Characteristics of waveforms recorded by azimuthally spaced hydrophones of sonic logging tool for incident plane waves

The borehole acoustic reflection survey (BARS) is a method for imaging near-borehole structures using waveforms acquired by a sonic logging tool: Signals from a monopole or dipole source are reflected from geologic interfaces and recorded by arrays of the hydrophones of the same tool. Due to the nearly 1D configuration of the source and hydrophones, BARS provides only 2D images, in which the dimensions are the axis of the well and the distance from the center of the well. We have developed methods for identifying the azimuthal direction of the reflector, which is not given by the BARS image, by using the differences of the signals recorded by hydrophones at varying azimuths. We have conducted a theoretical analysis for incident plane waves as follows. Analytic solutions in the frequency domain are numerically computed at discrete frequencies and converted to time-domain synthetics using the fast Fourier transform for a newly derived model that includes the effect of the tool in the fluid-filled borehole. For event signals from the monopole and dipole sources, the hydrophones recording the largest signal amplitude are located on the diameter parallel to the wavenumber vector of the incident wave, on the side from which incident wave is coming, and in the azimuth oriented parallel to the incident wave, respectively. Based on the synthetic results, we discuss methods for identifying the azimuthal direction of the reflectors in observed data obtained by the BARS surveys.