A scattering model for seismic attenuation and its global applications

The attenuation characteristics of Indian lithosphere and its comparison with different tectonic settings in the world are determined from the observations of the Q for Lg(QLg)-, and S(QS)-waves in the 1–30 Hz frequency range. The scattering is approximated with a Gaussian distribution of spherical scatterers. To approximate single scattering, we use Daintyʹs [Geophy. Res. Lett. 8 (11) (1981) 1126] model that attenuation is given by 1/Q(ω) = 1/Qi + g(ω) v /ω, where Qi is intrinsic Q due to anelastic attenuation, v is shear wave velocity, ω is angular frequency, g = ∫n(a)σ da is the total scattering coefficient for S-to-S scattering, n(a) da is the number of scattering spheres of radius a per unit volume, and σ is the scattering cross-section for the sphere. We find that if n(a) is described by a simple two parameter (a0 and c) Gaussian of amplitude c and standard deviation and mean a0, the attenuation data for different regions of the world are well approximated over the frequency band of seismic observations. Our major findings are: (1) the maximum effect of scattering on attenuation occurs at 0.84 Hz or a wavelength of 4.16 km; (2) the values of g are frequency dependent. Values of g are of the order of 10−3 km−1 at 1–30 Hz, varying from 0.0031 to 0.01 and 0.001 to 0.0083 km−1 for tectonically active and stable regions, respectively; (3) regions of active tectonics and seismicity generally have lower Qi values (1000) than that in stable regions (2000); and (4) regions of high Qi value exhibit low intensity of scattering.