分形反褶积方法研究及应用

Research and application of fractal deconvolution

分形反褶积技术是把标度地质学的概念引入到地震信号处理之中，在标度（Scale）和分形（Fractal）领域里结合自组织理论，用数学表达式论证了地质学与地震学的统一，使地震信号反褶积赋于实际的地质约束。因此，它是一种并约束条件下的信号增频技术，又称1／fβ地质滤波技术。本文结合ZB地区古生界气田的实际地震资料，对若干口井的声波和密度测井资料做了详细的研究，证明其声阻抗功率谱呈f-β分布（0．5＜β＜1．5），相应反射系数序列功率谱呈fa分布（a=2-β），指出反射序列的相关函数均具有小滞后的负值，由此证明反射系数是具有分形结构的序列，而非白噪序列。并导出了反射序列滞后项比值与a参数的数学关系式，进而从预测误差滤波器的正则方程出发，将自相关函数0滞后项以后开始舍位处理改为从1滞后项以后做舍位处理，从而得到分形预测误差滤波器的正则方程，采用迭代法求解滤波器系数，并应用于地震记录处理中。实际地震资料处理表明：分形反褶积与预测反褶积或脉冲反褶积处理相比，明显地提高了分辨率，拓宽了频带，是一种有效的增频新技术。

By introducing the concept of scale geology into scismic signal processing, and together withse1f-organization theory in the field of scale and fractal, we can demonstrate the unity of gcologyand scismology in mathcmatical cxpression which gives the deconvolution of seismic signalpractical geologic constraints. This is thc so called ftactal deconvolution. Thercfore this is a wellconstraincd signal frequcncy enhancement technique,or 1 /fβ geologic filtering technique.In this paper, acoustic Iogging data and density logging data of wells are studied in detail withthe practical seismic data in ZB Paleozoic gas field. It is domonstrated in the study that the powerspectra of their acoustic impodance exhibit distribution (0. 5 < β<1.5 ) andcorrcspondingly t he powcr spectra of thcir rcflcct ion coefficients series exhibit f' distribution (a=2 -β ). Thc study shows that all the correlation functions of the reflection series have negativesmall lag value from which it call bc demonstrated that the reflection coefficients arc fractal series,not white noise scrics. and t be ralat ional cxprcssion betwecn the parameter a and thc reflectionseries lag terms ratio is infcrrcd, thcn from the canonical equation used to predict crror filter thecanonical cquation of fractal prcdiction crror filtor is obtaincd by rounding off after 1 lag terminstcad of 0 lag tcrm as usuai. Thc filtcr coefficicnts can be found with iteration method which areapplicd in thc proccssing of scismic record.The practical data proccssings show that compared with predictive dcconvolution or impulsedeconvolution, fractal deconvolution improves resolution, widens frequeney band. And hence it isa effective new technique for frequency in enhanccment.