2-D viscoelastic and elastic wave simulations for SH-waves

They are applied and further developed in various research projects of our group.

Full waveform tomography

Full waveform tomography (FWT) is a cutting-edge inverse method that accounts for the full seismic waveform recorded over a broad range of frequencies and apertures. It iteratively retrieves multiparameter models of the subsurface by solving the full wave equations each time. It allows for a mapping of structures on spatial scales down to less than the seismic wavelength, hence providing a tremendous improvement of resolution compared to traveltime tomography based on ray-theory. Especially in exploration geophysics and earthquakes seismology the interest in FWT is increasing continuously.

In our work we concentrate on the implementation of FWT and its application to seismic problems. It comprises two- and three-dimensional modeling of acoustic and elastic wavefields in the time-domain. The main advantage of the this method is the efficient parallelization by domain decomposition leading to a significant speedup on parallel computers.

The following full waveform inversion code is currently being optimized:

• DENISE - 2-D elastic FWT

It is applied and further developed in various research projects of our group.

Funding

The methodological developments are financially supported by Verbundnetz Gas AG (Leipzig), Baker Hughes INTEQ (Celle), the Waveform Inversion Technology Consortium (WIT), the Department of Physics, Karlsruhe Institute of Technology (KIT) and German Research Foundation, Federal Ministry for Education and Research, Program GEOTECHNOLOGIEN.

References

Bohlen, T., Lorang, U., Rabbel, W., Müller, C., Giese, R., Lüth, S. & S. Jetschny: Rayleigh-to-shear wave conversion at the tunnel face - from 3D-FD modeling to ahead-of-drill exploration, Geophysics, 72, No. 6, T67-T79, 2007.

Essen, K., Bohlen, T., Friederich, W. & T. Meier: Modelling of Rayleigh-type seam waves in disturbed coal seams and around a coal mine roadway, Geophysical Journal International, 170, 511-526, 2007.

Huang, J.-W., Bohlen, T. & B. Milkereit: Numerical Solutions of Seismic Scattering in Heterogeneous Media, Canadian SEG Recorder, November 2006, Vol. 31, 44-47, 2006.

Bohlen, T. & E.H. Saenger: Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves, Geophysics, Volume 71, No. 4, Pages T109-T115, 2006.

Bohlen, T.: Analysis of Seismic Waves in the Presence of Small-Scale Strong Material Discontinuities, Habilitation (professorial dissertation), 2004.

Saenger, E. & T. Bohlen: Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid, Geophysics, 69, No. 2, 583-591, 2004.

Bohlen, T.: Parallel 3-D viscoelastic finite-difference seismic modelling , Computers@Geosciences, 28 (8) pp. 887-899, 2002.