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3D Full Waveform Inversion for Laterally Varying Layered Media
  • Michael Zuev,
  • Petr Petrov,
  • Magomed Magomedov
Michael Zuev
WaveLab, LLC

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Petr Petrov
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Magomed Magomedov
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Abstract In order to decipher complex subsurface structures, various seismic imaging techniques have been developed. Full Waveform Inversion (FWI) is one of the most sophisticated approaches in the new generation of seismic imaging algorithms for 2D/3D Earth modeling. An effective implementation of FWI requires a good initial model and intensive computations, among other challenges. To address these challenges, we developed a new FWI scheme, where we perform just a few local inversions under the assumption that the layers present only small lateral variations. We then upscale the local inversions to reconstruct 3D media. This approach also includes Source Signature inversion and does not require an initial model. The algorithm is based on the exact analytical solution of the Navier-Lame equation for a visco-elastic multi-layer model. This solution is represented in the form of Fourier-Bessel integrals, and performs forward modeling calculations about 106 – 107 times faster than conventional finite differences (FD) algorithms. It is free from various numerical artifacts inherent to FD methods, and allows modeling of all known types of seismic waves. The solution also indicates numerous unknown waves in various layered systems (some of the waves are practically impossible to reproduce numerically for the thin layers, using the grids, typical for 3D modeling). The comparison of the exact solution with 3D FDTD results shows excellent agreement. Here we applied this approach to stratified media with small lateral variations (the Earth, consisting of the inclined multi-layer structures). The feasibility of the method was analyzed using traces from synthetic seismograms for the Marmousi model, which were simulated by the 3D elastic SW4 code. A few sources with surrounding geophones were chosen. At the first stage we invert the traces from each geophone to the local stratum under the source, deciphering thicknesses, densities and P,S-wave velocities for each layer. At the second stage we identify the layer boundaries’ slopes and reconstruct the full 3D model. For the Marmousi model we obtained an accurate image down to 2.3 km deep, after which lateral variations were excessive. This result demonstrates that a new FWI scheme exploiting separate inversions, can be applied successfully to the reconstruction of 3D media.