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这里提出一种运用最小熵准则重新建立反射系数谱的方法。此种算法(FMED)可与传统的最小熵反褶积(MED)以及线性规划(LP)、自回归(AR)方法相比较,就与地震道反褶积的线性算子的系数而言,MED方法是通过使一个熵达到极大来进行。通过比较,这里提出的算法可使与反射系数系列谱的频率损失有关的范数达到极大。此方法可简化为一种非线性算法,即能进行有限频带数据的反褶积,避免了线性算子的固有限制。 这里提出的方法通过各种合成例子来说明。为检查此种算法的正确性,还运用了野外数据。结果表明,此种方法是处理有限频带数据行之有效的方式。 FMED和LP方法的原理相类似。在频率约束条件下,这两种方法都是寻找一个特殊范数的极值。在LP方法中,线性规划问题采用了十分昂贵的单纯形法来解决。FMED法在每次迭代中仅用了两次快速富氏变换,减少了反演计算成本。
Here, we propose a method to reconstruct the reflection coefficient spectrum by using the minimum entropy criterion. This algorithm (FMED) can be compared with the traditional minimum entropy deconvolution (MED) and linear programming (LP) and autoregressive (AR) methods. For the coefficients of the linear operators of deconvolution with the seismic traces, The MED method is done by maximizing an entropy. By comparison, the algorithm presented here can maximize the norm associated with the frequency loss of the series of reflection coefficients. This method can be reduced to a non-linear algorithm that can de-convolve finite-band data, avoiding the inherent limitations of linear operators. The method presented here is illustrated by various synthesis examples. To check the correctness of this algorithm, field data is also used. The results show that this method is an effective way to deal with the limited band data. The principles of the FMED and LP methods are similar. Under frequency constraints, both methods seek the extreme of a particular norm. In the LP method, the linear programming problem is solved by a very expensive simplex method. The FMED method uses only two fast Fourier transforms in each iteration, reducing the cost of inversion computations.