Seismic Trace Reconstruction via Discrete Wavelet Transform
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Solution Overview
Problem
Existing seismic data processing methods, such as those described in U.S. Pat. No. 6,745,129, face inaccuracies in calculating Hölder exponents due to non-linear structures in wavelet coefficient data, leading to unreliable analysis of seismic traces and hydrocarbon reservoir detection.
Innovation Solution
A method involving discrete wavelet transforms, singularity spectra analysis, and fitting a function with three or more independent parameters, including a parameter associated with the seismic wavelet, to accurately separate seismic wavelet effects from earth properties, allowing for more precise extraction of earth attributes and reconstruction of seismic traces with increased bandwidth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If linear least squares regression analysis is used to calculate Hölder exponent from wavelet coefficients, then the calculation process is simple, but the measurement precision is degraded due to non-linear structure in the data
Solution Approach 1:
The patent transforms the non-linear relationship between wavelet coefficients and scale into a linear relationship by changing the parameters through logarithmic transformation. By taking logarithms of both the wavelet coefficients and scale values, the non-linear power-law relationship becomes a linear relationship, enabling accurate linear regression analysis while maintaining computational simplicity.
2Measurement precision
If mid-range scales are selected to reduce standard deviation of linear regression, then the measurement precision improves slightly, but the manufacturing precision is degraded because the wavelet coefficients still do not follow a linear relationship
Solution Approach 1:
The patent applies logarithmic transformation to both wavelet coefficients and scale values, converting the non-linear relationship into a linear one. This parameter transformation ensures that wavelet coefficients follow a linear relationship with scale in the log-log domain, eliminating the need to select mid-range scales and allowing the entire scale range to be used effectively.
3Device complexity
If seismic wavelet effects are not separated from earth properties, then the device complexity is low, but the measurement precision is degraded leading to unreliable reservoir detection
Solution Approach 1:
The patent extracts and separates the seismic wavelet effects from the earth property signals by using wavelet transform at multiple scales. The wavelet transform decomposes the seismic signal into different scale components, allowing the wavelet-related artifacts to be identified and removed, thereby isolating the true earth property information for accurate reservoir detection.
Solution Approach 2:
The patent segments the seismic signal into different scale components through wavelet transform. By dividing the signal into multiple scale bands, the method can separately analyze and process wavelet effects from earth properties, enabling precise separation and subsequent accurate detection of reservoir characteristics.
Data Source
AI summary
A method of processing seismic data, wherein a digital seismic trace is provided comprising at least one seismic loop. A selected discrete wavelet transform of the digital seismic trace is obtained as a function of scale sj and shifted sample time tk. From the discrete wavelet transform, a singularity spectrum is obtained for the at least one seismic loop, and a selected function is fitted to the singularity spectrum. Based on the fitted function, a reconstructed seismic trace may be calculated. The method may be embodied in the form of software code instructions in a computer program product.