Q Tomography Using Frequency-Weighted Exponential Function
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Solution Overview
Problem
Existing Q tomography methods face challenges in accurately estimating seismic attenuation due to assumptions about frequency-independent quality factor Q and limitations in source amplitude spectrum fitting, leading to errors and unrealistic Q models, especially when dealing with noisy seismic data.
Innovation Solution
A ray-based centroid frequency shift Q tomography method using a frequency-weighted exponential function to fit asymmetric source amplitude spectra, combined with a multi-index active-set method for constrained optimization to enforce box constraints on Q values, improving the accuracy and reliability of Q model reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional centroid frequency shift method uses Gaussian, boxcar, or triangular function to fit source amplitude spectrum, then the method is simple to implement, but significant fitting error is introduced because source spectrum cannot be approximated by these functions
Solution Approach 1:
The patent changes the mathematical function parameters from standard Gaussian/boxcar/triangular forms to a frequency-weighted exponential function with adjustable parameters (a, b, c) that can adapt to different source spectrum characteristics. This allows the function to flexibly fit various asymmetric source amplitude spectra while maintaining computational simplicity.
2Productivity
If unconstrained optimization methods are used in Q tomography, then the computation time is reduced, but unrealistic Q models are produced with negative Q values or extremely low Q values, especially when seismic data are contaminated by noise
Solution Approach 1:
The patent applies different optimization strategies to different regions of the Q model based on local characteristics. Constrained optimization is applied to regions where physical realism is required (Q > 0), while unconstrained methods can be used where data quality allows. The multi-index active-set method dynamically adjusts constraints based on local data characteristics and convergence behavior.
Solution Approach 2:
The optimization algorithm dynamically adjusts constraint boundaries and active-set membership during iteration based on convergence progress and data characteristics. The multi-index active-set method allows flexible updating of constraint active sets, enabling the algorithm to adapt to varying data quality and model complexity throughout the optimization process.
3Productivity
If simple nonnegative constrained optimization methods are used, then computation time is reduced compared to fully constrained methods, but artifacts and unrealistic Q values are still produced
Solution Approach 1:
The patent segments the optimization problem into multiple sub-problems using a multi-index active-set approach. The constraint active sets are divided and updated independently based on local Q value ranges and data characteristics, allowing efficient parallel processing while maintaining overall model accuracy. This segmentation enables complex constraints to be managed through simpler, localized optimization steps.
Data Source
AI summary
Method for reconstructing subsurface Q models (110) from seismic data (10) by performing ray-based (60), centroid frequency shift (50) Q tomography. The seismic source waveform's amplitude spectrum is approximated by a frequency-weighted exponential function of frequency (40), having two parameters to adjust to fit the frequency shift data, thereby providing a better fit to various asymmetric source amplitude spectra. Box constraints may be used in the optimization routine, and a multi-index active-set method used in velocity tomography is a preferred technique for implementing the box constraints (100).