Borehole Wave Propagation In Isotropic And Anisotropic Media II: Isotropic Formation

Abstract

In this paper we apply the 3-D finite difference method to simulate borehole wave propagations in an isotropic formation. The scheme is tested in a fluid-filled borehole surrounded by the homogeneous elastic formation. The finite difference synthetics results are in good agreement with the discrete wavenumber solutions for both monopole and dipole sources in hard as well as soft formation. These tests also show the good performance of Higdon's absorbing boundary condition for the body waves as well as the guided waves. In the isotropic borehole formation, the following results are obtained: 1. Off-centered dipole sources generate almost the same waveforms as the centered dipole source. The slight amplitude differences are due to the different values of the excitation function at the different source positions. The off-centered monopole shows a larger Stoneley wave than the centered one. 2. In an elliptic borehole, where the source is in line with the minor axis of ellipse, the dipole waveforms have similar waveforms to the circular borehole with the same radius as the minor axis. This corresponds to the odd flexural mode. The waveform similarity demonstrates that the odd flexural mode is insensitive to the major axis. When the dipole is in line with the major axis of the ellipse, the waveforms shift to the low frequency range. The waveforms are dominated by the even flexural mode. 3. For a borehole near a horizontal bed, the monopole log can be used to detect it by using refracted P waves from the bed boundary. Because a dipole is a directional source, when it is parallel to the bed, there is little effect of the bed on the waveforms, and when it is perpendicular to the bed, there are strong flexural wave interferences. For a borehole which penetrates a 45 degree tilted layer interface, the monopole log has less reflection and transmission than the horizontal interface. The dipole log also transmits less flexural waves across the tilted boundary than the horizontal one. The horizontally layered formation seismograms clearly show the two flexural modes in the different layers. There are no clear flexural wave reflections in both cases.