Pure and Applied Geophysics

, Volume 176, Issue 1, pp 189–202 | Cite as

Dynamic Convolution-based Misfit Function for Time Domain Full Waveform Inversion

  • Xuebao GuoEmail author
  • Hong Liu
  • Ying Shi
  • Weihong Wang
  • Zhen Zhang
  • Hongliang Jing


Under the same propagation operator, the precision of the seismic wavelet determines whether synthetic data can match field data accurately. By constructing the convolution wavefield objective function, the source difference between simulated and observed data is ignored, thus avoiding the source wavelet estimation. Theoretically, this process has no restriction on the accuracy of the wavelet, and a multi-scale inversion strategy can be implemented by using a source wavelet with different dominant frequencies. When the propagation operator used does not conform with reality, even if both the wavelet and the parameter mode are accurate, it is impossible to simulate the full waveforms of the observed data. Meanwhile, the difference in the Green function brings new discrepancy to the convolution wavefield objective function and affects the final inversion results. The method presented in this paper is based on the convolution wavefield objective function. On the basis of an original single reference trace, we discuss the performance of the convolution wavefield-type objective function under multiple reference traces selected from different offsets. After introducing the changed wavefield information, the objective function has the ability to adapt to different types of data. The analysis shows that nonlinearity is significantly increased after introducing the different wavefield information and also increases with inversion frequency. Even for anisotropic data, it is still possible to give a relatively accurate structure at the low-frequency stage, which shows that the wavefield information from different offsets can help to weaken the artifacts introduced by operator mismatch, thus providing more possibilities for the application of acoustic wave equation inversion.


Convolved wavefield dynamic convolution Green function nonlinearity reference trace 



This research was supported by the Elastic Wave Seismic Imaging Technology Cooperation R & D Project of China National Petroleum Corporation, Major State Research Development Program of China (Grant No. 2016YFC0601101), as a Project of the National Natural Science Foundation of China (Grant Nos. 41574117 and 41474118), Heilongjiang Province Natural Science Fund for Distinguished Young Scholars (Grant No. JC2016006), Northeast Petroleum University Excellent Scientific Talent Fund (GLJHB201601).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Key Laboratory of Petroleum Resources Research, Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.School of Earth ScienceNortheast Petroleum UniversityDaqingChina
  4. 4.Research Institute of Exploration and Development, Tarim Oilfield Company, PetroChinaKorlaChina
  5. 5.Tuha DivisionBGP Inc., CNPCHamiChina

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