A Stable Single Station Estimator of Magnitude

Stable single-station estimates of magnitude have been made using the 1-Hz Lg coda envelope of regionally recorded nuclear explosions from the Nevada Test Site (NTS). After empirical relations describing the Lg coda envelope were found for each NTS-station path, single station magnitudes based on the Lg coda envelope were made with precision in the range of 0.03 to 0.04 magnitude units, whereas magnitudes based on third peak Lg amplitude, rms Lg amplitude, and Pn amplitude had scatter on the order of 0.15 to 0.2 magnitude units, generally five times larger than the coda scatter. Despite the high station correlations, the magnitude-yield residuals for events above the water table using the network average mb(LgCoda) were only marginally better than the other magnitude estimates, roughly 10% smaller. Magnitude-yield residual for events above the water table between mb(LgCoda) and mb(Lg) are strongly correlated suggesting that the source region properties, such as gas porosity, affect both magnitudes. Using only a single station, the standard deviation for magnitude-yield residuals using mb(LgCoda) were roughly 25% smaller than those derived from mb(Lg) or mb(Pn). These results show that the method is ideally suited to monitoring efforts in sparsely instrumented regions where little is known about the lateral variations of medium properties. INTRODUCTION The stable decay of the local S-wave coda relative to the origin time was recognized by Aki (1969) as a stable estimator of magnitude. Aki (1987) used a single borehole site near the Newport-Ing]ewood fault in Southern California and found an empirical relation linking S-wave coda amplitude and momentmagnitude for small local earthquakes. In this study we extend this approach to the l-Hz Lg coda of nuclear explosions recorded at near-regional distances on paths predominantly sampling the Basin and Range. We then compare magnitudes based on near-regional Lg coda with mb(Pn) (Vergino and Mensing, 1990) and third peak and rms mb(Lg) (Patton, 1988b), all of whom used the same data set as in this study. The study of direct Lg recorded at near-regional distances has recently gained much interest for purposes of magnitude-yield relationships (Patton, 1988b) and discrimination between nuclear explosions and earthquakes (Taylor et al., 1988; Taylor and Denny, 1991). Hansen et al. (1990) studied the rms Lg from 16 nuclear explosions form the Shagan River test site in east Kazakhstan. They found that relative rms Lg amplitudes recorded at various pairs of regional stations were very stable, in sharp contrast to Pn which were highly variable. They used a 120-sec time window approximately centered at a group velocity of 3.5 km/sec, corresponding roughly with direct Lg, and found interstation data standard deviation around 0.03 in logarithmic units. They concluded that very accurate single station estimates of magnitude could be made after proper path correction. 851 852 K. MAYEDA The high frequency S-wave coda (> 1 Hz) of locally recorded earthquakes have been shown to obey a very simple empirical relation with the property that their decay rate is common within a region, independent of source-receiver distance and recording site properties (Aki, 1969; Aki, 1980; Rautian and Khalturin, 1978; Phillips and Aki, 1986; Sato, 1988; Mayeda et al., 1991; Koyanagi et al., 1992). The fundamental separability of source, site, and path effects for local coda waves is described by the following well-established empirical relation for lapse times usually greater than twice the S-wave travel time. Ac( oJ, t ) = So( w ) R s ( w ) C ( oJ, t ) (1) S o is the coda source term, R s is the station site term, and C is a lapse time-dependent common path term given by t ~ exp(-bt). The constants 7 and b describe the shape of the coda amplitude as a function of lapse time at frequency ~. Aki and Chouet (1975) used a stochastic approach to model the high-frequency coda envelope as single scattered waves from randomly distributed heterogeneities in the lithosphere. The form of their single-scattering model is nearly identical to the empirical relation shown in equation 1, however, in their case ~/ and b are the geometrical spreading and frequency-dependent coda attenuation coefficients, respectively. At lapse times sufficiently greater than the arrival of the direct S-wave and at depths below which the site-effect if negligible, the coda wave energy is observed to be homogeneously distributed in the crust (Aki, 1969; Fig. 3 of Mayeda et al. 1992). The generation of the coda is due to scattering but its decay appears to be largely controlled by anelastic losses (Hoshiba et al., 1991; Fehler et al., 1992; Mayeda et al., 1992; Frankel and Wennerberg, 1987; Sato, 1977). Near-site amplification and attenuation control the absolute amplitude, but the decay rate of the coda depends only on the average medium properties of the crust sampled by the coda waves. These properties of coda waves offer an alternative approach for studying the source and site effects on high-frequency seismic waves, different from classical approaches which consider the direct phases such as P and S which are affected by particular travel paths and are sensitive to directional source radiation effects. Because local coda waves are likely backscattered S waves from heterogeneities distributed in a volume surrounding the source and receiver (Tsujiura, 1978; Aki, 1980), the effect of source radiation is averaged over all directions as is the effect of path heterogeneity. Studies using spectral ratios of the local S wave coda use large lapse times relative to the S-wave travel time and therefore scattered waves sample a large region surrounding source and receiver (Mayeda et al., 1991; Koyanagi et al., 1992). This explains why local S wave coda recordings decay at the same rate for all source-station pairs (i.e., the path effect, C, is the same for all source-station pairs within a region). Unlike local recordings, at regional distances the Lg phase dominates the record and is followed by a long slowly decaying coda (Singh and Herrmann, 1983; Xie and Nuttli, 1988). Xie and Mitchell (1990) considered the highfrequency (0.5 to 2.0 Hz) Lg coda as scattered surface waves and observed distinct regional differences in the Lg coda decay rate in Africa. Lg coda waves that sampled the shield region of North Africa decayed much slower than coda waves which predominantly sampled the East African rift zone. For Lg coda A STABLE SINGLE STATION ESTIMATOR OF MAGNITUDE 853 measurements , the source-station distance is large and the region sampled by scattered Lg is more elliptical than that sampled in local coda studies (Xie and Mitchell, 1990). In the case of Africa, source-station pairs were widely separated resulting in Lg coda sampling distinctly different tectonic regions. DATA The data consist of roughly 140 nuclear explosions recorded at four digital, broadband, three-component stations operated by Lawrence Livermore National Laboratory all sampled at a rate of 40 samples /sec . Roughly 75% of the events are above the water table. Figure 1 shows the Basin and Range region and the four broadband stations that range in distance from NTS between 240 and 400 kin. Figure 2 shows representat ive three-component records for the HARZER explosion ( M o = 5.96 × 1022 dyne-cm, Patton, 1988a) recorded at station Mina, Nevada (MNV). Notice that for all three components, the Lg coda is roughly the same level, in contrast to the direct phases such as P n and Lg . The lack of dependence of Lg coda amplitude on component is consistent with previous observations which report tha t local S-wave coda are depolarized and incoherent (Fehler et al., 1992, Menke et al., 1990). All records were corrected for ins t rument response and then bandpass filtered between 0.75 and 1.25 Hz. The frequency band was chosen because of excellent