Viscoelastic wave propagation along a borehole using squirt flow and Biot poroelastic theory
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Observations of seismic waves provide valuable understanding of Earth subsurface properties. These measurements are used to study large-scale subsurface features, kilometers in width, borehole-scale situations, meters of interest, and with core samples, a few centimeters in length. A common practice is to assume that the elastic rock-properties (P- and S-wave velocities) are the same for all frequencies. This is why sonic logs without corrections, for example, are used to constrain velocity models that transform seismic data from time to depth and to calibrate rock physics models used in seismic inversion to link elastic properties to reservoir properties. However, when seismic waves propagate in Earth materials, they are subject to different dispersion mechanisms, which makes the velocities frequency dependent. Understanding these effects on acoustic wave propagation can improve our models that constrain the subsurface and ultimately give us better hydrocarbon predictability. The main objective of this dissertation is to contribute to the understanding of how fluid in the pore space affects acoustic wave propagation. To achieve this goal, I first developed a frequency-dependent wave equation that accounts for local (squirt) and global (Biot) flow. The new model is tested against other squirt-Biot flow theories for both synthetic cases and utrasonic velocity data. I find the developed model to be consistent with the compared models in the synthetic cases. For the utrasonic velocity data, I find predictions from the new model to be closest to the measured data. In the second part of the dissertation, I use the developed squirt-Biot flow wave equation to simulate wave propagation in fluid-filled boreholes containing formations with different quantities of compliant pores. These are compared with formations where no compliant pores are present. I use the discrete wavenumber summation method with both a monopole and a dipole source to generate the wave fields. I find that fluid-saturated compliant pores can significantly affect the effective formation P- and S-wave velocities. This in turn affects the various acoustic wave modes causing increasing dispersion and attenuation. Thus, knowledge of the micro-scale structure of the fluid-saturated rock is of importance for understanding the acoustic waveforms and the dispersive behavior of the various modes. Depending on the locations where the critical frequencies for the different dispersion mechanisms occurs, acoustic velocity estimates can differ from the seismic-frequency velocities. Having a frequency dependent model accounting for the various dispersion mechanisms can help better connect the various velocity measurements and ultimately serve to give us an even more realistic picture of the subsurface.