Defining a p-Δ curve in terms of the Δ of the turning point of a ray rather than the point of emergence at the surface allows a p-Δ curve to be produced for a low-velocity zone. This curve can be explicitly inverted by performing three Weichert-Herglotz integrals, two of which are for the low-velocity zone contribution.
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George A. McMechan (1979) studied this question.