Multiscale and Wavelet Transform with Applications in Well LOG Analysis

摘要

Theoretical concepts and applications of the multiscale transform and the wavelettransform are discussed with attention given to well logs. A well log is a sequence of measures obtained from a borehole and a record of the variation in lithology. As part of a geophysical survey, well logs are taken from different boreholes in a certain area. The well logs exhibit differences due to different geological circumstances at the various locations. Dissimilar rates of sedimentation cause the well logs to be stretched or compressed with respect to each other. The multiscale transform and the wavlet transform are defined. Theory concerning inversion and sampling are reviewed. Some properties and examples are given. The theory of discrete orthogonal wavelet bases for discrete time signals is presented. Examination of well logs leads to the observation that they exhibit characteristic behavior over a wide range of scales, differing from one foot to hundreds of feet, not accounted for in conventional segmentation methods. A segmentation method is proposed to solve this problem, based on the multiscale transform and the wavelet transform of the well log. Examples and possibilities for further applications of the segmentation are provided. A signal matching method that can determine the shifts, stretches and compressions of which the deformation between two well logs may consist, is derived and examined. The method involves a minimization technique based on dynamic programming. Experiments are carried out on synthetic data as well as on real well logs.