This report reviews the physical bases and the observations of strong earthquake ground motion for quantitative extrapolation of pseudo relative velocity spectral amplitudes to long (T > 10 sec) and to short (Y < .04 sec) periods. This will serve as a basis for subsequent use of these scaling equations in hazard calculations in the same broad frequency band. At present, empirical scaling equations of response spectrum amplitudes are limited to periods between .04 and several seconds. The design of long structures and of structures on multiple distant supports requires knowledge and specification of design ground motions well beyond this frequency range. This report addresses the first approximate extrapolation of the available response spectrum amplitudes, and deals with formulation of the physical basis for such extrapolation.