SEISMIC VIBRATOR MODELLING1
SEISMIC VIBRATOR MODELLING1
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DOI：
10.1111/j.1365-2478.1988.tb02149.x
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发表时间：
1988
影响因子：
2.6
通讯作者：
G. J. M. Baeten;Jacob T. Fokkema;Anton Ziolkowski
中科院分区：
文献类型：
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作者：
G. J. M. Baeten;Jacob T. Fokkema;Anton Ziolkowski
研究了均匀、各向同性、理想弹性半空间中的波场，以及由介质表面的牵引力分布所激发的波场。发射波场是表面引力和空间脉冲响应的空间卷积。导出了介质远场波场的性质，指出远场质点速度实质上等于积分面力的时间导数的加权和，即“地面力”分量的加权和。该理论适用于任意几何形状和任意方位的表面引力，并且与介质表面的边界条件无关。表面引力与由质量分布和施加在其上的任意力分布组成的源有关。引入了一个边界条件，该边界条件考虑了质量载荷和施加在其上的力，但忽略了质量内的振动。边界条件来源于表面质量载荷的运动方程。将该理论应用于可控震源结构，采用P波振子模型，在底板上施加均布力，并假定没有水平表面牵引力分量。研究了单个可控震源和一组可控震源底板正下方的位移和应力分布。采用三种不同的边界条件：(1)假设均布压力，(2)均布位移，(3)用底板运动方程作为边界条件。对不同弹性介质和不同工作频率的板的应力和位移分布的计算表明，只有混合边界条件得到的结果与现场测量结果一致。利用合成数据比较了三种不同相位反馈信号的精度。基板速度相反馈导致对远场子波的确定有很大偏差；反作用质量加速度相反馈看起来很稳定，但忽略了微分地滤波；基板和反作用质量加速度加权和的相反馈随着频率的增加而变得不稳定。这种不稳定性可以通过对整个底板进行测量来克服。该模型可推广到有耗层状土体中。
The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half-space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far-field of the medium are derived and it is shown that the far-field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium. The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load. The theory is applied to the Vibroseis configuration, using a P-wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field. The accuracy of three different phase-feedback signals is compared using synthetic data. Baseplate velocity phase-feedback leads to huge deviations in the determination of the far-field wavelet; reaction mass acceleration phase-feedback looks stable but neglects the differentiating earth filter; and phase-feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate. The model can be extended to a lossy layered earth.