Seismograms recorded at selected points along the travel path of a multiply reflected ray can be decomposed into three wavelets that in turn can be used to construct synthetic seismograms for each of the ray turning points. The three wavelets correspond to a source term and two terms that give the impulse response of the medium. The decomposion provides a direct source function estimate if the reflection and conversion coefficients can be determined for the depth at which the source is located. Application of the process to the construction of synthetic seismograms is demonstrated.