Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields

Using a Poroelastic Theory to Reconstruct Subsurface Properties: Numerical Investigation

International audienceThe quantitative imaging of the Earth subsurface is a major challenge in geophysics. In oil and gas exploration and production, aquifer management and other applications such as the underground storage of CO2 , seismic imaging techniques are implemented to provide as much information as possible on fluid-filled reservoir rocks. Biot theory (Biot, 1956) and its extensions provide a convenient framework to connect the various parameters characterizing a porous medium to the wave properties, namely, their amplitudes, velocities and frequency contents. The poroelastic model involves more parameters than the elastodynamic theory, but on the other hand, the wave attenuation and dispersion characteristics at the macroscopic scale are determined by the intrinsic properties of the medium without having to resort to empirical relationships

Seismic tomography for velocity and attenuation model reconstruction

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Parsimonious finite-volume frequency-domain method for 2D P-SV-wave modeling

International audienceA new numerical technique for solving the 2D elastodynamic equations based on a finite volume approach is proposed. The associated discretization is through triangles. Only fluxes of required quantities are shared between cells, relaxing meshing conditions compared to finite element methods. The free surface is described along the edges of the triangles which may have different slopes. By applying a parsimonious strategy, stress components are eliminated from the discrete equations and only velocities are left as unknowns in triangles, minimizing the core memory requirement of the simulation. Efficient PML absorbing conditions have been designed for damping waves around the grid. Since the technique is devoted to full waveform inversion, we implemented the method in the frequency domain using a direct solver, an efficient strategy for multiple-source simulations. Standard dispersion analysis in infinite homogeneous media shows that numerical dispersion is similar to those of O(¢x2) staggeredgrid finite-difference formulations when considering structured triangular meshes. The method is validated against analytical solutions of several canonical problems and with numerical solutions computed with a well-established finite-difference time-domain method in heterogeneous media. In presence of a free surface, the finite-volume method requires ten triangles per wavelength for a flat topography and fifteen triangles per wavelength for more complex shapes, well below criteria required by the staircase approximation of finite-difference methods. Comparison between the frequency-domain finite-volume and the O(¢x2) rotated finite-difference methods also shows that the former is faster and less-memory demanding for a given accuracy level. We developed an efficient method for 2-D P-SV-wave modeling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to assess the method on unstructured meshes