The Distribution of Multiple Shot Noise Process and Its Integral

In this paper, we study multiple shot noise process and its integral. We analyse these two processes systematically for their theoretical distributions, based on the piecewise deterministic Markov process theory developed by Davis [1] and the martingale methodology used by Dassios and Jang [2]. The analytic expressions of the Laplace transforms of these two processes are presented. We also obtain the multivariate probability generating function for the number of jumps, for which we use a multivariate Cox process. To derive these, we assume that the Cox processes jumps, intensity jumps and primary event jumps are independent of each other. Using the Laplace transform of the integral of multiple shot noise process, we obtain the tail of multivariate distributions of the first jump times of the Cox processes, i.e. the multivariate survival functions. Their numerical calculations and other relevant joint distributions’ numerical values are also presented.

地震数据处理中的CT积分变换理论和实践

以二维傅里叶变换为基础,从新的角度把 CT 技术引入到地震数据处理中,提出了一套新的 CT 积分变换式,分析了截断效应,给出了提高方向分辨率的加权正变换。CT 积分变换的主要特点是:CT 积分正变换是按波的到达方向对波场进行分解,将时—空域信号变换到时间—慢度域,时间—慢度域中的强波形对应于时—空域中的同相轴,它的位置指出了波的到达方向和时间;CT积分反变换是平面波的合成,把时间—慢度域中的数据反变换到原来的时—空域中去。文中还讨论了利用 CT 积分变换压制多次波、压制随机干扰和规则干扰、进行波场分离和道间内插的方法。将这些方法应用于实际地震资料的数据处理,取得了良好的地质效果。