Well-log analysis using localized transforms

The wavelet transform (WT) is used to analyze and characterize well-logs in location and scale. In the WT domain, a well-log can be decomposed into de terministic and statistical components. The deterministic component consist s of smooth WT coefficients at the largest scale and large WT coefficients at the rest of the scales. The remaining coefficients represent the statist ical component which can be modeled as a fractional Brownian motion (FBM). A well-log is used to illustrate this decomposition. To test the fractal mo del, we have used both 1-D and 2-D wavelet transforms to simulate FBM proce sses. These simulated FBM series look like well-logs, which verifies the pr oposed approach. Both orthogonal and continuous WT's are used for analyzing fractal parameters of FBM processes. The orthogonal WT is used to compute a fractal parameter for a particular time series,and the continuous WT is u sed to estimate the time variant fractal parameter.