Borehole Effects on Downhole Sesimic Measurements

The first part of this thesis was concerned with the interaction of an incident elastic wave with open, cased, and noncircular boreholes. Exact formulations for borehole coupling were given. Explicit solutions for cased boreholes at low frequencies were also obtained. The borehole reception patterns for both the pressure in fluid (hydrophone measurement) and the solid displacement on the borehole wall (geophone measurement) were computed. The borehole effects on particle motion and the effect of geophone orientation were investigated in detail. We found that a significant fluid resonance exists when the formation is very soft and when the incident wave is of the SV-type. This resonance is associated with the excitation of a tube wave in the fluid. In an open borehole, it only prevails at low frequencies. However, in a cased borehole it is also prominent at very high frequencies, because the tube wave velocity is raised well above the formation shear wave speed by the steel pipe. In a cased borehole, for plane P-wave incidence at low frequencies, the pressure in the fluid vanishes at a particular angle of incidence if the casing thickness exceeds a critical value - the cased borehole screening effect. This behavior prevails in both hard and soft formations. In a borehole of irregular cross-section, the pressure in the fluid splits into two distinct branches depending on the azimuthal angle of the incident wave. The branch of larger amplitude is associated with incident waves propagating along the effective minor axis, and the one of smaller amplitude is associated with the incident waves along the effective major axis. Correction of the borehole effects on downhole geophone measurements should be made for frequencies above 500 Hz in the hard formation. In the soft formation, if the angle of incidence differs significantly from the resonance angle for SV-wave incidence, no borehole correction is needed for frequencies below 300 Hz. For downhole experiments with frequency above 1000 Hz, boreholes can significantly alter the particle motion direction, thus data-based horizontal component rotation is unreliable.

The second part of this thesis was concerned with the modeling of hydrophone data in VSP and crosswell experiments. We first considered the case where the fluid-filled borehole was embedded in a stratified formation. A method was proposed for computing the pressure in the borehole fluid for a source in the formation, in which the borehole coupling theory was hybridly combined with the discrete wavenumber/global matrix algorithm. This method is accurate at low frequencies and is as fast as existing ones for modeling elastic wave propagation in a horizontally layered medium. We used this method to simulate the Kent Cliffs borehole experiment, where synthetic predictions of both the traveltime and the RMS amplitude were found to match the observed hydrophone data. We also considered the case where the formations adjacent to the borehole were neither homogeneous nor stratified. A method for calculating the pressure in the fluid-filled borehole was developed by cascading the 3-D elastic finite difference formulation with the borehole coupling theory. An optimal absorbing boundary condition was discovered and incorporated into the 3-D finite difference algorithm. Directly including the borehole in the finite difference model was found not to be feasible even for the currently available parallel computer. We circumvented this difficulty by dividing the whole problem into two parts: propagation from the source to the presumed borehole location by the finite difference method, and coupling into the fluid by applying the borehole coupling equations. This method was applied to simulate the Kent Cliffs hydrophone VSP data with a 3-D geological model including dipping formations. The synthetic P-wave amplitudes were found to match the observed ones better than the previous predictions with a stratified medium.

In the third part of this thesis, we developed a method for removing the borehole effects from downhole hydrophone data by applying inverse borehole coupling filters. In this method, the hydrophone VSP and crosswell data were transformed into the borehole squeeze pressures, whereby the tube waves were effectively eliminated and the P-wave and S-wave were partially compensated for the borehole effects on their amplitudes. A follow-up procedure was then employed to convert the borehole squeeze pressure to either the pressure or the displacement of an incident wave in the formation. This procedure was successfully applied to process the Kent Cliffs hydrophone VSP data. The processed data could be directly used as inputs to tomographic imaging and full-waveform inversion schemes in which the receiver borehole is not taken into account.