探讨声波时差的计算误差和计算速度

On Errors of Calculating Sonic Slowness and Velocity.

讨论测井资料处理中用线性插值方法和抛物线插值方法对不同波形的计算误差和计算速度影响。首先给出已知时差的一组人工阵列声波波形 ,然后针对时差计算中滞后时间取整数个和实数个取样时间间隔的情形 ,分别对两种不同插值方法使用多道相关与根式叠加进行测试 ,比较其相对误差大小。研究发现线性插值方法更适用于 4次根式相关 ,时差相对误差可小于 2 / 10 0 0 ;抛物线插值方法更适用于多道相关 ,计算经过线性压缩或放大的原始波形时差 ,相对误差可小于 3/ 10 0 0 ;它们都对幅度变化不敏感。对幅度变化不敏感这一点对于实际资料处理非常有利。在搜索区间确定在一个取样间隔的范围以后 ,采用对分法搜索 ,可以大大节省计算时间 ;并且提出在停止搜索的条件中 ,用“相关值不再增大”特别重要 ,这样有助于避免出错。相关值也不可能非常高 。

How to improve the accuracy of slowness and how to decrease the time for calculating slowness are discussed in this paper. Professor Qiao put forward in 1997 that using interpolation can improve slowness accuracy. This paper shows further that different interpolations, chiefly linear interpolation and 4th root stack, have different effects on waves. An artificial array of acoustic waves is designed to compare their relative errors. The main correlation method is multi channel correlation or 4th root stack. It has been found that linear interpolation is more suitable for 4th root stack, and the relative slowness error could be less than 2/1000; parabola interpolation is more suitable for the waves that have been enlarged or decreased by linear scale, and the error could be less than 3/1000. Both interpolation methods are not sensitive to changes of wave amplitude, and they are very useful for processing acoustic waves. Another problem is calculated time which could be reduced by using dichotomy when the hunting zone is smaller than one sampling time. That the correlation coefficient doesn’t increase is necessary for stopping searching slowness. This is very important to avoid wrong result. This article also shows that the semblance coefficient can not be very high, and the relative error can not be infinitely small in correlation analysis.