A long-spaced sonic survey may be thought of as a special case of ray theoretical tomographic imaging. With such an approach estimates of borehole properties at a resolution of 6 inches (0.15 m) have been obtained by inversion compared with a resolution of 2 ft (0.6 m) from standard borehole-compensated techniques (BHC). The inversion scheme employs the conjugate gradient technique which is fast and efficient. Unlike BHC, the method compensates for variable refraction angles and provides estimates of errors in the measurements. Results from synthetic data show that these factors greatly improve the imaging of the properties of a finely layered medium, though amplitude decay and coupling are less well defined than velocity and mud traveltime. Results from real data confirm the superior quality of logs from inversion. Furthermore, they indicate that measured amplitudes can be dominated by errors that cause deterioration of BHC estimates of amplitude decay and coupling.

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