Full waveform inversion (FWI) using an energy-based objective function has the potential to provide long wavelength model information even without low frequency in the data. However, without the back-propagation method (adjoint-state method), its implementation is impractical for the model size of general seismic survey. We derive the gradient of the energy-based objective function using the back-propagation method to make its FWI feasible. We also raise the energy signal to the power of a small positive number to properly handle the energy signal imbalance as a function of offset. Examples demonstrate that the proposed FWI algorithm provides a convergent long wavelength structure model even without low-frequency information, which can be used as a good starting model for the subsequent conventional FWI.


Article metrics loading...

Loading full text...

Full text loading...


  1. Choi, Y. and Alkhalifah, T.
    [2015] Unwrapped phase inversion with an exponential damping. Geophysics, 80, R251–R264.
    [Google Scholar]
  2. Jeon, S., Ha, W., Kwon, J. and Shin, C.
    [2014] Full waveform inversion using the energy objective function. 76th EAGE Conference & Exhibition, Expanded Abstracts, Amsterdam, Tu E106 02.
    [Google Scholar]
  3. Wu, R.S., Luo, J. and Wu, B.
    [2014] Seismic envelope inversion and modulation signal model. Geophysics, 79, WA13–WA24.
    [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