Resolution limits for Crosswell migration and travel-time tomography

Gerard T. Schuster*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

I derive the formulas for the seismic response of a line scatterer for the crosswell migration and traveltime tomography operators. These formulas are used to estimate the limits of spatial resolution in reflectivity images obtained from migration and slowness images reconstructed from traveltime tomography. In particular, for a crosswell geometry with borehole length L, well offset 2x o, source wavelength λ, and a centered line scatterer I show that: (1) The vertical resolution Δ z mig of the migration image is equal to 2λx o/L under the far-field approximation. (2) The horizontal resolution Δ x mig of the migration image is equal to 16λx 2 o/L 2. The lateral resolution of the migrated image is worse than the vertical resolution by the factor 8x o/L (where x o/L > 1 under the far-field approximation). (3) For inverting traveltimes associated with a localized slowness perturbation midway between the wells, the vertical resolution Δ x tomo of the slowness tomogram is proportional to √λx o. This estimate agrees with that of a previous study. (4) The horizontal resolution of the slowness image in a traveltime tomogram is equal to [4x o/L]√3x oλ/4, a factor 4√3x o/L worse than the vertical resolution. (5) For N s and N g geophones, the dynamic range of the migrated image is proportional to N sN g. The dynamic range of the slowness tomogram is proportional to √N gN s.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsSiamak Hassanzadeh
Pages97-108
Number of pages12
Volume2571
StatePublished - 1995
Externally publishedYes
EventMathematical Methods in Geophysical Imaging III - San Diego, CA, USA
Duration: Jul 12 1995Jul 13 1995

Other

OtherMathematical Methods in Geophysical Imaging III
CitySan Diego, CA, USA
Period07/12/9507/13/95

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Fingerprint

Dive into the research topics of 'Resolution limits for Crosswell migration and travel-time tomography'. Together they form a unique fingerprint.

Cite this