Shear velocity and density contrast across the inner core boundary are essential for stud- ying deep earth dynamics, geodynamo and geomagnetic evolution. In previous studies, amplitude ratio of PKiKP/PcP at short distances and PKiKP/P at larger distances are used to constrain the shear veloc- ity and density contrast, and shear velocity in the top inner core is found to be substantially smaller than the PREM prediction. Here we present a large dataset of PKiKP/P amplitude ratio measured on 420 seismic records at ILAR array in Alaska for the distance range of 800-90~, where the amplitude ra- tio is sensitive to shear velocity and density contrast. At high frequency （up to 6 Hz）, mantle attenuation is found to have substantial effects on PKiKP/P. After the attenuation effects are taken into account, we find that the density contrast is about 0.2-1.0 g/cm3, and shear velocity of inner core is 3.2-4.0 km/s, close to the PREM （Preliminary Reference Earth Model） prediction （0.6 g/cm3 and 3.5 kin/s, respec- tively）. The relatively high shear velocity in inner core does not require large quantities of defects or melts as proposed in previous studies.
The method of extracting Green＇s function between stations from cross correlation has proven to be effective theoretically and experimentally. It has been widely applied to surface wave tomography of the crust and upmost mantle. However, there are still controversies about why this method works. Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space, and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green＇s function. His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green＇s function. However, his derivation ignores influence from the two stationary points at infinities, therefore it may fail when attenuation is absent. In order to obtain accurate noise-correlation function due to scatters over the whole space, we compute the total contribution with numerical integration in polar coordinates. Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function, in both amplitude and phase, when the frequency is low with reasonable quality factor Q. Our results argue that the dis- tance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method, and only the station pairs whose distances are above several （〉5） wavelengths can be used.
