An optimized parallel LSQR algorithm for seismic tomography

The LSQR algorithm developed by Paige and Saunders (1982) is considered one of the most efficient and stable methods for solving large, sparse, and ill-posed linear (or linearized) systems. In seismic tomography, the LSQR method has been widely used in solving linearized inversion problems. As the amount of seismic observations increase and tomographic techniques advance, the size of inversion problems can grow accordingly. Currently, a few parallel LSQR solvers are presented or available for solving large problems on supercomputers, but the scalabilities are generally weak because of the significant communication cost among processors. In this paper, we present the details of our optimizations on the LSQR code for, but not limited to, seismic tomographic inversions. The optimizations we have implemented to our LSQR code include: reordering the damping matrix to reduce its band-width for simplifying the communication pattern and reducing the amount of communication during calculations; adopting sparse matrix storage formats for efficiently storing and partitioning matrices; using the MPI I/O functions to parallelize the date reading and result writing processes; providing different data partition strategies for efficiently using computational resources. A large seismic tomographic inversion problem, the full-3D waveform tomography for Southern California, is used to explain the details of our optimizations and examine the performance on Yellowstone supercomputer at the NCAR-Wyoming Supercomputing Center (NWSC). The results showed that the required wall time of our code for the same inversion problem is much less than that of the LSQR solver from the PETSc library (Balay et al., 1997).

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NOTICE: This is the author's version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.


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Author Lee, E.
Huang, H.
Dennis, John M.
Chen, P.
Wang, L.
Publisher UCAR/NCAR - Library
Publication Date 2013-12-01T00:00:00
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Topic Category geoscientificInformation
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Metadata Date 2025-07-12T01:14:15.462949
Metadata Record Identifier edu.ucar.opensky::articles:18218
Metadata Language eng; USA
Suggested Citation Lee, E., Huang, H., Dennis, John M., Chen, P., Wang, L.. (2013). An optimized parallel LSQR algorithm for seismic tomography. UCAR/NCAR - Library. https://n2t.org/ark:/85065/d79z96f9. Accessed 03 August 2025.

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