Acoustic Dispersion Extraction Using Continuous Wavelet Transform
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Solution Overview
Problem
Current methods for processing borehole acoustic data with dispersive characteristics are limited by the need for physical models, sensitivity to user input, and inability to accurately extract dispersion characteristics from short sensor arrays, particularly in automated unsupervised settings, due to limitations in resolution and accuracy.
Innovation Solution
A method involving time-frequency analysis to extract group slowness, phase slowness, and attenuation from acoustic data using time-frequency representations, where characteristic features are identified, and a kernel is defined to estimate these parameters without relying on physical models, allowing for automated dispersion curve generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If 2D FFT (f-k transform) is used to estimate dispersion characteristics, then the technique can indicate dispersion characteristics of propagating waves, but the resolution and accuracy are insufficient for short sensor arrays (2-13 sensors)
Solution Approach 1:
The patent transitions from frequency-domain analysis (2D FFT) to time-frequency domain analysis using continuous wavelet transform. This dimensional change allows the method to achieve high resolution dispersion estimation for short sensor arrays by analyzing both time and frequency characteristics simultaneously, rather than only frequency characteristics as in traditional f-k transform methods.
Solution Approach 2:
The patent changes the analysis parameters by using wavelet scale and central frequency instead of traditional frequency-wavenumber pairs. By parameterizing the dispersion relationship in terms of group slowness and phase slowness derived from wavelet coefficients, the method achieves improved accuracy for short arrays while maintaining computational efficiency.
2Reliability
If physical models are used to relate rock properties to predicted dispersion curves, then the method can characterize reservoir properties, but the results are sensitive to model mismatch and input parameter errors
Solution Approach 1:
The patent implements a self-service approach by directly estimating dispersion characteristics from the acoustic data itself through continuous wavelet transform analysis, rather than relying on external physical models. The method extracts group slowness and phase slowness directly from the data, making the results independent of model assumptions and input parameter accuracy.
Solution Approach 2:
The patent extracts the essential dispersion characteristics (group slowness and phase slowness) directly from the acoustic signals using time-frequency analysis, separating these key parameters from the complex physical modeling process. This extraction approach provides reliable dispersion characterization without requiring complete physical models of the subsurface.
3Measurement precision
If narrow band array processing techniques are used in frequency domain, then the method is effective for studying dispersion behavior, but it produces unlabelled dots and loses time of arrival information
Solution Approach 1:
The patent performs preliminary time-frequency decomposition using continuous wavelet transform before extracting dispersion characteristics. This preliminary action preserves the time-of-arrival information in the wavelet coefficient domain, allowing subsequent identification of characteristic features and accurate estimation of group and phase slowness without losing temporal information.
Solution Approach 2:
The patent uses continuous wavelet transform coefficients as an intermediary representation that retains both time and frequency information. This intermediary domain allows the method to identify characteristic features and track their evolution across frequencies while maintaining the time-of-arrival information that would be lost in pure frequency-domain analysis.
4Extent of automation
If automated unsupervised processing is implemented, then the method can operate without expert user input, but the accuracy may depend on skilled user expertise for correct processing
Solution Approach 1:
The patent implements self-service automation by using the continuous wavelet transform to automatically identify characteristic features and track their evolution across frequencies. The algorithm autonomously extracts group slowness from the slope of characteristic feature locations and phase slowness from phase differences, eliminating the need for expert user intervention while maintaining high accuracy.
Solution Approach 2:
The patent incorporates feedback mechanisms where the estimated dispersion characteristics are used to guide the processing of subsequent frequency components. The method uses the extracted group slowness to constrain the search for phase slowness, creating a feedback loop that improves accuracy while maintaining automation.
Data Source
AI summary
This invention pertains to the extraction of the slowness dispersion characteristics of acoustic waves received by an array of two or more sensors by the application of a continuous wavelet transform on the received array waveforms (data). This produces a time-frequency map of the data for each sensor that facilitates the separation of the propagating components thereon. Two different methods are described to achieve the dispersion extraction by exploiting the time frequency localization of the propagating mode and the continuity of the dispersion curve as a function of frequency. The first method uses some features on the modulus map such as the peak to determine the time locus of the energy of each mode as a function of frequency. The second method uses a new modified Radon transform applied to the coefficients of the time frequency representation of the waveform traces received by the aforementioned sensors. Both methods are appropriate for automated extraction of the dispersion estimates from the data without the need for expert user input or supervision.