Resolution limits for Crosswell migration and travel-time tomography

Gerard T. Schuster

doi:10.1117/12.218508

1 September 1995 Resolution limits for Crosswell migration and travel-time tomography

Gerard T. Schuster

Proceedings Volume 2571, Mathematical Methods in Geophysical Imaging III; (1995) https://doi.org/10.1117/12.218508
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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 (lambda) , and a centered line scatterer I show that: (1) The vertical resolution (Delta) _z^mig of the migration image is equal to 2(lambda) x_o/L under the far-field approximation. (2) The horizontal resolution (Delta) _x^mig of the migration image is equal to 16(lambda) x²_o/L². 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 (Delta) _x^tomo of the slowness tomogram is proportional to (root)(lambda) x_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](root)3x_o(lambda) /4, a factor 4(root)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 (root)N_gN_s.

Citation Download Citation

Gerard T. Schuster "Resolution limits for Crosswell migration and travel-time tomography", Proc. SPIE 2571, Mathematical Methods in Geophysical Imaging III, (1 September 1995); https://doi.org/10.1117/12.218508

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available