Evaluation of the effective cross-section of scattering in the lithosphere

The theory of scattering affirms that, when a wave enters a scattering volume, secondary waves develop having propagation directions which form various angles with the ray of the primary wave. The energy of the scattered wave depends on the effective cross-section of scattering from a unit volume in a unit solid angle. The seismic phase P′·P′ is produced mainly by the scattering of P′₁ in the uppermost layer of the Earth. If the epicentral distances of the observation point of P′·P′ vary between 30 and 70°, the corresponding angles of scattering of P′ vary between 22° and a few degrees. This relationship enables us to evaluate the effective cross-section of scattering as a function of the angle of scattering. The latest world-average estimates of this quantity, which are based on a large number of seismic data, are presented. The values obtained are in good agreement with those calculated for the Gaussian auto-correlation function of the fluctuating part of the refractive index if the correlation interval is close to 13 km. The lower limit of the fractional r.m.s. of velocity variation in the lithosphere is close to 1.6%.