Modern multi-pole acoustic logging tools require addition and subtraction of signals from different combinations of receivers. To enable the correct subtraction and addition of acquired signals it is essential that the receivers are well balanced. However, correctly balanced receivers may change their properties as the acoustic tool is lowered into a borehole and experiences vastly different pressures and temperatures. By using the properties of the Stoneley wave, it is possible to create a balancing scheme such that subtraction and addition of waveform data can be performed as if the receivers were perfectly balanced.
Modern multi-pole acoustic logging tools have the ability to generate and detect different acoustic wave modes propagating along the borehole and in the formation. A requirement to accomplish this is the summation and subtraction of the acoustic signals detected at receivers distributed around the circumference of the tool. For example, in the WaveSonic? tool, there are four receivers located at the four orthogonal positions around the circumference of the tool, at 8 different distances from the source position, resulting in a receiver array consisting of 32 receivers. A schematic layout of the tool is shown in Figure 1.
A monopole (or compressional or P) wave measurement is performed by firing the monopole wave transmitter, and summing the received waveforms at the four receiver positions around the tool (A, B, C, D). A dipole (or flexural) wave measurement is performed by firing the dipole (or displacement) source in one of the two orthogonal directions (X or Y), and subtracting the observed waveforms from the receivers on opposite side of the tool (e.g. A-C, B-D). A crossed dipole measurement is performed by firing both X and Y dipole sources in succession, and subtracting the observed waveforms. Higher order modes such as the quadrupole mode can be generated in a similar manner.
Figure 1. Schematic layout of a wireline acoustic tool
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In this paper we describe a procedure that can correct for the receiver imbalance of the measured waveforms. In order to better understand the effect of receiver imbalance on full waveform acoustic logging data, we simulated a number of examples of receiver miss-match using the algorithm of Byun and ToksÃ¶z (2003).
Figure 2, 3, 4, and 5 show the slowness-time semblances and the high-resolution dispersion estimates (Araya et al., 2003) for synthetic monopole and dipole data in a "slow" formation.