The significance of near-surface attenuation in bedrock, as distinct from attenuation in unconsolidated soft soil sediments, has been identified. The k parameter, which characterizes the extent of this attenuation mechanism, is generally difficult to measure, particularly in regions of low and moderate seismicity. Empirical correlation of k with the near-surface shear wave velocity parameter in rock has been developed using global information obtained from limited independent studies. The influence of shaking intensity on the value of k has been found to be negligible in conditions that are consistent with the average seismicity of Australia (as also for other intraplate regions). Thus, adjustment in the value of k to account for variations in earthquake magnitude, or the intensity of ground shaking, has not been recommended for intraplate conditions. In parallel with the empirical correlations, values of k have also been obtained from calibration analyses employing stochastic simulations of the seismological model, along with onedimensional non-linear shear wave analyses of the rock layers. Good agreement in the values of k obtained from the different approaches has been demonstrated. The correlation of k with the near-surface shear wave velocity of rock, as recommended in this paper, has thereby been reaffirmed.