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本文研究了多层介质中地震分界面的数学解析表示法.其目的是为将多层介质中透射波和反射波的运动学正演理论应用于生产实践作一基础工作,以便在地震勘探的进一步实践中,能够获得较精确的正演地震图象和实现地震资料反演过程的人机联作,从而获得较好近似的反演地震结果.为此,我们具体地研究了双三次Coons曲面逼近地震分界面的问题,并将之应用于HQ地区碳酸盐岩三维地质结构.理论证明,无论地震分界面的埋藏深度如何,双三次Coons曲面可以等精度地逼近它们.而实际计算表明,在50×50m~2的采样网格上,由Coons曲面公式计算出的插值与原始采样数据的绝对误差一般小于采样读数误差,在倾角小于50°时,其值一般小于5m.由Coons曲面公式计算出的网格中点插值绘制的构造图和网状透视图,与由对应的原始采样数据绘制的构造图和网状透视图几乎完全相同.于是,我们得到以下结论:双三次Coons曲面可以相当好地逼近三维地质结构所具有的诸地震分界面.
In this paper, the mathematical analytic representation of the seismic interface in multi-layered media is studied.The purpose of this paper is to make a basic work for applying the theory of forward kinematics of the transmitted wave and the reflected wave in multi-layered media to production practice, In further practice, the more accurate forward seismic images can be obtained and the human-computer interaction of seismic data inversion process can be obtained, so as to get a better approximation of the inversion results.For this purpose, we have studied the Bi-Cubic Coons surface Approaching the interface of the earthquake and applying it to the 3D geological structure of carbonate rocks in HQ.It has been proved theoretically that bicubic Coons surfaces can approach them with equal accuracy regardless of the buried depth of the seismic interface.According to the actual calculations, The absolute error between the interpolated data and the original sample data calculated by the Coons surface formula is generally less than the sample read error on a sampling grid of 50 × 50m 2 and less than 5m when the dip angle is less than 50 °. The calculated construction and mesh perspectives interpolated at the midpoint of the grid are almost identical to the construction and reticular perspectives drawn from the corresponding raw sample data.Thus, We get the following conclusions: bicubic Coons surface can be quite good approximation of three-dimensional geological structure has various seismic interface.