Finite Difference Synthetic Acoustic Logs
Author(s)
Stephen, R. A.; Pardo-Casas, F.; Cheng, C. H.
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Other Contributors
Massachusetts Institute of Technology. Earth Resources Laboratory
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Synthetic seismograms of elastic wave propagation in a fluid-filled borehole were generated using both the finite difference technique and the discrete wavenumber summation technique. The latter is known to be accurate for both body and surface (guided) waves. The finite difference grid has absorbing boundaries on two sides and axes of symmetry on the remaining two sides. A grid size no less than 10 points per wavelength was used. The far absorbing boundary was located at a distance of five to 10 radii from the borehole. Two types of solid-liquid interfaces were investigated: 1) a velocity gradient using the heterogeneous formulation, and 2) a sharp boundary using a second order Taylor expansion of the displacements. The results from the finite difference modeling were compared with the synthetic seismograms generated by the
discrete wavenumber summation method. No comparison the heterogeneous formulation and the discrete wavenumber method has been made. The second order approximation to the solid-liquid interface produced seismograms that compared 'well with the discrete wavenumber seismograms. A detailed comparison between the seismograms generated by the two methods showed that the body waves (refracted P and S waves) are identical. while the guided waves showed a slight difference in both phase and amplitude. These
differences are believed to be due to the approximations introduced in the
fluid-solid interface, the absorbing boundary at the edge of the grid, and the
grid and time step sizes involved. Owing. to the fact that they are interface
waves, the guided waves, especially the higher modes, are much more sensitive
to the above mentioned approximations.
Date issued
1983Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1983-04