Acoustic fields excited by an eccentric point source in a borehole: High‐order mode analyses

Abstract

In order to understand borehole waves generated by eccentric sources and behaviors of high order modes, the acoustic fields excited by centric and eccentric point-like sources in a borehole are studied in terms of multipole expansion technique. Full waveforms along the borehole generated by centric and eccentric sources at different frequencies and offsets are investigated and compared with each other. The dispersion of high-order modes such as those associated with hexapole, octapole and decapole are given. The numerical results show that the cut-off frequencies of non-symmetrical modes vary greatly with the order of corresponding modes. At low frequencies, high-order multipole sources can not effectively generate non-symmetrical modes. They generate relatively strong shear arrivals only when the center frequency is near the cut-off frequency of the modes. For eccentric sources, shear waves in full waveforms, similar to that of the centric source are rather weak when the center frequencies of the sources are far away from the cut-off frequencies of the corresponding modes. With the increase of the center frequencies and approaching to the cut-off frequencies, full waveforms excited by an eccentric point source become more complex. At the same time, shear waves, as the first arrivals, become evident. This is different from the waveform generated by a centric source. In addition, source eccentricity has an impact on amplitudes of the full waveforms.