We study a database of more than 119,000 measurements of the mantle magnitude Mm introduced by Okal and Talandier (1989), obtained since 1999 as part of the operational procedures at the Pacific Tsunami Warning Center. The perfor- mance of this method is significantly affected by the seismic instrumentation at the recording station, with the very-broadband STS-1 and KS54000 systems offering the lowest residuals between measured values of Mm and those predicted from the Har- vard Centroid Moment Tensor (CMT) catalog, and also by the period at which spec- tral amplitudes are measured, with the best results between 70 and 250 sec. With such mild restrictions, estimates of seismic moments can be obtained in real time by retaining either the maximum value of Mm measured on each record, or its average over the various mantle frequencies, with the resulting residuals, on the order of 0.1 0.2 moment magnitude units. Mm deficiencies in the case of the two large earthquakes of Peru (2001) and Hokkaido (2003) are attributed to azimuthal bias from an excess of stations (principally in North America) in directions nodal for the focal mechanism and directivity patterns. We further study a group of more than 3000 measurements of the energy-to-moment ratio H introduced by Newman and Okal (1998), which allows the real-time identification of teleseismic sources violating scaling laws and, in particular, of so-called tsunami The use of a sliding window of analysis in the computation of H allows the separation of late earthquakes, characterized by a delayed but fast moment release, from truly slow earthquakes. Many such events are recognized, notably on major oceanic and con- tinental strike-slip faults. Introduction and Background We present detailed analyses of a large dataset resulting from implementation, as part of the operational procedures of the Pacific Tsunami Warning Center (PTWC), of the real- time calculation of the mantle magnitude Mm and of the slowness parameter H, as defined and introduced by Okal and Talandier (1989) and Newman and Okal (1998), re- spectively. During the past five years, more than 119,000 individual measurements of Mm and 3000 values of H have been computed through automated algorithms. These values contribute to the estimation of the source characteristic of distant earthquakes in the framework of the real-time as- sessment of their tsunamigenic potential. This study offers a progress report on the performance of the algorithms and, in particular, discusses the influence of instrumentation at the various reporting stations. As the final revision of this article was being prepared, the occurrence of the great Sumatra earthquake on 26 De- cember 2004 provided an opportunity to extend the concepts of Mm and H to a range of magnitudes unexplored for the