COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*
COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*
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DOI：
10.1111/j.1365-2478.1985.tb00422.x
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发表时间：
1985-02
影响因子：
2.6
通讯作者：
B. Ursin;B. Arntsen
中科院分区：
文献类型：
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作者：
B. Ursin;B. Arntsen
B乌尔辛和ARNTSEN，B. 1985，包括几何扩散和吸收的零炮检距垂直地震剖面计算，地球物理勘探33，72 -96。合成垂直地震剖面（VSP）为VSP数据解释提供了一种有用的工具，使解释人员能够分析地震波在不同地层中的传播。零偏移距VSP建模程序也可以用作反演程序的一部分，用于估计地下分层模型中的参数。计算合成VSP的方法大多是基于水平层状弹性或滞弹性介质中的平面波。为了将这些合成VSP与真实的数据进行比较，常用的方法是用一次反射的球面扩展因子来缩放数据。在大多数情况下，这将导致多次反射的人为增强。本文将射线级数法应用于线性粘弹性介质的运动方程，对时间变量作了傅立叶变换。这导致了一个复杂的程函方程，一般来说，似乎很难解决。对于水平层状粘弹性介质中的垂直行波，很容易找到解是复传播速度的倒数的沿着射线的积分。由于点源引起的球面扩展也是复的，并且它等于复传播速度沿射线的沿着积分。合成数据的例子说明了弹性和粘弹性层状介质中的球面波，柱面波和平面波之间的差异。
URSIN, B. and ARNTSEN, B. 1985, Computation of Zero-Offset Vertical Seismic Profiles including Geometrical Spreading and Absorption, Geophysical Prospecting 33,72-96. Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero-offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface. Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections. We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity. Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media.