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Seismic wavefield reconstruction using a pre-conditioned wavelet–curvelet compressive sensing approach

Muir, Jack B. and Zhan, Zhongwen (2021) Seismic wavefield reconstruction using a pre-conditioned wavelet–curvelet compressive sensing approach. Geophysical Journal International, 227 (1). pp. 303-315. ISSN 0956-540X. doi:10.1093/gji/ggab222.

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The proliferation of large seismic arrays have opened many new avenues of geophysical research; however, most techniques still fundamentally treat regional and global scale seismic networks as a collection of individual time-series rather than as a single unified data product. Wavefield reconstruction allows us to turn a collection of individual records into a single structured form that treats the seismic wavefield as a coherent 3-D or 4-D entity. We propose a split processing scheme based on a wavelet transform in time and pre-conditioned curvelet-based compressive sensing in space to create a sparse representation of the continuous seismic wavefield with smooth second-order derivatives. Using this representation, we illustrate several applications, including surface wave gradiometry, Helmholtz–Hodge decomposition of the wavefield into irrotational and solenoidal components, and compression and denoising of seismic records.

Item Type:Article
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URLURL TypeDescription ItemCSN data for the Mw 7.1 Ridgecrest Earthquake ItemHelmholtz-Hodge decomposition code
Muir, Jack B.0000-0003-2617-3420
Zhan, Zhongwen0000-0002-5586-2607
Additional Information:© The Author(s) 2021. Published by Oxford University Press on behalf of The Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2021 June 3. Received 2021 May 23; in original form 2021 February 21. Published: 07 June 2021. The authors would like to thank the editor, Andrew Valentine, and an anonymous reviewer, for their insightful reviews that clarified several points. They would also like to thank Charles Langston for a particularly enthusiastic review. JBM acknowledges the financial support of the Origin Energy Foundation and the General Sir John Monash Foundation during his PhD studies. ZZ thanks the support from NSF CAREER award EAR 1848166 and the NSF/IUCRC GMG Center. Seismic data were processed using Obspy (Beyreuther et al. 2010), and figures were created using Matplotlib (Hunter 2007) using Cartopy for mapping (Met Office 2010). Data Availability: Data for the Mw 7.0 Loyalty Islands Earthquake were obtained through the obspy FDSN service using the Southern California Earthquake Data Center as a provider (SCEDC 2013). CSN data for the Mw 7.1 Ridgecrest Earthquake are available through the CSN website at Code and data to recreate the Helmholtz–Hodge decomposition are available at
Group:Seismological Laboratory
Funding AgencyGrant Number
Origin Energy FoundationUNSPECIFIED
General Sir John Monash FoundationUNSPECIFIED
Subject Keywords:Wavelet transform, Computational seismology, Seismic tomography
Issue or Number:1
Record Number:CaltechAUTHORS:20211102-203603665
Persistent URL:
Official Citation:Jack B Muir, Zhongwen Zhan, Seismic wavefield reconstruction using a pre-conditioned wavelet–curvelet compressive sensing approach, Geophysical Journal International, Volume 227, Issue 1, October 2021, Pages 303–315,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111716
Deposited By: Tony Diaz
Deposited On:02 Nov 2021 21:10
Last Modified:02 Nov 2021 21:10

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