Abstract

It is known that in the presence of a waveguide the one-dimensional kinematic inverse problem does not have a unique solution, i.e., the velocity-depth function is not uniquely determined by a travel time curve. Let $u(y)$ be one of the possible solutions. How other solutions can be found? For clarity of presentation we assume that $u(y)$ has only one waveguide (the results can be automatically extended to the case of several waveguides). A new constructive technique is suggested to find a large part of the set of all velocity-depth functions $u^{*}(y)$ with exactly the same travel time curve $\Gamma $ as that of $u(y)$.