Frequency-dependent Reflection Coefficient of Spherical Wave in Acoustic Medium

Spherical Wave Reflection Coefficient (SWRC), a more precise description of seismic wave propagating in subsurface, is the superposition of plane wave reflection coefficient (PWRC). In this paper, frequency-dependent SWRC is investigated in two semi-infinite acoustic media with a planar interface. The frequency-dependent phenomenon occurs in the case of low-frequency and near-field. In general, the lower the frequency (or the near the propagation distance), the larger the difference between SWRC and PWRC. The amplitude and phase of SWRC reposefully approach to that of PWRC at pre-critical angles and oscillate around the value of PWRC at post-critical angles. Moreover, we project the SWRC on complex plane and find an elliptical distribution at pre-critical angles. Curves fitting using different frequency band illustrates that high-frequency information is redundant and low frequency information is indispensable from the perspective of geometry, especially for the estimation of density parameter.