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Data regularization and datuming by conjugate gradients
DANIEL R. SMITH1 ,
MRINAL K. SEN2 ,
ROBERT J. FERGUSON3
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1
Hess Corporation, 500 Dallas St., Houston, TX 77002, U.S.A.,
2
John A. and Katherine G. Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X Austin, TX 78713-8972, U.S.A.,
3
Department of Geoscience, University of Calgary, 2500 University Drive N.W., Calgary, Canada T2N 1N4.,
JSE 2010, 19(4), 321–347;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Smith, D.R., Sen, M.K. and Ferguson, R.J., 2010. Data regularization and datuming by conjugate gradients. Journal of Seismic Exploration, 19: 321-347. Irregular spacing of seismic sources and receivers, and strong topographic variations plus velocity heterogeneity, cause spatial and temporal irregularity in seismic data. Because so much of seismic processing, imaging. and inversion relies on the Fast Fourier transform for efficiency, and because seismic modelling requires continuous reflectors for analysis, seismic regularization is desirable. Here, we address spatial and temporal irregularity simultaneously. We use weighted, damped least-squares to extrapolate data from an irregularly sampled, topographic surface to a regularly sampled datum. This process requires an accurate velocity model of the near-surface, and it returns seismic traces with a constant trace-to-trace distance and more continuous reflection events. As an inverse problem, the Hessian in process is costly to compute, so the method of conjugate gradients (CG) are employed so that the required matrix-matrix multiplication is reduced to two matrix-vector multiplications. We find that use of the CG method reduces the total number of multiplication operations from O(n°) for the direct solution to O(n’) where n is the number of trace locations.
Keywords
conjugate gradients
data regularization
seismic interpolation
damped least-squares
seismic inversion
wave equation statics
wave equation redatum
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