We present a method to obtain a misfit function for robust waveform inversion. This method, designated as adaptive traveltime inversion (ATI), computes a matching filter that matches the measured data to the predicted one. If the velocity model is accurate, the resulting matching filter reduces to an (approximate) Dirac delta function. Its traveltime shift, which characterizes the defocusing of the matching filter, is computed by minimization of the cross-correlation between a penalty function like $t$ and the matching filter. The ATI misfit function is constructed by the minimization of the least square error of the calculated traveltime shifts. Further analysis shows that the resulting traveltime shifts correspond to the first-order moment, the mean value, of the resulting matching filter distribution. We extend ATI to a more general misfit function formula by computing different order moment of the resulting matching filter distribution. Choosing the penalty function in adaptive waveform inversion (AWI) as $t$, the misfit function of AWI can be interpreted as the second-order moment. We use the Marmousi model to verify the effectiveness of the proposed method.


Article metrics loading...

Loading full text...

Full text loading...


  1. Luo, S. and Sava, P
    . [2011] A deconvolution based objective function for wave equation inversion. SEG Technical Program Expanded Abstracts, 2788–2792.
    [Google Scholar]
  2. Luo, Y. and Schuster, G.T
    . [1991] Wave-equation traveltime inversion. Geophysics, 56(5), 645–653.
    [Google Scholar]
  3. Sun, B. and Alkhalifah, T.
    [2018] Mitigate Cycle Skipping In FWI: A Generalized Instanatenous Travel-Time Approach. 80th EAGE Conference and Exhibition.
    [Google Scholar]
  4. Warner, M. and Guasch, L
    . [2016] Adaptive waveform inversion: Theory. Geophysics, 81(6), no. 6, R429–R445.
    [Google Scholar]
  5. Zhou, C., Cai, W., Luo, Y., Schuster, G.T. and Hassanzadeh, S
    . [1995] Acoustic wave-equation travel-time and waveform inversion of crosshole seismic data. Geophysics, 60(3), 765–773.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error