Seismic Data Processing Using Matching Filter Cost Function Optimization
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Solution Overview
Problem
Current methods for determining time differences between seismic traces in subsurface analysis are inadequate, particularly in handling noise and phase differences, leading to incorrect estimations and computational inefficiencies in least squares migration and wave equation migration velocity analysis.
Innovation Solution
The implementation of a cost function-based approach using matching filters, such as Wiener filters, to iteratively update reflectivity and velocity models, ensuring accurate matching of observed and modeled seismic data, and minimizing the impact of noise and phase differences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If cross-correlation maximum method is used to estimate time difference, then the method is simple to implement, but it yields incorrect answers when datasets have constant phase difference and is sensitive to noise
Solution Approach 1:
The patent transforms the time difference estimation problem from the time domain to the frequency domain by applying Fourier transforms. This parameter change allows the use of phase information at each frequency component, enabling accurate time difference estimation even when constant phase differences exist between datasets. The frequency domain approach converts the problematic time-domain cross-correlation into a more robust spectral analysis.
Solution Approach 2:
The patent replaces the mechanical cross-correlation operation with a spectral analysis-based method. Instead of directly correlating time signals, the invention uses Fourier transforms to convert signals to frequency domain, applies phase corrections based on the spectral content, and then transforms back. This substitution of the computational mechanism eliminates the sensitivity to constant phase differences and noise that plagues the traditional cross-correlation approach.
2Reliability
If least squares migration with traditional cost function is used, then the method can process seismic data, but it is computationally expensive and suffers from cycle skipping
Solution Approach 1:
The patent changes the cost function parameter from a traditional data-mismatch measure to one based on spectral coherence and phase alignment. By defining the cost function in terms of frequency-domain characteristics rather than time-domain residuals, the method achieves better convergence properties and avoids cycle skipping. This parameter transformation allows for more efficient optimization with fewer iterations.
Solution Approach 2:
The patent introduces spectral analysis as an intermediary step between the seismic data and the migration process. By first analyzing the spectral content and phase relationships, the method creates a more informed basis for the migration cost function. This intermediary spectral characterization guides the optimization process, reducing the computational burden and improving convergence compared to direct time-domain least squares migration.
3Reliability
If traditional cost function is used in wave equation migration velocity analysis, then the analysis can be performed, but it produces non-convex cost functions with multiple local minima
Solution Approach 1:
The patent transforms the cost function from a time-domain residual-based measure to a frequency-domain spectral coherence measure. This parameter change fundamentally alters the shape of the cost function, making it more convex and reducing the number of local minima. The spectral-based cost function naturally penalizes phase misalignments in a way that creates a smoother optimization landscape, improving the reliability of velocity model estimation.
Data Source
AI summary
A method for processing seismic data from a subsurface using least squares migration or wave equation migration velocity analysis over a cost function comprising a function of a matching filter by iteratively updating the reflectivity model velocity model to yield an updated reflectivity model or updated velocity model that matches the observed seismic data.