Seismic measurements at different scales have different objectives and may result different observations. However, the measured property still pertains to a unique medium. Thus in theory it should be possible to relate differently scaled measurements to one another. In the past, there seems to have been a lack of success in this regard. Typically, NMO velocities from surface seismics do not tie well with sonic logs. This has been a long recognized problem. For example, check shots are used to stretch the seismic log to a surface seismic scale. I assume that velocity varies not to drastically over the given frequency interval, such that velocity dispersion will not be accounted for. However, equivalent medium schemes suggest ways how to relate measurements carried out at different scales. Additionally one knows exactly which quantities are preserved in the rescaling process.
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