Following a homogeneous formulation, a new finite-difference (FD) representation of the SH-wave field at first-order lateral discontinuities is introduced. The new scheme, in contrast to previous schemes, represents a consistent second-order approximation of the truncation error. By means of a new, generalized sufficient criterion of stability, the time increment can always be chosen so that the numerical errors of the new scheme remain bounded. Consequently, this FD approximation necessarily converges to the exact solution of the corresponding initial value problem. A numerical example of a Ricker wavelet, vertically incident on a basin structure, illustrates that the new FD scheme converges faster than previous schemes.

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