Frequency-dependent inversion considering spherical wavefront curvature
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摘要:
实际地震采集中的点震源激发产生球面波场，反射界面处球面波前曲率的改变会导致反射波的振幅和相位随频率而变化，而基于高频远场近似的常规平面波勘探忽略了球面波前曲率的低频频变效应.为此，本文首先利用高精度的数值积分法和有限差分法模拟了柱坐标系下的反射波记录，揭示了球面波反射系数的低频频变特征.为解决常规叠前反演需要多个偏移距反射波的限制，进一步提出利用球面波前曲率引起的频变效应进行叠前反演的新思路.敏感度和分辨率分析证明了低频频变反演的可行性，基于模型数据和实际近地表资料的反演结果验证了频变反演方法的稳定性和有效性.实验结果表明，考虑球面波前曲率的低频频变反演方法仅需要单一偏移距的反射波即可实现密度和速度参数的估计，为叠前反演提供新的思路.
Abstract:Local sources excited in actual seismic acquisition usually generate spherical wavefield rather than plane wavefield, and the change of spherical wavefront curvature at the reflection interface generally makes the amplitude and phase of reflected wave frequency-dependent. However, conventional prestack inversion is based on plane-wave approximation hypothesis in high frequency and far field condition and thus the frequency-dependent effect is usually ignored. Therefore, by numerical integration and finite difference simulation in cylindrical coordinate, this paper demonstrates the existence of frequency-dependent characteristics for spherical wave reflection coefficients. Spherical reflection coefficient is frequency-dependent, while plane wave reflection coefficient is frequency-independent in homogeneous medium. The frequency-dependent effect is prominent under low frequency and near field conditions and becomes weaker with increasing frequency and distance. To further solve the limitation that conventional prestack inversion requires the reflected waves of multiple offset, the frequency-dependent inversion considering spherical wavefront curvature is proposed. The feasibility of frequency-dependent inversion is demonstrated by sensitivity and resolution analysis. The error of the inversion parameters based on the model data is all within 5%, and the inversion based on the near-surface data also gets more accurate parameter estimation than that of plane wave inversion, which further proves the stability and practical application potential of the proposed frequency-dependent inversion. The experiment results indicate that the proposed frequency-dependent inversion can estimate the density and velocity parameters by using the reflection coefficient of a single offset, which provides a new idea for prestack parameter inversion.
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图 1
声学介质中波的反射和透射射线示意图
Figure 1.
The ray paths of incident, reflected and transmitted waves in acoustic medium
图 3
平面波和球面波反射系数振幅(a)和相位(b)对比
Figure 3.
The amplitude (a) and phase (b) comparisons between plane wave and spherical wave
图 4
球面波反射系数振幅(a)和相位(b)的频变AVO特征
Figure 4.
The frequency-dependent amplitude (a) and phase (b) of spherical wave reflection coefficient
图 5
敏感度(a)和分辨率矩阵(b)分析
Figure 5.
The analysis of sensitivity (a) and resolution matrix (b)
图 6
多次随机反演的结果(a)和反射系数的对比(b)
Figure 6.
The analysis of sensitivity(a) and resolution matrix (b)
图 7
(a) 观测系统示意图；(b)井底处的共检波点道集
Figure 7.
(a) The geometry of the field data; (b) The common-receiver gather
图 8
(a) 多次随机反演结果；(b)反演前后的反射系数对比
Figure 8.
(a) Inversion results of multiple random realizations; (b) The comparisons of reflection coefficients
表 1
参数表
Table 1.
Parameter table
参数 上层密度
/(kg/m3)下层密度
/(kg/m3)上层速度
/(m/s)下层速度
/(m/s)界面深度
/m数值 2500 2000 2500 2000 100 
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