EGU2020-15228, updated on 12 Jun 2020
https://doi.org/10.5194/egusphere-egu2020-15228
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

On the link between Beamforming and Kernel-based Source Inversion

Daniel Bowden1, Korbinian Sager2, Andreas Fichtner1, and Małgorzata Chmiel3
Daniel Bowden et al.
  • 1Institut für Geophysik, ETH (Eidgenössische Technische Hochschule Zürich), Zürich, Switzerland (daniel.bowden@erdw.ethz.ch)
  • 2Earth, Environmental, and Planetary Sciences, Brown University, Providence, Rhode Island, U.S.A.
  • 3Department of Civil, Environmental and Geomatic Engineering, ETH (Eidgenössische Technische Hochschule Zürich), Zürich, Switzerland

Beamforming and backprojection methods offer a data-driven approach to image noise sources, but provide no opportunity to account for prior information or iterate through an inversion framework. In contrast, recent methods have been developed to locate ambient noise sources based on cross-correlations between stations and the construction of finite-frequency kernels, allowing for inversions over multiple iterations (i.e., Tromp et al., 2010, Ermert et al. 2017, Sager et al. 2018). These kernel-based approaches show great promise, both in mathematical rigour and in results, but may remain difficult to understand or implement for the wider community. Here we show that these two different classes of methods, beamforming and kernel-based inversion, are achieving exactly the same result in certain circumstances. This means existing beamforming and backprojection methods can also incorporate prior information in a mathematically correct manner.

We start with a description of a relatively simple beamforming or backprojection algorithm, based on time-domain shifting and measurement of waveform coherence. Only by changing the order of steps, we begin to resemble the kernel-based approaches. By adding a physical model for the distribution of noise sources, and therefore synthetic correlation functions, we can extend backprojection to an iterative, gradient-based inversion scheme. Adjoint methods and a direct simulation of correlation wavefields can later be used to increase computational efficiency, but we stress that these are not needed to understand the approach.

Given the equivalence of these approaches between these two communities, both sides can benefit from bridging the gap. For example, for kernel-based inversion schemes, a current challenge lies in defining the misfit and time window over which a correlation will be scored; a windowing function based on beamform images offers a more intuitive way to identify significant contributions in the noise wavefield, exploiting more than just the direct surface-wave arrivals.

How to cite: Bowden, D., Sager, K., Fichtner, A., and Chmiel, M.: On the link between Beamforming and Kernel-based Source Inversion, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-15228, https://doi.org/10.5194/egusphere-egu2020-15228, 2020

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Presentation version 1 – uploaded on 30 Apr 2020
  • CC1: Comments from the video chat, Laura Ermert, 05 May 2020

    Q: If I understand well, you don't need to correlate the data right?

    A: Normal beamforming does not need to collect a noise-correlation function like we would in interferometry. The inversion frameworks, however, do! Actually that's one of the key links between the two methods - you can precompute NCF's to do either method

     

    Q: @Daniel Bowden so you do beamforming with the correlations, so what is the difference to matched field processing?

    A: In my poster, beamforms and MFP are lumped together as similar methods. Beamforming performs a gridsearch over possible azimuths/slownesses. MFP gridsearches over possible locations in space, but otherwise they're similar

    Comment: Matched Field Processing can be extended way further than just grid search over location. The point is that for MFP you can design to match the field you are looking for.One could easily insert P and S wave Green's functions as replica vectors and then grid search, instead of the plane waves like in normal beamforming.

    A: You're absolutely right - both MFP and beamforming can go much deeper than I show here. I was focusing on keeping it simple to make the link, but I do not mean to offend!