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Presentation of the Master's Thesis: 2D elastic full-waveform inversion of land seismic data with topographic variations

Presentation of the Master's Thesis: 2D elastic full-waveform inversion of land seismic data with topographic variations



Daniel Krieger

Areas with strong topography and complex subsurface geology like the Canadian foothills are of interest for exploration geophysics. They pose particular processing and imaging challenges, though.
In order to create under these circumstances subsurface images with high resolution, sophisticated methods such as full-waveform inversion (FWI) have to be applied. FWI is, in principle, capable of producing highly detailed parameter models of the subsurface by iteratively updating a starting model to match both traveltimes and amplitudes of simulated data with data recorded in the field.
When using land data, in particular when strong surface waves are observed that lead in combination with topographic variations to significant surface wave scattering effects, elastic wave propagation has to be considered. Previous works studying FWI in areas with topographic variations used, e.g., the spectral element method. While this method has the advantage that it has the intrinsic ability to meet the free surface condition in case of a non-planar top surface, it is also hard to implement and hard to use efficiently. Hence, the aim of this work is to investigate, if the use of the finite-difference method paired with the improved vacuum formulation that fully satisfies the free surface boundary condition is also justifyable.
The finite difference method has the advantage that it is widely used and much simpler than the spectral element method. I show that the staircase effect has a major influence on Rayleigh waves but not on body waves. This influence can be reduced by choosing a discretization which is much finer than that needed for body waves. However, even without such fine discretization my approach is able to simulate wavefields with sufficient accuracy for FWI applications. I perform simultaneous reconstruction of P-wave velocity, S-wave velocity and density using synthetic data simulated with the spectral element method. I demonstrate that errors in my scheme result only in a thin high-velocity layer below the topographic surface of the P-wave velocity model. Furthermore, I investigate the impact of strong 3D effects, like they occur in mountainous regions, on 2D FWI. The result of this investigations is that in case of a 3D model which is constant in one dimension the recorded data can be easily transformed such that it is almost eqivalent to the 2D data regardless of the surface topography. In this case 2D FWI still produces sufficiently accurate results. In case of topographic variations perpendicular to the acquisition line, however, this transformation is no longer applicable. Thus, 2D FWI fails under such conditions.