地震反射序列谱幂指数的求取

The abstraction of the power spectrum exponent of seismic reflection sequence

实际研究结果表明，地震反射序列的功率谱与频率的幂fα（f为频率）之间呈正比关系（即具有分形特征）。一般可简单地根据地震道的对数功率谱进行直线拟合，以求取功率谱指数α值，然而所得结果误差较大。本文对此方法作了进一步改进，提出了一种通过多次运用保持直线准则的平滑、拟合等手段，从地震记录的对数功率谱提取分形反射序列谱幂指数α的快速、有效的方法。合成地震记录的试算结果表明，此方法较之原方法精度提高几倍，相对误差由百分之几十减少到只有百分之几。

The results of practical research show that the power spectrum of seismic reflection sequenceis propotional to fα(f is frequency),or it possosses fractai feature. The exponent acan generally beextracted very simply through linear fitting to the logarithm of the power spectrum of seismictraces. But this method results in striking error. In this paper we elaborate an effective and rapidmethod to extract exponent αof power spectrum of fortal rofleotion sequence from the logarithmof power spectrum of seismic record by smoothing and fitting repeatedly under the condition ofkeeping linear criterion. The results of test on some theoretical models with this improved methodshow that the precision can be improred by several times and the relative crrors can be diminishedfrom tens percent to less than ten percent.