从鸣震记录估计海底反射系数的一种新方法

A NEW TECHNIQUE FOR ESTIMATING THE SEA BOTTOM REFLECTION COEFFICIENTS FROM THE REVERBERANT RECORDS

1. 中国科学院系统研究所;2. 地质矿产部北京计算中心

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_θ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。

When using the three-points filter or the reverse elimination technique to suppress the reverberants ofshallow and deep sea,the evaluation of the sea bottom reflection coefficients has great significance. In the technique formerly used, it is to assume that the autocorrelation function of the non-reverberant recordsγ_yy(·)satisfiesryy(j) = 0, |j|≥τ/2where τ is the vertical reverberant cylcle.Obviously,it's a harsh term hardly to satisfy. In the paper presented here, the condition required has been reduced to a great extent and no restriction is needed to the seismic wavelets as well as to the strata reflection series. If the autocorrelation function of the non-reveberant records is expressed byγ_yy(·), the autocorrelation function of receberant records by γ_{xx/SUB>(·) and the sea bottom reflection coefficients by ξe, thus, when there is a "n",which can make γyy(·)(j) = 0, |j| ≥ n, there isγxx(·)(n) + ξeγxx(·)( n -τ ) = 0(reverberation of grade 1 )γxx(·)(n) + 2ξeγxx(·)(n - τ) + ξe2γxx(·)(n- 2τ) = 0( reverberation of grade 2 )The sea bottom reflection coefficients could thus be estimated from the above two equations. But owing to the evaluation of the sea bottom reflection coefficients from the reverberation records of grade 2 is to solve a quadratic with an unknown term, hence,the two solutions are generally different. For this reason, even both of them are real roots,it is hard to decide which one is the root required. In order to solve the problem, we find the solutions by solving a simultaneous equations (both of the two equations of which satisfy the later equation mentioned above) and the final results are satisfying.The determination of "n" is also a rather difficult matter. Two ways for solving it were recommended. One of which is by statistical method, the other is by the fact that the mathematic model of all reverberant records are the model of ARMA.}