Abstract Recognition of stratigraphic patterns or boundaries of any formation through well log data is a very decisive and critical part of hydrocarbon exploration in the petroleum industry. In the conventional method, the stratigraphic boundaries are not clearly distinguishable due to interference of low and high frequency noise in well log data. The Fourier transform and wavelet transform are spectrum based filtering method to delineate the stratigraphic boundaries using well log data, but it has some disadvantage of introducing the undesirable component of noise from log data into result. In the present study, we used the combined application of wavelet transform and Fourier transform to demarcate the stratigraphic boundaries. This two-fold frequency filtering operation is applied to natural gamma ray log data. Apart from this, we also demarcated these boundaries by wavelet based fractal dimension value and made a comparison with the previous method. We applied the proposed method on the natural gamma-ray log because it is sensitive to only the rock matrix of formation and indicates lithology better than other logs. In a comparative study of the result of both methods, it is clear that the wavelet-Fourier method fails to identify some boundaries in cases of the thin layers while wavelet based fractal of logging signal (WBFA) is able to resolve all boundaries and well correlated with the boundary identified by the conventional method. We have tested and validate the method on three synthetic signals including a thin layer in one signal and then demonstrated to the natural gamma ray well log data of the Limbodara oil field, Cambay basin.

中文翻译：

---

结合应用小波-傅里叶变换和分形维数的地层格局划分：以印度坎贝盆地为例

摘要 通过测井数据识别任何地层的地层模式或边界是石油工业油气勘探的一个非常决定性和关键的部分。在常规方法中，由于测井数据中低频和高频噪声的干扰，地层边界不能清楚地区分。傅里叶变换和小波变换是利用测井数据划定地层边界的基于频谱的滤波方法，但它有一些缺点，即在结果中引入了测井数据中不需要的噪声成分。在本研究中，我们结合应用小波变换和傅里叶变换来划分地层边界。这种双重频率滤波操作适用于自然伽马射线测井数据。除此之外，我们还通过基于小波的分形维数值划定了这些边界，并与之前的方法进行了比较。我们将所提出的方法应用于天然伽马射线测井，因为它仅对地层的岩石基质敏感，并且比其他测井更好地指示岩性。在对两种方法结果的比较研究中，很明显小波傅里叶方法在薄层的情况下无法识别某些边界，而基于小波的测井信号分形（WBFA）能够解决所有边界并且相关性良好用常规方法确定的边界。我们已经在三个合成信号上测试并验证了该方法，包括一个信号中的一个薄层，然后在 Cambay 盆地 Limbodara 油田的天然伽马射线测井数据中进行了验证。