Solutions of P-SV and SV-P waves in single-well imaging through reciprocity relations

Abstract

Single-well imaging (SWI) is a borehole measurement technique for detecting geological structures outside a borehole by using arrays of receivers to record the waves reflected from these structures. The asymptotic solutions of P-P, SV-SV, and SH-SH waves in SWI have been obtained, but the P-SV and SV-P waves were ignored in previous studies. It is necessary to know when these conversion waves are large and to estimate these waves when they are not ignorable. The analytical solutions of P-SV and SV-P waves are first derived using reciprocity relations between virtual concentrated forces and acoustic sources. The analytical results agree well with finite-difference solutions for both monopole and dipole sources. We find that for a given source-receiver offset, the detected converted waves first increase and then decreases with increasing the source-reflector distance. The relative amplitudes of converted waves to the reflected waves are larger than 20% and cannot be ignored when the ratio of source-reflector distance to source-receiver offset is smaller than 4. However, when source-reflector distance is ten or more times the source-receiver offset and the dip angle of the reflector is smaller than 10 degrees, the amplitudes of converted waves are smaller than 5% of reflected waves. Furthermore, the relative amplitudes of converted waves increase with the dip angle of the reflector. The analytical solutions of converted waves are useful for simulating SWI wavefields and checking the inversion results in field logging.

Unsupervised deep domain adaptation framework in remote acoustic time parametric imaging

“…In contrast, the piezoelectric pulse-echo rotating transducer, which scans strata and obtains structural information, is demonstrated as a succinct and low-cost scheme. As illustrated in Figure 1, the instrument with ceramic electroacoustic transducer can scan the geological structure at the specified depth, where the motor and the rotator control the scanning speed and the pixel accuracy of the imaging [9]. The estimation over the times and amplitudes of the reflected waveforms reflects the stratigraphic information [10].…”