The Mantle Magnitude Mm and the Slowness Parameter H: Five Years of Real-Time Use in the Context of Tsunami Warning

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 performance 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 Harvard Centroid Moment Tensor (CMT) catalog, and also by the period at which spectral 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 earthquakes.” 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 continental 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 realtime 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), respectively. 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 assessment 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 December 2004 provided an opportunity to extend the concepts of Mm and H to a range of magnitudes unexplored for the past 40 years. Preliminary results on the Sumatra earthquake are given in the Appendix. The Magnitude Mm The mantle magnitude Mm was initially developed by Okal and Talandier (1989) and implemented at the Papeete, Tahiti, tsunami center (Centre Polynésien de Prévention des Tsunamis, CPPT), where it has been used routinely for more than a decade in the context of tsunami warning. It was introduced to alleviate the saturation of the classical surfacewave magnitude Ms at values of 8.3, which is caused by destructive interference effects when the source duration of large earthquakes becomes significantly longer than the fixed period (20 sec) at which Ms is measured (Geller, 1976). In particular, Ms is of little use in the context of tsunami warning, because it fails to separate merely large events with little or no transoceanic tsunami risk (approximately M0 10 dyne cm) from those truly gigantic ones, such as the 780 S. A. Weinstein and E. A. Okal 1960 Chilean, 1964 Alaskan, and now 2004 Sumatran earthquakes (M0 10 29 dyne cm), capable of exporting death and destruction to distant shores. Consequently, the main idea behind Mm was to make measurements at variable periods, which for large events means in the window of mantle surface waves, anywhere between 50 and 300 sec, while keeping the concept of magnitude, that is, a “quick-and-dirty” real-time one-station measurement ignoring source details such as focal mechanism and exact focal depth. In practice, the measurement is made on each spectral component of the Rayleigh wave, and Mm is computed as M log X(x) C C 0.90 (1) m 10 S D where X(x) is the spectral amplitude of ground motion in lm*s, CD is a distance correction compensating for geometrical spreading on the spherical Earth and anelastic attenuation during propagation, and CS is a frequencydependent source correction, compensating for the variable excitation of Rayleigh waves of different periods by a seismic dislocation of unit moment. In keeping with the philosophy of a magnitude scale, CS is computed for an average focal mechanism and source depth. The exact expressions of CS and CD are justified theoretically (as well as the locking constant C0 0.90 in equation 1) in Okal and Talandier (1989); Mm is then expected to represent the seismic moment M0 of the earthquake through: M log M 20 (2) m 10 0 where M0 is in dyne cm. The performance of Mm was tested initially on a dataset of 256 records by Okal and Talandier (1989). Defining a logarithmic residual, r M log M 20 , (3) m 10 0 with respect to the published value M0, they obtained an average value and a standard deviation r of 0.14 and 0.25 r̄ logarithmic units, respectively. A few years later, and after the implementation of an automatic procedure at CPPT, Hyvernaud et al. (1993) obtained and r 0.22 for r̄ 0.07 a dataset of 474 measurements. A series of later studies extended the concept to Love waves (Okal and Talandier, 1990), nonshallow events (Okal, 1990), and historical earthquakes (Okal, 1992a,b) and verified its performance for truly gigantic earthquakes (Okal and Talandier, 1991) and in the regional field (Talandier and Okal, 1992; Schindelé et al., 1995).