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在利用三点式滤波或反向消去法压制浅海、深海鸣震时,海底反射系数的估计有重要意义。过去的方法是假定无鸣震记录的自相关函数γ_(yy)(·)满足γ_(yy)=0,|j|≥τ/2。τ为垂直鸣震周期。这个条件相当苛刻。本文的方法大大减弱了这个条件,同时对地震子波和地层反射序列不加限制。以γ_(yy)(·)、γ_(xx)(·)和ξ_(?)分别表示无鸣震记录自相关函数、鸣震记录自相关函数和海底反射系数,则只要存在n,使γ_(yy)(j)=0,|j|(?)n,就有由上两方程即可给出海底反射系数的估计值。但由于利用二级鸣震记录求海底反射系数是解一元二次方程的问题,一般有两个不同的解,因此,即使都是实根也难确定哪个根为所求的海底反射系数。为此,我们用满足该方程的两个方程联立求解,得到满意的结果。n的确定也是较困难的,我们介绍两种方法:一种是用统计的方法;另一种是根据鸣震记录的数学模型都为ARMA模型来确定的。
The estimation of seabed reflection coefficient is of great significance in the suppression of shallow sea and deep sea by using three-point filtering or inverse elimination method. In the past, it is assumed that the autocorrelation function γ_ (yy) (·) of the unvoiced earthquake record satisfies γ_ (yy) = 0 and | j | ≧ τ / 2. τ is vertical ringing cycle. This condition is quite harsh. The method in this paper has greatly reduced this condition, and at the same time, it does not limit seismic wavelet and stratigraphic reflection sequence. Γy (·), γ (xx) (·) and ξ_ (?) Represent the autocorrelation function, the autocorrelation function and the seafloor reflection coefficient of the noises, respectively, as long as there exists n such that γ_ ( y) (j) = 0, | j | (?) n, there is the estimation of the sea bottom reflection coefficient given by the above two equations. However, since the seabed reflection coefficient is a solution to the quadratic equation with two levels of sonic recording, there are generally two different solutions. Therefore, it is difficult to determine which root is the desired submarine reflection coefficient even though they are both real roots. To this end, we solve the equations by using the two equations solved together, get satisfactory results. n is also more difficult to determine, we introduce two methods: one is to use statistical methods; the other is based on the mathematical model of song recording are determined for the ARMA model.