Pure and Applied Geophysics

, Volume 176, Issue 1, pp 165–188 | Cite as

Seismic Envelope Inversion Based on Hybrid Scale Separation for Data with Strong Noises

  • Pan Zhang
  • Ru-Shan Wu
  • Liguo HanEmail author


When the source lacks low-frequency information, the linear deconvolution method based on the convolution signal model can only extract effective information within the bandwidth of the source. The envelope inversion method based on the modulation signal model can reconstruct the low-wavenumber components of the subsurface media. However, both methods have problems because seismic reflection data always show a poor S/N at low frequencies. In this article, we propose a hybrid scale separation method that combines the linear reconstruction and non-linear demodulation methods to recover the ultra-low-frequency information contained in seismic data. First, we propose an improved linear scale separation method, which can extract effective low-frequency information in the presence of strong low-frequency noises. Then, we conduct demodulation on seismic data after the improved linear scale separation, which we call hybrid scale separation. The analysis of the modulation signal model theory demonstrates that the hybrid scale separation method is good for refining the smooth Green function contained in the direct demodulation result. Based on the hybrid scale separation, we propose a new envelope inversion strategy with a strong anti-noise property. We first conduct the improved reconstruction using the synthetic observed data to suppress low-frequency noises and determine the effective signal bandwidth. Then, we calculate the envelope using the reconstructed data. By changing the parameters in the improved linear scale separation process, we can conduct envelope inversion in different scales. Our method can handle the inversion using seismic data that show a poor S/N at low-frequency components. The numerical examples using the Marmousi data set with different S/N illustrate the effectiveness of our method.


Envelope inversion hybrid scale separation low-frequency reconstruction modulation signal model full waveform inversion 



We thank the associated editor, Luca Bianchin, and the other two anonymous reviewers for their insightful suggestions and contributions to this manuscript. Thanks to the sponsors of the WTOPI Research Consortium at the University of California, Santa Cruz, CA, USA, the China Scholarship Council (CSC), the National Natural Science Foundation of China (nos. 41674124 and 41374115), the National High Technology Research and Development Program of China (863 project) (no. 2014AA06A605) and the Graduate Innovation Fund of Jilin University (project no. 2016098).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.College of Geo-exploration Science and TechnologyJilin UniversityChangchunChina
  2. 2.Modeling and Imaging Laboratory, Earth and Planetary Science DepartmentUniversity of CaliforniaSanta CruzUSA

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