Slowness image reconstruction

According to ray theory, the traveltime T(R,S) between any source S and receiver R is related to the slowness distribution ŋ at any point X by the integral: T(R,S) = ∫ г(ŋ) ŋ(X)dl, where г(ŋ) is the ray path which yields the minimum traveltime and dl is the arc length. Because the ray path г(ŋ) depends upon the actual slowness ŋ, the inverse problem consisting of recovering the slowness distribution from the traveltime T(R,S) is non linear. A common approach is to linearize the traveltime with respect to a known slowness and iteratively update the current estimate. This requires ray tracing to compute the traveltime misfit.