Inversion Velocity Analysis

Migration-based imaging techniques aim at characterising the subsurface by analysing focusing panels such as Common Image Gathers (CIGs), whereas Full Waveform Inversion relies on the misfit between observed and synthetic data. In essence, migration-based techniques assumes a scale separation between the large spatial scales (background model) and the short scales (reflectivity images). The first step consists of producing a series of images, for example from subsets of the input data. For a correct background velocity model, these images are expected to be consistent (Symes, 2008).

We investigate and develop two new aspects in this context: (1) the direct inverse approach to create the reflectivity images, and (2) the extension beyond reflected waves. The direct inverse

  • aims at replacing the standard migration scheme or boosting the iterative migration schemes (Figures 1 and 2);

  • can be used as a preconditionner for the FWI approach. This is an important element for the stochastic approaches;

  • is an essential element for a more robust Migration Velocity Analysis to determine proper background velocity models.

Figure 1: Inversion in a model with a low velocity anomaly (−900 m/s): a) velocity model and interface positions, b) inverted reflectivity after summation over all subsurface offsets, c) observed data dobs, reconstructed data and e) extracted traces from c) in solid black and d) in dashed red, for offsets 100 and 550 m.

 

Figure 2: Direct versus iterative approaches. Top: exact and smoothed macro-models, left: exact and inverted reflectivity model, middle: exact and reconstructed shots, right: extracted traces, top right: convergence curves. The three approaches are the direct inverse, the iterative LCG and the iterative P-LCG, respectively.

Main references

  • Chauris, H. and E. Cocher, 2018, Review of different expressions for the extended born approximate inverse operator: Expanded Abstracts, 80th Annual EAGE Meeting, accepted to Workshop 07 – Seismic Imaging with Ray and Waves – Where do we stand? Part II: Imaging.
  • Chauris, H. and E. Cocher, 2017, From migration to inversion velocity analysis: Geophysics, 82, S207–S223.
  • Cocher, E., H. Chauris, and R.-E. Plessix, 2017, Seismic iterative migration velocity analysis: two strategies to update the velocity model: Computational Geosciences, 21, 759–780.
  • Lameloise, C.-A and H. Chauris (2016), Extension of Migration Velocity Analysis to transmitted wave fields, Geophysical Journal International, 207(1): 343–356, doi:10.1093/gji/ggw284