Modeling of the point-source reflection response of a buried interface within a layered earth, recorded at the upper surface, is of importance in Seismic Processing studies. The mathematical formulation of the problem leads to a system of two parametric equations, one for the source-receiver separation (offset), x = x(p), at the surface and one for the traveltime, t = t(p), along the source-receiver reflection ray.
Geophysists measure traveltime against offset, T = T(x); the
parameter p is ''eliminated''. Mathematically, this elimination
cannot be carried out in closed form, but the function T = T(x)
can be represented by a power series. The radius of convergence
of this power series as a function of the model is not known. In
this talk, I formulate and discuss this interesing problem and
provide a minimum radius of convergence. Not more than elementary
Complex Variables concepts are required to understand the talk.
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