弹性介质中球面纵波反射系数研究

Spherical P-wave reflection coefficient in elastic media

实际点震源激发产生球面波前,球面反射波数据可以提供远偏移距下频变的振幅和相位信息,因此,获取准确的球面波反射系数是三维波场正演和叠前频变反演的基础.针对两层弹性介质模型,分别利用有限差分法和数值积分法实现了柱坐标系下高精度球面反射波模拟,并证明了弹性介质中有限差分解和数值积分解的一致性.在此基础上,基于简洁高效的数值积分公式,推导并计算单频球面纵波反射系数,分析了频率和界面深度等参数对权函数和反射系数的影响.考虑到地震数据的有限带宽,进一步提出利用频域加权叠加法和时域希尔伯特变换法获取带限球面纵波反射系数,并发现两种方法具有很好的一致性.单频球面纵波反射系数和带限球面纵波反射系数的准确计算为单偏移距下的频变反演和远偏移距地震资料的充分利用奠定了理论基础.

The spherical wavefront is generated by actual seismic point source,and spherical reflected wave data can provide the amplitude and phase at long offsets,therefore,obtaining accurate spherical wave reflection coefficient is the basis of 3D wavefield forward modeling and prestack frequency-dependent inversion.In this paper,with the two-layer elastic medium model,the finite difference method and numerical integration method are used to simulate the displacement of spherical reflection wave in cylindrical coordinates,and the consistency of finite difference and numerical integration is verified.Based on the simple and efficient numerical integration formula,we calculate the spherical P-wave reflection coefficient of single-frequency and analyze the influence of frequency and depth parameters on the weight function and reflection coefficient.Finally,considering the limited bandwidth of seismic data,the weighted superposition method in frequency domain and the Hilbert transform method in time domain are proposed to obtain the band-limited spherical P-wave reflection coefficient,and the equivalence of the two methods is also verified.The accurate calculation of single-frequency and band-limited spherical P-wave reflection coefficients lays a theoretical foundation for frequency-dependent inversion with reflection wave of one single offset and the full utilization of seismic data with long offset.