Accurate determination of seismic threshold requires consideration of the seismic recurrence rates, mean and variance of signals and noise, and sometimes the relationship between different magnitude scales. A three-level conceptual framework for magnitude is postulated: true, operational, and observed magnitudes. Empirical thresholds based on observed magnitudes are biased relative to the true or operational thresholds. Determination of this bias when only single stations are involved is analytically tractable, but bias for a network of stations is treated by a Monte Carlo simulation approach. This bias is examined for the cases of direct, incremental, and cumulative threshold determinations. The simulation technique demonstrates that the effects on threshold of correlated signals and noise over a network is slight but that the effects of the feedback between LR and P threshold may be significant. Both analytical and simulation results show that any casual approach to determining threshold magnitude may produce an error of several tenths of a magnitude unit. A comparison of simulated detection results is made with real data from LASA on the Kuril-Kamchatka region, and good agreement is obtained between predictions and observations.

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