Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia

Abstract

Frequency‐dependent regional wave attenuation is estimated for continental paths to the NORESS array in Norway. Regional Lg and Pn spectra from 186 events at ranges between 200 and 1400 km and local magnitudes between 1.1 and 4.8 are inverted for both seismic moment and apparent attenuation. The Lg spectra were inverted between 1 and 7 Hz, and the Pn spectra were inverted between 1 and 15 Hz. The method uses both the spectral and spatial decay of observed signal amplitudes to separate source and path contributions. The assumptions include the geometric spreading rate and the source spectrum to be uniquely defined by its long‐period level. Most events considered have local magnitudes less than 3.0, so the source corner frequencies are near or beyond the upper limit of the inverted bandwidth. The Q results, particularly for Lg, are therefore not very sensitive to the details of our source parameterization. The inversion parameters are source moment (for each event), a constant relating corner frequency and moment for the entire data set, and two parameters describing a power law frequency dependence of Q in the region. For fixed source and spreading assumptions the inversion defines clear trade‐offs among model parameters. These trade‐offs are resolved by adding the constraint that the separately derived source parameters for Lg and Pn are consistent. The “preferred” estimates for the apparent attenuation are QLg(f) = 560f0.26 and QPn(f) = 325f0.48. These Q values correspond to assumed geometric spreading rates of r−0.5 for Lg and r−1.3 for Pn. For fixed Lg spreading, the Pn spreading rate is constrained by requiring that the relative Lg amplitude for earthquakes and explosions of the same moment be consistent with well‐supported results from previous empirical studies. The relationship between the inverted seismic moment values and local magnitude is generally consistent with values from near‐field studies. Since magnitude does not enter the inversion, this result lends considerable support to the derived Q models. Whatever the physical interpretation of the results, they certainly provide an accurate parameterization of observed amplitude spectra in this region. This is valuable for representing wave propagation in the region, and it provides important data for assessing the event monitoring capabilities of small regional networks.

Geometric Spreading of Pn and Sn in a Spherical Earth Model

“…The 0.75-to 6-Hz P n Q values that they estimated are between 283 and 768 for Scandinavia and between 260 and 735 for eastern Kazakhstan. Although Sereno et al (1988) and Sereno (1990) assume a power-law P n geometric-spreading model with an exponent of 1:3, their P n Q estimates are more in line with the average P n Q estimates that we obtain using the new P n spreading model than with those from power-law model corrections (Table 2). A possible explanation for this observation is that the majority of their data are recorded within 1000-km epicentral distance.…”

“…Figure 7 compares the new geometric-spreading model and a power-law model with synthetic P n amplitudes. The power-law model has an exponent of 1:3 (Sereno et al, 1988). The difference between the new spreading model and synthetic P n amplitudes is almost indistinguishable.…”

“…r 0 and f 0 are included in equations (6) and (7) in order for the new model to have the same dimension as standard power-law models (e.g., Street et al, 1975;Sereno et al, 1988). The main differences between the new geometric-spreading model (equations 6 and 7) and the standard frequency-independent power-law model are the addition of the first term in the exponent and the frequency dependence of parameters n i .…”

“…Sereno et al (1988) and Sereno (1990) obtain P n Q models for Scandinavia and eastern Kazakhstan, respectively, by inverting broadband P n spectra. The 0.75-to 6-Hz P n Q values that they estimated are between 283 and 768 for Scandinavia and between 260 and 735 for eastern Kazakhstan.…”

“…In spite of these conclusions, seismologists commonly use a frequency-independent power-law model to approximate P n geometric spreading in the real Earth when analyzing observed data (e.g., Sereno et al, 1988;Zhu et al, 1991;Taylor et al, 2002). Occasionally, researchers combine P n geometric spreading and attenuation into a single distance-decay term in order to avoid the difficulty of isolating P n geometric-spreading effects (e.g., Chun et al, 1989;Tinker and Wallace, 1997).…”