Deconvolution of the PSF of a seismic lens

Jianhua Yu, Yue Wang, Gerard T. Schuster*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

10 Scopus citations


We show that if seismic data d is related to the migration image by mmig = LTd, then mmig is a blurred version of the actual reflectivity distribution m, i.e., mmig = [LTL]m. Here L is the acoustic forward modeling operator under the Born approximation where d = Lm. The blurring operator [LTL], or point spread function, distorts the image because of defects in the seismic lens, i.e., small source-receiver recording aperture and irregular/coarse geophone-source spacing. These distortions can be partly suppressed by applying the deblurring operator [LTL]-1 to the migration image to get m = [LTL]-1 mmig. This deblurred image is known as a least squares migration (LSM) image if [LTL]-1 LT is applied to the data d using a conjugate gradient method, and is known as a migration deconvolved (MD) image if [LTL]-1 is directly applied to the migration image mmig in (kx ky, z) space. The MD algorithm is an order-of-magnitude faster than LSM, but it employs more restrictive assumptions. We also show that deblurring can be used to filter out coherent noise in the data such as multiple reflections. The procedure is to, e.g., decompose the forward modeling operator into both primary and multiple reflection operators d = (Lprim + Lmult)m invert for m, and find the primary reflection data by dprim = Lprimm. This method is named least squares migration filtering (LSMF). The above three algorithms (LSM, MD and LSMF) might be useful for attacking problems in optical imaging.

Original languageEnglish (US)
Pages (from-to)135-145
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2002
Externally publishedYes
EventImage Reconstruction from Incomplete Data II - Seattle, WA, United States
Duration: Jul 8 2002Jul 9 2002


  • Inverse problem
  • Least squares migration filtering
  • Migration deconvolution
  • Point spread function
  • Seismic migration

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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