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本文第Ⅰ部分论及的数学公式的推导都是用常用的统计术语和记号来表示的。在地震勘探中,振幅恢复有三种办法:(1)重复放炮或连续变频振荡,(2)相关的连续变频振荡信号,(3)共深度点迭加。这样我们可以达到讯噪比小于1的要求。对于未满足该要求的结果,即限幅问题,我们依次在各处予以讨论。当讯噪比大于1时,振幅讯息通过限幅受到损失,但通过零的讯息被保存。讯息损失量与限幅程度成正比;损失量很小则影响不大。计算得到的期望值指出,假定讯噪比≤1.0,我们能选择某一无偏估计。这些无偏估计的方差总小于常规地震技术中估计的方差,对于弱讯号,差别可忽略不计。经过充分的重复,我们能得到满足所要求的动态范围的足够小的方差。随着这些发现受到恰如其分的注意,符号位数字资料将成为一种很有力的工具。
The derivation of the mathematical formulas covered in Section I of this paper is expressed in terms of commonly used statistical terms and notation. In seismic prospecting, there are three ways to recover the amplitude: (1) repeated blasting or continuous variable frequency oscillation, (2) related continuous variable frequency oscillation signal, and (3) total depth point superposition. In this way we can achieve the signal to noise ratio less than 1 requirements. For the result of not meeting the requirement, that is, the clipping problem, we will discuss it in turn. When the signal-to-noise ratio is greater than 1, the amplitude message is lost through clipping but the message passed through zero is saved. Loss of information is proportional to the degree of clipping; a small loss has little effect. The calculated expectation indicates that we can choose some unbiased estimate assuming a signal to noise ratio ≤1.0. The variance of these unbiased estimates is always less than the estimated variance of conventional seismic techniques, with negligible differences for weak signals. After sufficient repetition, we can get a small enough variance that satisfies the required dynamic range. As these discoveries receive the right attention, the sign-bit digital data will become a powerful tool.