Marchenko focusing and imaging are novel methods for processing seismic data while correctly handling multiply scattered energy. Strict requirements in the acquisition geometry, specifically co-location of sources and receivers as well as dense and regular sampling, currently constrain their practical applicability. We reformulate the Marchenko equations to handle the case where there are gaps in the source geometry while receiver sampling remains regular. Comparing different solvers for the newly formulated inversion problem, we find that sparse Marchenko inversion enhances the recovery of focusing functions, filling the gaps caused by the missing sources. This does, however, not translate into a significant improvement in the subsequently produced images, as both least-squares and sparse inversion struggle to eliminate overburden effects in the presence of gaps. Further, we develop a method for co-processing two time-lapse datasets with different source geometries using sparse Marchenko inversion to image 4D effects. Sparse joint Marchenko inversion of multiple datasets results in clear time-lapse images, despite non-repeated source geometries and large fractions of missing sources.


Article metrics loading...

Loading full text...

Full text loading...


  1. Broggini, F., Snieder, R. and Wapenaar, K.
    [2014] Data-driven Wavefield Focusing and Imaging with Multidimensional Deconvolution: Numerical Examples for Reflection Data with Internal Multiples. Geophysics, 79(3), 107–115.
    [Google Scholar]
  2. Hennenfent, G. and Herrmann, F.
    [2008] Simply Denoise: Wavefield Reconstruction Via Jittered Undersampling. Geophysics, 73(3), 19–28.
    [Google Scholar]
  3. Herrmann, F.
    [2010] Randomized Sampling and Sparsity: Getting More Information from Fewer Samples. Geophysics, 75(6), 173–187.
    [Google Scholar]
  4. van der Neut, J.R., Thorbecke, J.W., Wapenaar, C.P.A. and Slob, E.C.
    [2015] Inversion of the Multidimensional Marchenko Equation. In: 77th EAGE Conference and Exhibition, Extended Abstracts.
    [Google Scholar]
  5. Oghenekohwo, F., Esser, E. and Herrmann, F.J.
    [2014] Time-lapse Seismic without Repetition: Reaping the Benefits from Randomized Sampling and Joint Recovery. In: 76th EAGE Conference and Exhibition, Extended Abstracts.
    [Google Scholar]
  6. Wang, Y., Cao, J. and Yang, C.
    [2011] Recovery of Seismic Wavefields Based on Compressive Sensing by an L1-norm Constrained Trust Region Method and the Piecewise Random Subsampling. Geophysical Journal International, 187(1), 199–213.
    [Google Scholar]
  7. Wapenaar, K., Broggini, F., Slob, E. and Snieder, R.
    [2013] Three-Dimensional Single-Sided Marchenko Inverse Scattering, Data-Driven Focusing, Green’s Function Retrieval, and Their Mutual Relations. Physical Review Letters, 110(8), 245–250.
    [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