Numerical simulations of the reflected P-wave amplitude in azimuthal acoustic reflection logging

An acoustic phased-arc array transmitter is designed to be used in azimuthal acoustic reflection logging, in which the distance and azimuth of formation boundaries, fractures, and other small geological structures near the borehole can be determined by analyzing reflected waves. We simulate the acoustic field in boreholes with vertical interfaces up to 30m away from the borehole axis, using the 3D finite-difference method (FDM). By extracting and analyzing the reflected P-waves, we determine the relationship between the relative reflected P-wave amplitude and the distance of the interfaces from the borehole axis. The simulation results show that the relative amplitude of the reflected wave is about 0.2 % when the formation boundary is 10.0 m away from the borehole axis. For the case of a formation interface 20.0 m away from the borehole axis, the relative amplitude of the reflected wave is about 0.08%. For the case of a formation interface 30.0 m from the borehole axis, the relative amplitude of the reflected wave is about 0.04%. These simulation results are guiding the design of electronic sampling circuits for azimuthal acoustic reflection tools.