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A GENERALIZED SPECTRAL-ANALYTICAL METHOD IN THE PROBLEMS OF WELL LOGGING
Abstract
A generalized spectral-analytical method (GSAM) for analyzing data of various physical nature has been developed. It is based on the generalized Fourier representation of the original experimental and model digital arrays. In this report, it is used in the implementation of a resonant-impedance method for diagnosing and studying the characteristics of mechanical systems (in particular, linear one-dimensional acoustic systems with local anomalies). In the framework of this approach, the anomaly (damage) of the system is recognized, as well as the evaluation of its dynamic parameters including its localization. The proposed computational procedure involves carrying out a complete processing of the object under study in the space of the Fourier coefficients. Here we use the decomposition of the signal into generalized Laguerre polynomials. The main ideas of the method and the results of its application to the model and experimental data of well logging are considered. The use of expansions in generalized Laguerre polynomials allows one to obtain optimal representations of the original data? The optimal approximation is explained by the nature of the signal behavior and the ability of the method to adapt to the current part of the signal, as well as by the character of the attenuation parameters in the system. The advantages of the proposed approach can be attributed to a sufficiently high noise immunity, which is the consequence of the integrating operations of the analyzed signal in the process of its decomposition within the chosen basis. The method allows remote diagnostics of the geophysical system, placing a source of an external impact and a receiver on the earth surface at the open end of the well. The results obtained can also be used as initial and auxiliary data in more contact methods such as electromagnetic and radioactive logging.
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