Downscaling FWI images using the homogenization operator

Paul Cupillard and Morgane Viv{\`e}s and Guillaume Caumon. ( 2019 )
in: 2019 Ring Meeting, ASGA

Abstract

Full waveform inversion (FWI) is a powerful tool to image the seismic velocities within the Earth. Nevertheless, the resolution of this technique is intrinsically limited to lambda/2 (where lambda is the minimum wavelength of the inverted seismic wavefield), meaning that details smaller than lambda/2 (such as geological discontinuities) are subject to interpretation uncertainties. In this work, we propose a rigorous and quantitative method for interpreting small scale features from FWI images. To do so, we rely on the homogenization operator, which is able to compute the effective elastic properties of any complex 3D media for the wave propagation. This upscaling operator actually tells "what the seismic waves see', i.e. the smooth effective medium that we can retrieve from a FWI. In the frame of the present work, we use the homogenization to smooth various discontinuous models which sample the uncertainies on the geometry and the position of discontinuities. Doing this is equivalent to performing a FWI in these models, but at a much lower computation cost. We then compute a local distance between the obtained smooth media and the FWI image to assess the probability of presence of discontinuities. The SEG-EAGE overthrust model is used to illustrate our method.

Download / Links

BibTeX Reference

@INPROCEEDINGS{CupillardRM2019,
    author = { Cupillard, Paul and Viv{\`e}s, Morgane and Caumon, Guillaume },
     title = { Downscaling FWI images using the homogenization operator },
 booktitle = { 2019 Ring Meeting },
      year = { 2019 },
 publisher = { ASGA },
  abstract = { Full waveform inversion (FWI) is a powerful tool to image the seismic velocities within the Earth. Nevertheless, the resolution of this technique is intrinsically limited to lambda/2 (where lambda is the minimum wavelength of the inverted seismic wavefield), meaning that details smaller than lambda/2 (such as geological discontinuities) are subject to interpretation uncertainties. In this work, we propose a rigorous and quantitative method for interpreting small scale features from FWI images. To do so, we rely on the homogenization operator, which is able to compute the effective elastic properties of any complex 3D media for the wave propagation. This upscaling operator actually tells "what the seismic waves see', i.e. the smooth effective medium that we can retrieve from a FWI. In the frame of the present work, we use the homogenization to smooth various discontinuous models which sample the uncertainies on the geometry and the position of discontinuities. Doing this is equivalent to performing a FWI in these models, but at a much lower computation cost. We then compute a local distance between the obtained smooth media and the FWI image to assess the probability of presence of discontinuities. The SEG-EAGE overthrust model is used to illustrate our method. }
}