77 3. Seismic tomography 3.2.4 Conclusions A good agreement was obtained between the S-wave image and the S-wave sonic log, furthermore the enhanced S-wave reflection image revealed high vertical resolution, approximately 5 m, and allowed imaging of the region between two boreholes, nearly 400 m away from the borehole. This field experiment also demonstrated that the conventional borehole seismic receiver tools and the low-energy sources are well suited to obtain high-resolution lithological structure delineation. 3.3 Diffraction tomography example: Borehole field data Exploiting amplitude information in addition to arrival times, the diffraction tomography schemes are the most suitable to interpret the propagation of recorded seismic data through complex velocity structures. Diffraction tomography algorithms are available: • in the spatial domain and based on the Born approximation, most suited for the primary reflected or diffracted part of the wave field; • in the wavenumber domain and based on the Rytov approximation, most suited for the transmitted wave field. This section shows: • how to obtain elastic depth images (P and S-wave velocities and density) from P-P or S-S and P-S or S-P reflected and diffracted waves; • how to evaluate the elastic image confidence. We adopted the diffraction tomography algorithm developed by Beydoun and Mendes (1989) for the following depth imaging examples. This imaging technique, based on the Born approximation, uses a one-step conditioned gradient technique for optimization and is equivalent to an elastic pre-stack migration. The procedure requires the following input data: • gridded model defined for 3 elastic parameters (P and S-wave velocities and density), close to the actual medium; • elastic ray-Born approximation; • multi-component field data, with scattered waves (diffracted and reflected body waves). And the provided output data are: • quantitative elastic depth images.
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