Scattering kernels are the kernels of certain integral operators that transform incident waves into reflected and transmitted waves. For the wave equation \(u_{xx}-u_{tt}+A(x)u_ x+B(x)u_ t=0,\) in which A and B have compact support, the authors use ideas of invariant imbedding to obtain nonlinear equations for the four scattering kernels. Here the methods of invariant imbedding require the determination of the effect of perturbing the supports of A and B. The rather involved analysis is described clearly. The results are illustrated by applying them to an example in which A and B are equal and constant. The relatively simple analysis is contrasted with the more complicated investigation of this example by another method.