Assessment of earthquake risk and design basis ground motions for a construction site requires knowledge of frequencies and locations of carthquakes, which are likely to affect the site on the one hand and seismic signal attenuation characteristics of the site region on the other. When sites are not supported by adequate earthquake data and the assessment is made by adopting a certain degree of conservatism, it is desirable to relate the estimates of the ground motion parameters to the expected level of seismicity in the region and to estimate the uncertainties associated with the estimates. A procedure to determine bounds on a ground motion parameter for design basis of a site based on the observed maximum historical earthquake intensity has been suggested. The procedure also offers means to investigate the nature of the existing attenuations function in the light of certain constraints dictated by the procedure.