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What is XWI?

The XWITM toolkit extends conventional FWI in 3 key ways:

  • Reformulating the optimisation cost function for robustness against cycle skipping without low frequencies in the field data (AWITM)
  • Alternating long-wavelength and short-wavelength model updates for enhanced reflection moveout sensitivity (RWI)
  • Applying regularization to the model update direction for incorporating geological constraints (ATV)

Why use XWITM over conventional FWI alone?

Conventional full-waveform inversion of surface seismic data is normally able to recover an accurate and well-resolved velocity model down to the depth of penetration of the deepest recorded diving waves. This depth depends upon the acquisition geometry and the background velocity model, but it seldom extends much deeper than about 2 to 3 km below mud line, and can be shallower where there are strong velocity inversions.

Below this depth, conventional FWI applied directly to reflection data can usefully update the high-wavenumber velocity model but normally makes little useful contribution to longer wavelengths. AWITM which redefines the optimisation cost function and RWI which further separates the migration and tomographic aspects of FWI, are capable of modifying the macro velocity model successfully below the diving waves, to cover the target area and predict the sonic measurements taken at well locations at these depths.

The key difference in the AWI and the FWI model updates occurs at the backpropagation stage of the model gradient computation and in particular with the form of the adjoint source which is backpropagated. For the AWITM cost function, the expression is as follows:

where w=(DTD)-1DTp i.e. the filter which transforms observed data into predicted data and f is the AWITM cost function i.e. the norm of w weighted by diagonal matrix T divided by the unweighted norm of w. This contrasts with conventional FWI where instead and i.e. simply the norm of the residual.

Why use XWITM on the Cloud?

  • Register for the S-Cube Cloud SaaS cluster on Amazon Web Services (AWS) and access a managed compute environment configured for wave equation velocity optimisation computations
  • Upload your existing job directories directly to the cloud virtual cluster with a few commands
  • Parameterise a new job and view the computational load per shot
  • Select the number of shots per iteration and number of iterations to run
  • Monitor and QC the live job on the S-Cube Cloud dashboard accessed via a URL
  • Always deploy the latest XWITM installations

XWITM on the Cloud Example


  • Total number of shots: 5186 (9 saillines)
  • Grid size: 25m
  • Average runtime per shot (16 core instances): 0.15 hours
  • Percentage of shots per iteration: 20%
  • Number of shots per AWS compute instance: 2
  • Number of passes through the shots (epochs): 24
S-Cube Cloud

Try S-Cube Cloud with your Seismic Data

Zero-management cloud HPC platform configured for seismic velocity optimisation.

Launch a cloud-optimised XWITM cluster in minutes - no need for a supercomputer.