EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Wavefield reconstruction inversion for ambient seismic noise

Sjoerd A.L. de Ridder1, James R. Maddison2, Ali Shaiban3, and Andrew Curtis3
Sjoerd A.L. de Ridder et al.
  • 1School of Earth and Environmental Sciences, University of Leeds, United Kingdom
  • 2School of Mathematics, University of Edinburgh, United Kingdom
  • 3School of GeoSciences, University of Edinburgh, United Kingdom

With the advent of large and dense seismic arrays, there is an opportunity for novel inversion methods that exploit the information captured by stations in close proximity to each other. Estimating surface waves dispersion is an interest for many geophysical applications using both active and passive seismic data. We present an inversion scheme that exploits the spatial and temporal relationships of the Helmholtz equation to estimate dispersion relations directly from surface wave ambient noise data, while reconstructing the full wavefield in space and frequency. The scheme is a PDE constrained inverse problem in which we jointly estimate the state and parameter spaces of the seismic wavefield. Key to the application on ambient seismic noise recordings is to remove the boundary conditions from the PDE constraint, which renders a conventional waveform inversion formulation singular. With synthetic acoustic and elastic data examples we show that using a variable projection scheme, we can iteratively update an initial estimate of the medium parameters and recover an estimate for the true underlying velocity field. Our examples show that the we can reconstruct the full wavefield even in the case of strong aliasing and irregular sampling. This works forms the basis for a new approach to inverting ambient seismic noise using large and dense seismic arrays.

How to cite: de Ridder, S. A. L., Maddison, J. R., Shaiban, A., and Curtis, A.: Wavefield reconstruction inversion for ambient seismic noise, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22018,, 2020

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Presentation version 1 – uploaded on 04 May 2020
  • CC1: Comment on EGU2020-22018, Alison Malcolm, 04 May 2020

    Interesting slides, thank you.  Which of your two equations do you use to fill-in the data in your example?

    • AC1: Reply to CC1, Sjoerd de Ridder, 04 May 2020


      wavefield reconstruction inversion is the step used to fill in the data between receivers. This is done in an iterative way. One of the innovations in this paper, is that the BC's are omitted from the wave equation regularisation term in the wavefield reconstruction inversion step. See (De Ridder & Madisson GJI 2018).

  • CC2: Comment on EGU2020-22018, Alison Malcolm, 05 May 2020

    Sjoerd, nice talk I understood a lot more with words ;-). 

    When you say there is a singularity, how does that arise?  (And no I haven't read the paper yet ... )

  • CC3: Comments from the video chat :), Laura Ermert, 05 May 2020

    Q: Sjoerd, how much data do you need, how does it converge?

    A: So a conventional FWI approach, where one solves the adjoint wave equation for the back projection, could not work. You need sufficiently densely recorded data to constrain wave oscillations. The more freedoms you are able to take away from the oscillations (by picking where your recordings are) the more you can constrain the inversion.

    The inversion converges relatively fast, depending on additional regularisation parameters. But the inversion is also quite expensive (each step).

    For now, unfortunately, this is a theoretical contribution.

  • CC4: From video chat: Aliasing, Laura Ermert, 05 May 2020

    Q: the aliasing induces prominent artifacts only at certain frequencies that appear to be correlated with the velocity structure. Is there any way to potentially exploit that? Thanks

    A: Most of the 'difference' between true ED wavefield and inverted wavefield, are non-surface wave related feautures.

    So, indeed, near the step function.

    perhaps that can be further exploited.