We derived a method to compute the differential seismogram directly in a layered elastic half-space. This method first computes a differential field caused by the velocity change in the layer and then multiplies it with the original elastic wave field. This product acts like a source, and the seismogram caused by this source term is the differential seismogram. The differential waves are propagated directly to the receiver in frequency/wavenumber domain using the generalized reflection and transmission coefficient method. In comparison with the typical finite-difference approach to compute a complete set of differential seismograms at one station in an N-layered earth model, our method not only saves about N/2 folds of computation time but also leads to a more accurate solution. Thus, it provides an efficient and direct procedure to compute the differential seismogram for a complete waveform fitting in a layered elastic earth model.

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