Full Waveform Inversion (FWI)

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FWI, providing high resolution earth models

Prestack acoustic full waveform inversion (FWI) uses the two-way wave-equation to estimate subsurface elastic parameters, providing high-resolution images. It goes beyond refraction and reflection tomography techniques, which use only the travel time kinematics of the seismic data, and uses the additional information provided by the amplitude and phase of the seismic waveform.


Given a background parameters model, FWI aims to minimize the difference between acquired and calculated data through an optimization process. Classical FWI involves the minimization of a least-squares misfit function between the calculated and observed data, but other norms can also be used. For successful FWI applications, low frequency data and background velocity model plays an important role. Data regularization and preconditioning can be necessary to handle Noisy data.

FWI iteratively calculates the gradient to update the actual velocity model in a process very similar to Reverse Time Migration (RTM). The velocity model provided from FWI can be used to Reservoir characterization or even to improve the RTM. FWI can be included in the Depth Imaging Workflow providing better background models for RTM, thus improving the results in the imaging process.

We can perform FWI in time or frequency domains, exploiting the benefits of each mathematical model. Mathematical models can beĀ Isotropic, Vertically Transversely Isotropic (VTI), or Tilted Transversely Isotropic (TTI).

Hugely compute-intensive, High Performance Computing (HPC) techniques is used to make the FWI process faster and to reduce computational cost. The usage of an optimization algorithm with high convergence rate can also help in the FWI processing time, but Hessian matrix estimation may require high computational cost for a large number of parameters, as is the FWI case.



  • Estimate of seismic source from recorded data
  • Regularization and preconditioning for noisy data
  • Multi scale techniques
  • High efficient minimization process (QUASI-NEWTON, GAUSS-NEWTON, and such)
  • Pseudo Hessian estimation for the minimization process
  • Efficient stop criteria for minimization process
  • High level I/O in order to store forward wave fields
  • Low memory requirement
  • Optimized back propagated wave field calculation
  • High order and optimized finite difference operators
  • Optimized computational grids
  • Optimized for high performance computing environment
  • Isotropic 2D solution
  • Highly efficient absorbing boundaries (CPML)
  • Shot parallelization and domain decomposition high level techniques