Abstract

This short note presents a 1-D analytic generalized inverse for VSP transmission + reflection tomography. Its validity is restricted to evenly layered media and negligible ray bending. The significance of the result is that the reliability estimate of slowness for 1-D VSP tomography can be analyzed analytically, rather than by empirical guesswork. This can lead to the design of optimal tomography algorithms and field experiments. For example, Salo and Schuster (1989) observed empirically that reflection + transmission VSP data provided a better velocity reconstruction than do transmission VSP data alone. However, the underlying reason for this improvement was not clearly identified. This short note gives an unambiguous explanation.

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