DIFFRACTION RESPONSE FOR NONZERO SEPARATION OF SOURCE AND RECEIVER
DIFFRACTION RESPONSE FOR NONZERO SEPARATION OF SOURCE AND RECEIVER
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DOI：
10.1190/1.1440781
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发表时间：
1977-10
期刊：
影响因子：
3.3
通讯作者：
J. R. Berryhill
中科院分区：
文献类型：
--
作者：
J. R. Berryhill
现有的一种基于基尔霍夫延迟势方法的理论，对地下反射器的几何形状和衍射图样的振幅特性作出了独特的预测。将这一理论应用于地震叠加剖面，将为地球物理学家提供有用的信息，用于地下解释。然而，这种应用的一个可能的障碍是，最初提出的理论只适用于零源接收器分离记录的数据，而叠加剖面是通过在大范围的短检波器距离上平均记录的数据产生的。为了正确地处理实际记录的地震资料，最好有一种适用于震源和接收机非零分离的衍射振幅理论。本文通过对Kirchhoff方法的适当扩展，发展了这样一个理论。通过在特殊坐标系中表示问题，声波方程的Kirchhoff积分解被简化为源小波的时域卷积，其中一个算子被认为是所考虑的地下几何形状的脉冲响应。脉冲响应明确地计算了无限反射平面和衍射边缘垂直和平行于源-接收轴。通过对相关公式的数值计算，将非零分离理论与零分离理论进行了比较，证明了非零分离理论是前者的特例，而后者恰恰是前者的特例。更重要的是，得出了意想不到的结论，即在非零源-接收器分离时的衍射振幅几乎完全由源-接收器中点的位置控制。由于叠加的数据都有一个共同的短震检波器中点，因此叠加轨迹上的衍射振幅应该很好地近似于零分离理论。从而为零分离理论应用于叠置地震资料提供了理论支持。
An existing theory based on the Kirchhoff retarded potential method makes distinctive predictions relating the amplitude characteristics of diffraction patterns to the geometry of subsurface reflectors. The application of this theory to seismic stacked sections would offer the geophysicist useful information to be included in subsurface interpretations. However, a possible barrier to such applications arises from the fact that the theory as originally put forth applies only to data recorded with zero source-receiver separation, whereas stacked sections are produced by averaging data recorded over a wide range of shot-geophone distances.To deal properly with seismic data as actually recorded, it is desirable to have a theory of diffraction amplitudes formulated for nonzero separation of source and receiver. This paper develops such a theory through an appropriate extension of the Kirchhoff approach. By expressing the problem in a special coordinate system, the Kirchhoff integral solution of the acoustic wave equation is reduced to a time-domain convolution of the source wavelet with an operator recognized as the impulse response of the subsurface geometry under consideration. Impulse responses are computed explicitly for an infinite reflecting plane and for diffracting edges perpendicular and parallel to the source-receiver axis.The nonzero-separation theory is compared to the zero-separation theory through numerical evaluation of the relevant formulas, and the latter is shown to be a special case of the former, as it should be. More importantly, the unexpected conclusion emerges that diffraction amplitudes at nonzero source-receiver separation are controlled almost exclusively by the location of the source-receiver midpoint. Since the data summed together in stacking all share a common shot-geophone midpoint, the diffraction amplitudes on the stacked trace should behave in good approximation to the zero-separation theory. Theoretical support is thus obtained for applying the zero-separation theory to stacked seismic data.