A published method for the calculation of 1D synthetic seismograms with constant-Q attenuation is described and extended to the case of a VSP with a buried source. Based on layer matrices (or propagator matrices) the method is very accurate for a broad frequency range from low to high and efficiently models fine layering. Each layer has unique velocity, density, and Q and can be of any thickness. Receivers can be placed at any depth and upgoing and downgoing fields are computed separately. Extensions that allow internal multiples, surface related multiples, and attenuation to be included or not, are described. The method runs rapidly (a minute or less) in native Matlab code even with thousands of layers. This is suitable to study the effect of internal multiples and attenuation on a synthetic seismogram or VSP. The method also has the ability to create both pressure and displacement responses making it suitable to studying both geophone and hydrophone recordings. Examples from a simple conceptual model and from well logs are shown.
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