Earth Resources Laboratory :: Abstracts

Application of the Finite Difference Method in the Study of Wave Propagation in a Borehole

Federico Pardo Casas

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences in August 1984 in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

Synthetic seismograms of elastic wave propagation in a fluid-filled borehole were generated using the finite difference method to later understand the effect of variations in the geometry or properties of the borehole. A detailed comparison between the seismograms generated by the finite difference technique and the discrete wavenumber summation technique 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 dispersion generated by the finite difference method. We have studied the depth of investigation of the refracted body waves in an invaded or damaged borehole using the conventional ray theory approach and compared it to the finite difference methods. The results show that the minimum source-receiver separation necessary to observe the unaltered formation depends on both the velocity gradient and the lowest and highest velocity of the damaged zone. Models calculated for invaded or flushed zones show the effects of invasion on full waveforms. Generally, the effect on velocities is small. The amplitudes of P waves, however, are strongly affected by the properties of the damaged zones and invaded zones. The inclusion of a rigid tool makes the model more real, but it is important to understand the effects of its presence when analyzing seismograms.